Someone wanted us to evaluate the following integral: $$\int\limits_0^\pi dx{\frac{{{x^2}}}{{\sqrt 52\cos x}}}$$ This looks straightforward, although the factor of $x^2$ does seem to complicate things a little. Actually, a lot. The usual tricks to deal with powers leads us down a road that leads to interesting territory involving dilogarithms. Let’s define $$J(a) = \int_{\pi}^{\pi} dx […]

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