If $\int \frac{d x}{1-\sin ^4 x}=\frac{1}{2} \tan x+f(x)+c$ then $f(x)$ is

$\frac{1}{\sqrt{2}} \operatorname{Tan}^{-1}(\sqrt{2} \tan x)$

$\frac{1}{2 \sqrt{2}} \operatorname{Tan}^{-1}(\sqrt{2} \sin x)$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \frac{d x}{1-\sin ^4 x}=\frac{1}{2} \tan x+f(x)+c

then

f(x)

View answer and explanation

Correct option: C

\frac{1}{2 \sqrt{2}} \operatorname{Tan}^{-1}(\sqrt{2} \tan x)

Option C is correct because the integral can be solved by trigonometric manipulation and substitution, leading to the given expression for f(x).