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int(0)^(pi//2)x cot x dx=(pi)/(2)(log2)...

`int_(0)^(pi//2)x cot x dx=(pi)/(2)(log2)`

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To solve the integral \( I = \int_{0}^{\frac{\pi}{2}} x \cot x \, dx \), we will use integration by parts. ### Step 1: Set up integration by parts We choose: - \( u = x \) (which implies \( du = dx \)) - \( dv = \cot x \, dx \) (which implies \( v = \log(\sin x) \)) ### Step 2: Apply integration by parts formula ...
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