Question

If f is the antiderivative of g(x)=(x^3)/(1+x^5) such that f(1)=0, then f(5)=___.

Answer 1

Unless you meant 1 + x^4 in the denominator or x^4 in the numerator, that integral is a very difficult one to do. Are you sure you typed g(x) correctly?

There is a recursion formula for that integral in my Table of Integrals, but it leads to two new integrals that look even worse.