$\int \frac{x^3-x^2+x-1}{x^5+1} d x$ is

$\frac{1}{5} \ln \left(\frac{1+x^5}{\left(1+x^3\right)^5}\right)+c$

$\frac{1}{5} \ln \left(\frac{1+x^5}{1+x^3}\right)+c$

$\frac{1}{5} \ln \left(\frac{1+x^5}{1+x}\right)+c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

\int \frac{x^3-x^2+x-1}{x^5+1} d x

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Correct option: C

\frac{1}{5} \ln \left(\frac{1+x^5}{(1+x)^5}\right)+c

Option C (

\frac{1}{5} \ln \left(\frac{1+x^5}{(1+x)^5}\right)+c

) is correct because the integral can be simplified and then integrated term by term.