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Question Number 49761 by rahul 19 last updated on 10/Dec/18

$$Calculate:$$$$\int \frac{{\sin }^{2}x{\cos }^{2}x}{{({\sin }^{3}x+{\cos }^{3}x)}^2}dx$$

Answered by tanmay.chaudhury50@gmail.com last updated on 10/Dec/18

$$\int \frac{{tan}^2{xcos}^{4}x}{{cos}^{6}x{(1+{tan}^{3}x)}^3}dx$$$$\int \frac{{tan}^2{xsec}^{2}x}{{(1+{tan}^{3}x)}^3}dx$$$$=\frac{1}{3}\int \frac{d(1+{tan}^{3}x)}{{(1+{tan}^{3}x)}^3}dx$$$$=\frac{1}{3}\times \frac{{(1+{tan}^{3}x)}^{-2}}{-2}=\frac{1}{-6}\times \frac{1}{{(1+{tan}^{3}x)}^2}+c$$

Commented by rahul 19 last updated on 10/Dec/18

thank you sir!��

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