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Q.
$\int\limits_0^{\pi / 4} \frac{x \cdot \sin x}{\cos ^3 x} d x$ equals to:
Integrals
Solution:
$\int\limits_0^{\pi / 4} x \tan x \sec ^2 x d x=\left(x \frac{\tan ^2 x}{2}\right)_0^{\pi / 4}-\int\limits_0^{\pi / 4} \frac{\tan ^2 x}{2} d x$
$=\frac{\pi}{4}-\frac{1}{2}$