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int(0)^(pi//2)(sinx-cosx)log(sinx+cosx)d...

`int_(0)^(pi//2)(sinx-cosx)log(sinx+cosx)dx=0`

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To solve the integral \( I = \int_{0}^{\frac{\pi}{2}} (\sin x - \cos x) \log(\sin x + \cos x) \, dx \) and prove that it equals zero, we can use the property of definite integrals. Here’s a step-by-step solution: ### Step 1: Define the Integral Let \[ I = \int_{0}^{\frac{\pi}{2}} (\sin x - \cos x) \log(\sin x + \cos x) \, dx \] ...
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