Compute a long indefinite integral?

I’ve just joined Mathematica and I’m running the web app. I need to solve the following definite integral:

integrate[Norm[{e^2,e^3}/(e^2+e^3)-{e^(2+Cos[2Pi t]/10),e^(3+Sin[2Pi t]/10)}/(e^(2+Cos[2Pi t]/10)+e^(3+Sin[2Pi t]/10))]]

But instead of solving it, the output gives me the function still written in the integral form.
How can I compute the exact indefinite integral?

Thank you!

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The rules explain how to format your code properly. If you do not format code, it may become corrupted and useless to other members. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

Don’t expect every integral to have a nice closed form(antiderivative). I your case, analytical solving seems impossible.

Mathematica cannot do every integral that’s found in integral tables (no CAS can).

Regards Mariusz.