JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{x^9}{\left(4 x^2+1\right)^6} d x

is equal to

View answer and explanation

Correct option: D

\frac{1}{10}\left(\frac{1}{\mathrm{x}^2}+4\right)^{-5}+\mathrm{C}

Option D (

\frac{{1}}{{10}}(\frac{{1}}{{x^2}}+4)^{-5}+C

) is correct because simplifying the integral and using substitution leads to this result.

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\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

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{C}

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