Matlab can not evaluate integration

hello, I have problem with int function, after running the code, matlab return the equation without evaluation

syms t

v=(1/(sqrt(1+t^2)))*cos(4*t)

   s=int(v)

the result is

s =

int(cos(4*t)/(t^2 + 1)^(1/2), t)

[Walter Roberson]

Is there reason to expect that a closed-form integral exists for it?

[mohammad imad]

I am not sure

[Walter Roberson]

MATLAB cannot do it. Maple cannot do it (and cannot find any transformation of it that works.) I do not have Mathematica to test with.

Answer 1

[John D'Errico]

I'd also wager that no analytical solution exists. Wolfram Alpha seems to agree with me, and the symbolic toolbox, but I don't have Mathematica.

There are many problems for which no closed form solution exists. That does not mean a solution cannot exist. In fact though, special functions have been created because no closed form solution exists, and someone still needed a solution. The one I'd think of first is the Lambert W.

You do have some options. You can spend some time defining the result. Tabulate it. Develop a series solution, investigating the convergence properties. Can you find approximate solutions? Hey, publish your results.

Or, you can use numerical integration. It all depends on what you need in the end. But an analytical solution may be out of reach.