JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int\left(x+\frac{1}{x}\right)^{n+5}\left(\frac{x^2-1}{x^2}\right) d x

is equal to :

View answer and explanation

Correct option: A

\frac{\left({x}+\frac{1}{{x}}\right)^{{n}+6}}{{n}+6}+{c}

Option A (

\frac{\left(x+\frac{1}{x}\right)^{n+6}}{n+6}+c

) is correct because substituting

t = x + \frac{1}{x}

simplifies the integral, leading to the given result.

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