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Parametric Differentiation

Integrate: ∫...

Question

Integrate: $\int t a n^{- 1} (\frac{sin 2 x}{1 + cos 2 x}) d x$

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Solution

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

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

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

$I = \int t a n^{- 1} t a n x d x$

$I = \int x d x$

$I = \frac{x^{2}}{2} + C$

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