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Question Number 49760 by rahul 19 last updated on 10/Dec/18

Commented by rahul 19 last updated on 11/Dec/18

$$Thankyousir!$$

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

$$waitplstrying...$$

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

$$\int \frac{x^{5m-1}+2x^{4m-1}}{{(x^{2m}+x^m+1)}^3}dx$$$$\int \frac{x^{5m-1}+2x^{4m-1}}{x^{6m}{(1+x^{-m}+x^{-2m})}^3}dx$$$$\int \frac{x^{-m-1}+2x^{-2m-1}}{{(1+x^{-m}+x^{-2m})}^3}dx$$$$t=1+x^{-m}+x^{-2m}$$$$\frac{dt}{dx}=-{mx}^{-m-1}-2{mx}^{-2m-1}$$$$\frac{-dt}{m}=(x^{-m-1}+2x^{-2m-1})dx$$$$\int \frac{-dt}{m\times t^3}=\frac{-1}{m}\times \frac{t^{-2}}{-2}=\frac{1}{2m}\times \frac{1}{{(1+x^{-m}+x^{-2m})}^2}+c$$$$=\frac{1}{2m}\times \frac{x^{4m}}{{(x^{2m}+x^m+1)}^2}+c$$$$$$

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