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Integral involving arctan

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Post Fri Mar 17, 2017 1:12 pm

Posts: 1
\(\displaystyle \begin{align*}&\; \int_{0}^{1}\dfrac{\arcsin{\sqrt{x}}}{x^4-2x^3+2x^2-x+1}dx \\ &= \pi\sqrt{\frac{1+\sqrt{13}}{78}} \log \left(\frac{1+\sqrt{13}+\sqrt{2 \sqrt{13}-2}}{4} \right)+\pi\sqrt{\frac{\sqrt{13}-1}{78}}\tan ^{-1}\left(\frac{\sqrt{5+2 \sqrt{13}}}{3} \right) \end{align*}\)

Post Fri Jun 02, 2017 9:31 am
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