horrible integrel

Hi, I am making a model and need to take the integral of a rather disgusting function, I was wondering if anyone had am idea of how to solve it, if its possible to!

the function is 1 / tan (90 + Vt + at ² )

I need to integrate over t, a and V are constants, and limits 0 to T.

Any ideas ? And sorry if I put this in the wrong section, I wasn't sure where it belonged

Thanks
Ed

Wolfram says no standard antiderivative exists ...

integral of 1/tan(at^2 + bt + c) - Wolfram|Alpha

... if it's a definite integral, its value can be estimated numerically.