syms t x a p q r a1 a2 A pr
f(1)=x+p*x^2/2;g(1)=a*x+q*x^2/2;h(1)=1+r*x;
for i=1:5
fa(i) = subs(f(i),x,t);ga(i) = subs(g(i),x,t);ha(i) = subs(h(i),x,t);
f(i+1) =f(i)+a1*int(int(int((diff(fa(i),t,3)+(fa(i)+ga(i))*diff(fa(i),t,2)+ a1*diff(fa(i),t,1)*(diff(fa(i),t,1)+diff(ga(i),t,1))),t,0,x)));
g(i+1) =g(i)+a1*int(int(int((diff(ga(i),t,3)+(fa(i)+ga(i))*diff(ga(i),t,2)+ a1*diff(ga(i),t,1)*(diff(fa(i),t,1)+diff(ga(i),t,1))),t,0,x)));
h(i+1) =h(i)+pr*a2*int(int((diff(ha(i),t,2)+(fa(i)+ga(i))*diff(ha(i),t,1)+ A*ha(i)*(diff(fa(i),t,1)+diff(ga(i),t,1))),t,0,x));
end
f=f(1)+f(2)+f(3)+f(4)+f(5);
disp(f(i+1))
figure(1)
fplot(x,f)