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[SOLVED] Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$

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[SOLVED] Series as an integral (sophomore's dream)

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[SOLVED] Evaluate $\int_0^\pi xf(\sin x)dx$

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[SOLVED] A nasty integral of a rational function

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[SOLVED] Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$

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