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int(sin2x)/((sinx+cosx)^2)dx...

`int(sin2x)/((sinx+cosx)^2)dx`

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To solve the integral \( I = \int \frac{\sin 2x}{(\sin x + \cos x)^2} \, dx \), we will follow these steps: ### Step 1: Rewrite the Integral We start by rewriting the integral by adding and subtracting 1 in the numerator: \[ I = \int \frac{1 + \sin 2x - 1}{(\sin x + \cos x)^2} \, dx = \int \frac{1 + \sin 2x}{(\sin x + \cos x)^2} \, dx - \int \frac{1}{(\sin x + \cos x)^2} \, dx \] ...
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