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

$A=\sqrt{2}$ and $f(x)=\sqrt{2} \tan x$

$A=-\sqrt{2}$ and $f(x)=\sqrt{2} \tan x$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

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

, then

View answer and explanation

Correct option: A

A=\frac{1}{2 \sqrt{2}}

and

f(x)=\sqrt{2} \tan x

Option A is correct because after simplifying the integral using trigonometric identities and partial fractions, the given values for A and f(x) are obtained.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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