What would be a relatively simple method for computing the indefinite integral below?
$\displaystyle \int \frac{dx}{(x^4+1)^2}$
Furthermore, how would one evaluate the following, possibly by detouring the computation of the indefinite integral?
$\displaystyle\int\nolimits_{-\infty}^\infty \frac{dx}{(x^4+1)^2}$
Note: The resolved value of the definite integral (according to wolfram alpha) is $\displaystyle \frac{3\pi}{4\sqrt{2}}$