int 0 π / 4 frac cos 2 x sin 2 x (cos 3 x+sin 3 x ) 2 d x is equal to

Mathematics · Definite Integration

JEE Main 2024 — 6 April, Shift 1 — Question 3

$\int_{0}^{\pi / 4} \frac{\cos ^{2} x \sin ^{2} x}{\left(\cos ^{3} x+\sin ^{3} x\right)^{2}} d x$ is equal to

Divide Nr & Dr by cosx $\int_{0}^{\pi / 4} \frac{\tan ^{2} x \sec ^{2} x d x}{\left(1+\tan ^{3} x\right)^{2}} d x$

Let $1+\tan ^{3} \mathrm{x}=\mathrm{t}$

$\tan ^{2} x \sec ^{2} x d x=\frac{d t}{3}$

$\frac{1}{3} \int_{1}^{2} \frac{d t}{t^{2}}=\frac{1}{6}$

Answer key and solution verified before publishing.

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