JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \frac{\sin ^3 x}{\left(\cos ^4 x+3 \cos ^2 x+1\right) \tan ^{-1}(\sec x+\cos x)} d x=

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Correct option: B

\log _e\left|\tan ^{-1}(\sec x+\cos x)\right|+C

The correct answer is B (

\log _e\left|\tan ^{-1}(\sec x+\cos x)\right|+C

) because the integral simplifies to a form where the derivative of the inner function is present, allowing for a direct integration.

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