# Symbolic math integrals not solving at all

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Hi all, I am playing around with functions and the symbolic math toolbox.

I want to calculate an integral of a difficult function:

syms t t0 tau x;

syms l(t,t0,tau);

l(t,t0,tau)= exp(-1/2*exp(-(t-t0)/tau));

syms f(t,t0,tau);

f(t,t0,tau)= exp(-1/2*((t-t0)/tau));

syms p(t,t0,tau);

p(t,t0,tau)=l(t,t0,tau)*f(t,t0,tau);

It can not integrate p directly, which is not that difficult, wolfram alpha does is. But anyhow, I'll help a little and do the substitution:

p=tau*subs(p,(t-t0)/tau,x)

int(p,x,-inf,inf)

But it still just comes up with nothing. It just puts out a formated version of my input instead of calculating the integral.

The answer should be

sqrt(2*pi)*tau

Did I use the toolbox wrong or is it just not that powerfull?

##### 3 Comments

Walter Roberson
on 29 Jul 2021

### Accepted Answer

Tanmay Das
on 29 Jul 2021

Your function has no obvious closed form integral. You need to switch to numeric integration, such as with integral() or vpaintegral() which will require you to have a numeric value for x. Similar question has already been answered here:

Also, the same is mentioned in the Tips Section of the int documentation:

You can go through the documentations on integral and vpaintegral to try integrate the same function:

##### 8 Comments

Paul
on 27 Apr 2022

Nope. Also doesn't work anymore in 2021B.

However, that code yields the closed form solution in 2020B.

In 2021B I had to change the expression for the integrand

int(simplify(expand(p(t,t0,tau),'IgnoreAnalyticConstraints',true),'IgnoreAnalyticConstraints',true),t,-inf,inf,'IgnoreAnalyticConstraints',true)

to get the same integrand as in in 2020B, at least by visual comparison. But even though the integrands were the same, 2021B int() still did not yield the closed form solution.

Taw Tha
on 24 Apr 2023

Thank you everyone here, I would also like to contribute that simplify('Steps', \*int steps\*)

intFuncky = simplify(int((sqrt(tao^2 - (t-tao)^2) * (t-tao)^2),t,0,2*tao),"Steps",100)

or

intFuncky = simplify(int(( f ,x ,a, b), "Steps" ,100);%100 chosen as a small steps count medium is 400 steps

matlab 2022b

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