<s>[INST] Find $\int \frac{5x^4+4x^5}{(x^5+x+1)^2}$ $\displaystyle \int \frac{5x^4+4x^5}{(x^5+x+1)^2}$
Since in the denominator of the integrand,$(x^5+x+1)^2$ is there.So the answer must be in the form $\displaystyle \frac{f(x)}{(x^5+x+1)}$, but i could not figure out what $f(x)$ i should suppose.I could not imagine any other way out.Please help... 
 [/INST] Let $\displaystyle \frac{5x^4+4x^5}{(x^5+x+1)^2}dx = \frac{d}{dx}\left[\frac{ax+b}{(x^5+x+1)}\right] = \frac{(x^5+x+1)\cdot a-(ax+b)\cdot (x^5+x+1)}{(x^5+x+1)^2}$
Now Equate  above equation, and get the value of $a$ and $b$
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