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Today's calculation of Integral 140

Source: Kagawa University entrance exam/medical 1998

August 13, 2006
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

Evaluate ∫0π4(cos⁡xsin⁡x+cos⁡x)2 dx,   ∫0π4(sin⁡x+cos⁡xcos⁡x)2 dx.\int_{0}^{\frac{\pi}{4}}\left(\frac{\cos x}{\sin x+\cos x}\right)^{2}\ dx,\ \ \ \int_{0}^{\frac{\pi}{4}}\left(\frac{\sin x+\cos x}{\cos x}\right)^{2}\ dx.
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