Convergence of the improper integral $\int_{0}^{\pi/2}\tan^{p}(x) \; dx$ I need help solving this integral: for which values of the parameter $p$ is this improper integral convergent?
$$\int_{0}^{\pi/2}\tan^{p}(x) \; dx$$
Thanks a lot!

Hint: substitute $u=\tan{x}$. Then $x=\arctan{u}$, $dx=\dfrac{du}{1+u^2}$, and the integral becomes,
$$\int_{0}^{\pi/2}\tan^{p}{x}\,dx=\int_0^{\infty}\dfrac{u^p}{1+u^2}du.$$
