∫sin x/1+ cos^2xdx Put cos x= 6 sinx dx = dt ∫1/1+t^2dt= Tan^ 1t⇒ Tan^ 1(cos x) ...

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Integration of Trigonometric Functions

∫sin x 1+cos2...

Question

$\int \frac{sin x}{1 + {cos}^{2} x} d x$

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Solution

$\int \frac{s i n x}{1 + c o s^{2} x} d x$
Put $c o s x = 6$
$- s i n x d x = d t$
$- \int \frac{1}{1 + t^{2}} d t = - T a n^{- 1} t \Rightarrow - T a n^{- 1} (c o s x)$

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