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Mathematics · 2018
JEE Main 2018 · 2018-04-08 Offline · Q74
The integral ∫ (sin^2 x cos^2 x)/(( sin^5 x+ cos^3 x sin^2 x+ sin^3 x cos^2 x+ cos^5 x)^2) d x is equal to: (where C is a constant of integration)
The integral
$$\int \frac{\sin ^2 x \cos ^2 x}{\left(\sin ^5 x+\cos ^3 x \sin ^2 x+\sin ^3 x \cos ^2 x+\cos ^5 x\right)^2} d x
$$
is equal to :
(where C is a constant of integration)
Official answer
(2)
$\displaystyle \frac{-1}{3\left(1+\tan ^3 x\right)}+C$
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JEE Main 2018 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.