What do you mean "express its inverse as an integral?"
If you want to find the derivative of an inverse, implicit differentiation(or similar variations) is sometimes the only way.
To express arcsin(x) as an integral, one would find its derivative, and say arcsin(x) = ∫ darcsin(x) or ∫ sqrt(1x^{2})^{1} dx.
Is that what you mean, or do you want to know how to do implicit differentiation?
