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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \large\frac{\cos^2 x}{\sin ^4 x }$$dx$

$(a)\;-\cot x+c \\(b)\; \frac{-\tan ^3 x}{3}+c \\(c)\; \frac{-\cot ^3 x }{3}+c \\ (d)\;None$

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A)
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$\int \large\frac{\cos^2 x}{\sin ^4 x }$$dx$
=> $\int \cot^2 x . cosec ^2 x .dx$
=> $\cot x =t $
differentiate with respect to x
$-cosec ^2 x dx=dt$
=>$- \int t^2 .dt$
=> $-\large\frac{t^3}{3}$$+c$
=> $\large\frac{-\cot^3 x}{3}$$+c$
Hence c is the correct answer.

 

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