$\smallint \,\,\frac{1}{{x\left( {{x^n} + 1} \right)}}\,\,dx$ is equal to

$\frac{1}{n}\,\,\log \,\,\left( {\frac{{{x^n} + 1}}{{{x^n}}}} \right)$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{1}{{x\left( {{x^n} + 1} \right)}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{1}{n}\,\,\log \,\,\left( {\frac{{{x^n}}}{{{x^n} + 1}}} \right)\,\, + \,\,C

Option A (

\frac{1}{n}\,\,\log \,\,\left( {\frac{{{x^n}}}{{{x^n} + 1}}} \right)\, + \,C

) is correct because the integral is solved using substitution and partial fractions.