Question

Integrals! Calc! Ten Points!! Please help! Attaching photo of question!

Answer 1

Probably the first one, as the usual method for that integral is to factorize the denominator and decompose the integrand into partial fractions.

Meanwhile, the other three can be carried out quite easily with different substitutions. For instance, the first can be done with $x=\tan t$, the second with $u=x^2+1$, and the third with $v=x^4+1$.