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Definite Integral #3

sbhatnagar

Active member
Jan 27, 2012
95
This is classic one. Prove that

$$ \int_0^\infty \frac{dx}{\left\{x^4+(1+2\sqrt{2})x^2+1 \right\}\left\{x^{100}-x^{99}+x^{98}-\cdots +1\right\}}=\frac{\pi}{2(1+\sqrt{2})}$$