I=∫(cos x+sin x)^2 dx I=(sin^2x+cos^2x+2sin xcos x)dx I=∫(1+sin 2x)dx I=x cos 2x2+C ...

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Integration by Parts

∫cos x+sin x2...

Question

$\int (cos x + sin x)^{2} d x$

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Solution

$I = \int (cos x + sin x)^{2} d x$
$I = ({sin}^{2} x + {cos}^{2} x + 2 sin x cos x) d x$
$I = \int (1 + sin 2 x) d x$
$I = x - \frac{cos 2 x}{2} + C$

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