Evaluate this integral

[ee11p1002]

I am unable to Evaluate this integral. Can any one tell me what is the test we need to perform to tell whether the function is integrable or not:

[glebovg]

This function cannot be integrated in terms of elementary functions.

[glebovg]

Have a look at Liouville's Theorem on Integration in Terms of Elementary Functions if you are interested.

[glebovg]

There is also something known as the Risch algorithm.

[zhentil]

There's the ratio test from Calc 2 which might be helpful here.