JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{x^7}{\left(1+x^4\right)^2} \mathrm{~d} x=\frac{1}{4}\left[\log \left(1+x^4\right)+f(x)\right]+C

then

View answer and explanation

Correct option: C

f(x)=\frac{1}{1+x^4}

The correct answer is

f(x)=\frac{1}{1+x^4}

because after substituting

t=1+x^4

and integrating, we can identify

f(x)

by comparing with the given expression.

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