@_Maxim_ 

thanks! I'll give the bigger argument a try as black box function, lets see.

@Carl Love 

Thanks for the input, but I get errors when using fsolve instead of evalf(RootOf. When I try to integrate, I get: Error, (in fsolve) v1 is in the equation, and is not solved for

This error in some other threads here was solved by using RootOf, which worked for me too when I only integrate the inverse for example, but for this transformation not anymore..