Evaluating Integral: Is Function Integrable?

[ee11p1002]

I am unable to Evaluate this integral. Can anyone 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.