سیگما

`Q=int (dx)/(x^3root5(1+i/x))`
`t=1/x`
`(dx)/(dt)=-1/t^2`
`Q=-int (t)/(root5(1+t)) dt`
`t+1=u`
`dt=du`
`Q=-int (u-1)/(root5(u)) du`
`Q=-int u/(root5(u))-1/(root5(u)) du`
`Q=-int u^(4/5)-u^(-1/5) du`
`Q=5/4(1+1/x)^4/5-5/9(1+1/x)^9/5`

`Q=int root3(x)root7(1+rroot3(x^4)) dx`
`x=t^3`
`(dx)/(dt)=3t^2`
`Q=int t root7(1+t^4)3t^2 dt`
`Q=3 int t^3root7(1+t^4)`
`1+t^4=u`
`(du)/(dt)=4t^3`
`Q=3/4 int root7(u) du`
`Q=3/4(7/8u^(8/7))`
`Q=21/32root7((1+root3(x^4))^8)`

`Q=int root3(1+root4(x))/sqrt(x) dx`
`x=t^4`
`(dx)/(dt)=4t^3`
`Q=int root3(1+t)/t^2 4t^3 dt`
`t+1=u`
`du=dt`
`Q=4 int (u-1)root3(u) du`
`Q=4 int u^(4/3)-u^(1/3) du`
`Q=4(3/7u^(7/3)-3/4u^(4/3))`
`Q=12/7root3((1+root4(x))^7)-3root3((1+root4(x))^4)`

`Q=int (x^6)/sqrt(1+x^2) dx`
`Q=(Ax^5+Bx^4+Cx^3+Dx^2+Ex+F)sqrt(1+x^2)+K int (dx)/sqrt(1+x^2)`
`A=1/6,B=0,C=-5/24,D=0,E=5/16,F=0,K=-5/16`
`Q=(1/6x^5-5/24x^3+5/16x)sqrt(1+x^2)-5/16arcsinh(x)`

`Q=int (dx)/((x-1)sqrt(x^2-2))`
`t=1/(x-1)`
`x=1/t+1`
`(dx)/(dt)=-1/t^2`
`Q=int (-1/t)/sqrt(1/t^2+2/t+1-2) dt`
`Q=int (-1/t)/sqrt(1/t^2(1+2t-t^2)) dt`
`Q=-int (dt)/sqrt(2-(t-1)^2)`
`Q=-arcsin((t-1)/sqrt(2))`
`Q=arcsin((2-x)/(sqrt(2)(1-x)))`