{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":51456,"title":"Compute an improper integral of a ratio of algebraic functions","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105.083px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5417px; transform-origin: 407px 52.5417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 7.91667px; transform-origin: 152.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.0833px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5417px; text-align: left; transform-origin: 384px 22.5417px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\" style=\"width: 193px; height: 45px;\" width=\"193\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.217px 7.91667px; transform-origin: 138.217px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive real numbers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = integRatioAlg(a,b)\r\n  y = f(a,b);\r\nend","test_suite":"%%\r\na = 2;\r\nb = 1; \r\ny_correct = 0.523598775598299;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 1; \r\ny_correct = 0.392699081698724;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 5; \r\nb = 2; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 4;\r\nb = 5; \r\ny_correct = 0.174532925199433;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 7; \r\nb = 6; \r\ny_correct = 0.120830486676530;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 1; \r\nb = 6; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 9; \r\ny_correct = 0.092399783929112;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 3; \r\ny_correct = 0.142799666072263;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 11; \r\nb = 13; \r\ny_correct = 0.065449846949787;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 19; \r\nb = 17; \r\ny_correct = 0.043633231299858;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 23; \r\nb = 29; \r\ny_correct = 0.030207621669133;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 31; \r\nb = 37; \r\ny_correct = 0.023099945982278;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 41; \r\nb = 43; \r\ny_correct = 0.018699956271368;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 59; \r\nb = 53; \r\ny_correct = 0.014024967203526;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 61; \r\nb = 67; \r\ny_correct = 0.012271846303085;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 79; \r\nb = 71; \r\ny_correct = 0.010471975511966;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 83; \r\nb = 89; \r\ny_correct = 0.009132536783691;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 91; \r\nb = 97; \r\ny_correct = 0.008355299610611;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 50*rand;\r\nb = 0;\r\ny_correct = pi/(2*a);\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\nfiletext = fileread('integRatioAlg.m');\r\nillegalfns = contains(filetext, 'integral') || contains(filetext, 'quad'); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-17T03:39:24.000Z","updated_at":"2021-04-17T03:42:40.000Z","published_at":"2021-04-17T03:42:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\infty\\\\frac{x^2dx}{x^4+(a^2+b^2)x^2+a^2b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive real numbers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":51456,"title":"Compute an improper integral of a ratio of algebraic functions","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105.083px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5417px; transform-origin: 407px 52.5417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 7.91667px; transform-origin: 152.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.0833px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5417px; text-align: left; transform-origin: 384px 22.5417px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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alt=\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\" style=\"width: 193px; height: 45px;\" width=\"193\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.217px 7.91667px; transform-origin: 138.217px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive real numbers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = integRatioAlg(a,b)\r\n  y = f(a,b);\r\nend","test_suite":"%%\r\na = 2;\r\nb = 1; \r\ny_correct = 0.523598775598299;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 1; \r\ny_correct = 0.392699081698724;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 5; \r\nb = 2; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 4;\r\nb = 5; \r\ny_correct = 0.174532925199433;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 7; \r\nb = 6; \r\ny_correct = 0.120830486676530;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 1; \r\nb = 6; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 9; \r\ny_correct = 0.092399783929112;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 3; \r\ny_correct = 0.142799666072263;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 11; \r\nb = 13; \r\ny_correct = 0.065449846949787;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 19; \r\nb = 17; \r\ny_correct = 0.043633231299858;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 23; \r\nb = 29; \r\ny_correct = 0.030207621669133;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 31; \r\nb = 37; \r\ny_correct = 0.023099945982278;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 41; \r\nb = 43; \r\ny_correct = 0.018699956271368;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 59; \r\nb = 53; \r\ny_correct = 0.014024967203526;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 61; \r\nb = 67; \r\ny_correct = 0.012271846303085;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 79; \r\nb = 71; \r\ny_correct = 0.010471975511966;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 83; \r\nb = 89; \r\ny_correct = 0.009132536783691;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 91; \r\nb = 97; \r\ny_correct = 0.008355299610611;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 50*rand;\r\nb = 0;\r\ny_correct = pi/(2*a);\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\nfiletext = fileread('integRatioAlg.m');\r\nillegalfns = contains(filetext, 'integral') || contains(filetext, 'quad'); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-17T03:39:24.000Z","updated_at":"2021-04-17T03:42:40.000Z","published_at":"2021-04-17T03:42:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\infty\\\\frac{x^2dx}{x^4+(a^2+b^2)x^2+a^2b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive real numbers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"residue\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"residue\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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