JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int(\sin x)^{-3 / 2}(\cos x)^{-5 / 2} d x=

View answer and explanation

Correct option: C

-2 \sqrt{\cot x}+\frac{2}{3} \sqrt{\tan ^3 x}+c

Option C (

-2 \sqrt{{\cot x}}+\frac{{2}}{{3}} \sqrt{{\tan ^3 x}}+c

) is correct because it is the result of integrating the given expression after trigonometric manipulation and substitution.

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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

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