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Question Number 35015 by NECx last updated on 14/May/18

$$\int \frac{x^2}{{(1+x^3)}^2}dx$$

Answered by ajfour last updated on 14/May/18

$$I=\frac{1}{3}\int \frac{3x^{2}dx}{{(1+x^3)}^2}$$$$lett=1+x^3$$$$\Rightarrow I=\frac{1}{3}\int \frac{dt}{t^2}=-\frac{1}{3}\left(\frac{1}{1+x^3}\right)+c$$$$=-\frac{1}{3(1+x^3)}.$$

Commented by NECx last updated on 15/May/18

$$thankyousomuch$$$$$$

Answered by tanmay.chaudhury50@gmail.com last updated on 14/May/18

$$t=1+x^{3}dt=3x^{2}dx$$$$\frac{1}{3}\int t^{-2}dt$$$$=\frac{1}{3}\times \frac{t^{-1}}{-1}$$$$=\frac{-1}{3}\times \frac{1}{(1+x^3)}$$

Commented by NECx last updated on 15/May/18

$$Thankyousomuch$$

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