5x-4-4x-5-x-5-x-1-2-solve-the-intgration-

Question Number 19195 by vivek last updated on 06/Aug/17

\int \frac{5 x^{4} + 4 x^{5}}{{(x^{5} + x + 1)}^{2}} s o l v e t h e i n t g r a t i o n

Commented by vivek last updated on 07/Aug/17

p l e a s e s o l v e q u e t i o n

Answered by ajfour last updated on 07/Aug/17

\int \frac{{5 x}^{4} + {4 x}^{5}}{{(x^{5} + x + 1)}^{2}} dx

= \int \frac{{5 x}^{4} + 1}{{(x^{5} + x + 1)}^{2}} dx + \int \frac{{4 x}^{5} - 1}{{(x^{5} + x + 1)}^{2}} dx

= - \frac{1}{x^{5} + x + 1} + C_{1} + \int \frac{({4 x}^{3} - \frac{1}{x^{2}})}{{(x^{4} + 1 - \frac{1}{x})}^{2}} dx

= - \frac{1}{x^{5} + x + 1} - \frac{1}{(x^{4} + 1 - \frac{1}{x})} + C

I = - \frac{1}{(x^{5} + x + 1)} - \frac{x}{(x^{5} + x - 1)} + C .

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