∫ xsin^2xdx=∫ x(1 cosx/2)dx #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; =∫x/2dx ∫x cosx/2dx ...

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Integration by Parts

∫xsin2 x× dx

Question

$\int x {sin}^{2} x \times d x$

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Solution

$\int x s i n^{2} x d x = \int x (\frac{1 - c o s x}{2}) d x$
$= \int \frac{x}{2} d x - \int \frac{x c o s x}{2} d x$
$= \frac{x^{2}}{4} + \frac{x s i n x + c o s x}{2} + c$

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