سیگما

`Q=int (dx)/(x root3(x^5+1))`
`t=x^5+1`
`(dx)/(dt)=1/5(t-1)^(-4/5)`
`Q=int (1/5(t-1)^(-4/5))/(root5(t-1)root3(t)) dt`
`Q=1/5 int (dt)/((t-1)root3(t))`
`u^3=t`
`(dt)/(du)=2u^2`
`Q=1/5 int (3u^2)/((u^3-1)u) du`
`Q=3/5 int u/(u^3-1) du`
`u/(u^3-1)=A/(u-1)+(Bx+C)/(u^2+u+1)`
`A=1/3,B=-1/3,C=1/3`
`Q=3/5(int (1/3)/(u-1)+(-1/3u+1/3)/(u^2+u+1) du)`
`Q=1/5(ln(u-1)-1/2(int (2u+1-3)/(u^2+u+1) du))`
`Q=1/10ln((u-1)^2/(u^2+u+1))+sqrt(3)/5arctan((2u+1)/sqrt(3))`
`|u=root3(1+x^5)`