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Integration Using Substitution

Question

Evaluate :
$\int \sqrt{\frac{1 - cos 2 x}{1 + cos 2 x}} d x$

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Solution

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$I = \int \sqrt{\frac{1 - cos 2 x}{1 + cos 2 x}} d x$

$= \int \sqrt{\frac{2 {sin}^{2} x}{2 {cos}^{2} x}} d x$

$= \int tan x d x = log (sec x) + C$

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