JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int {\frac{{{{\cos }^3}xdx}}{{{{\sin }^2}x + \sin x}}}

is equal to

View answer and explanation

Correct option: B

\log \left| {\sin x} \right| - \sin x + c

Option B (

\log \left| {\sin x} \right| - \sin x + c

) is correct because after substituting

t = \sin x

and simplifying, the integral evaluates to this expression.

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\int \sin ^5 x \cos ^4 x d x=

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

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{C}

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