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Prove that int(0)^(pi)(xtanx)/((secx+tan...

Prove that `int_(0)^(pi)(xtanx)/((secx+tanx))dx=pi((pi)/(2)-1)`.

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To prove that \[ \int_{0}^{\pi} \frac{x \tan x}{\sec x + \tan x} \, dx = \pi \left( \frac{\pi}{2} - 1 \right), \] we will follow these steps: ...
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