## Evaluating by real methods $\int_0^{\pi/2} \frac{x^5}{2-\cos^2(x)}\ dx$ November 26 1

$\def\Li{{\rm{Li}}}$I'm sure you guys can briefly get the result by some methods of complex analysis, but nowI'm only interested in real analysis methods of proving the result. What would you proposefor that? \begin{align*} \int_0^{\pi/2} \frac{x^5}{