Question

∫2xdx/sqrt(x^4+16)

Answer 1

I believe you can rewrite this using trig substitution (replace the x's and dx):
\[x=4\tan(\theta)\] \[dx=4\sec^2(\theta)\ d(\theta)\]

You will also need this identity: \[1+\tan ^{2}(\theta) =\sec ^{2}(\theta) \]
Then when you evaluate the integral, use a right triangle to convert theta back to x's.

I got:
\[8\ln \left| \sqrt{x^2 +16}/4 \right| +C\], but I could not find something to confirm this answer. Hopefully you have a book with the answer in the appendix :) Hope this at least gives you a starting point.