The antiderivative of $\frac{1}{\sin ^2 x+\tan ^2 x}$ is

$(-1 / 2)\left[\tan x+(1 / \sqrt{2}) \tan ^{-1}(1 / \sqrt{2}) \tan x\right]+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The antiderivative of

\frac{1}{\sin ^2 x+\tan ^2 x}

View answer and explanation

Correct option: B

(-1 / 2)\left[\cot x+(1 / \sqrt{2}) \tan ^{-1}((1 / \sqrt{2}) \tan x)\right]+C

Option B is the correct antiderivative, obtained by simplifying the integrand, substituting \

t = \tan x

and integrating the resulting expression.

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