This question came up in a review assignment for my Calculus class, and I've been having difficulty solving it. I don't see what I could substitute for $u$, and it doesn't look like partial fractions are a viable method of doing this problem. Any pointers would be much appreciated.
Evaluate the following indefinite integral: $$\int{\frac{x^3}{1+x^8}}dx$$
Substitute $u=x^4$. The strategy is to get that numerator term $x^3$ to be someone's derivative. (Or a scalar multiple of it.)