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Today's calculation of Integral 198

Source:

April 21, 2007
calculusintegrationlogarithmstrigonometrycalculus computations

Problem Statement

Compare the values of the following definite integrals. ∫0∞ln⁡(x+1x)dx1+x2,  ∫0π2(θsin⁡θ)2dθ\int_{0}^{\infty}\ln \left(x+\frac{1}{x}\right)\frac{dx}{1+x^{2}},\ \ \int_{0}^{\frac{\pi}{2}}\left(\frac{\theta}{\sin \theta}\right)^{2}d\theta
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