∫sin2x 1+sin^ 2 x #160; dx =∫ 2sinxcosx 1+sin^ 2 x #160; dx Take #160; u=1+sin^ 2 x du=2sinxcosxdx ∴ #160; #160; ∫ ...

279

You visited us 279 times! Enjoying our articles? Unlock Full Access!

Integration by Substitution

∫sin 2 x 1 + ...

Question

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

Open in App

Solution

$\int \frac{sin 2 x}{1 + {sin}^{2} x} d x$
$= \int \frac{2 s i n x c o s x}{1 + {sin}^{2} x} d x$
Take $u = 1 + {sin}^{2} x$
$d u = 2 s i n x c o s x d x$
$∴$ $\int \frac{1}{u} d u = l o g (1 + {sin}^{2} x) + C$

Suggest Corrections

Similar questions

\frac{1 - \cos 2 x + \sin 2 x}{1 + \cos 2 x + \sin 2 x} = \tan x

y = \sqrt{\frac{1 - sin 2 x}{1 + sin 2 x}}

\frac{d y}{d x} + {sec}^{2} (\frac{π}{4} - x) = 0

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

\int \frac{\cos^{2} x - \sin^{2} x}{\sqrt{1} + \cos 4 x} d x

\int e^{2 x} (\frac{1 + \sin 2 x}{1 + \cos 2 x}) d x

Join BYJU'S Learning Program