∫ sin x√(1 cos 2x) dx 1 cos x = 2 sin^2x ⇒√(2)∫ sin x(sin x)dx ⇒√(2)∫ sin^2x dx ⇒+√(2)/2∫ 1 cos 2x dx 1/√(2)(x) 1/2√(2)sin 2x #160; ...

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Integration by Parts

∫sin x√1 - co...

Question

$\int sin x \sqrt{1 - cos 2 x} d x$

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Solution

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

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