If $f(x)=\int \frac{\tan ^3 x}{2+\tan ^2 x} d x$, then

$f(x)=\log \left|\frac{2-\cos ^2 x}{\sin x}\right|+C$

$f(x)=\log \left|\frac{2+\cos ^2 x}{\sin x}\right|+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

f(x)=\int \frac{\tan ^3 x}{2+\tan ^2 x} d x

, then

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Correct option: B

f(x)=\log \left|\frac{2-\sin ^2 x}{\cos x}\right|+C

The correct answer is

f(x)=\log \left|\frac{{2-\sin ^2 x}}{{\cos x}}\right|+C

(Option B) because the integral simplifies to this expression after trigonometric substitution and simplification.