Integrate: 5x^4+4x^5 / (x^5+x+1)^2

Answers (1)

Solution:   

          I=int frac5x^4+4x^5(x^5+x+1)^2dx \ \ Rightarrow hspace1cm I=int frac5x^4+4x^5x^10(1+frac1x^4+frac1x^5)^2dx\ \ Rightarrow hspace1cmI=int fracfrac5x^6+frac4x^5(1+frac1x^4+frac1x^5)^2dx\ \ Rightarrow hspace1cm Let hspace1cm1+frac1x^4+frac1x^5=tRightarrow -frac4x^5-frac5x^6dx=dt

         \ \ Rightarrow hspace1cmI=-int frac1t^2dt=frac1t+c\ \ Rightarrow hspace1cmI=fracx^5x^5+x+1+c

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