Evaluate `int(2zdz)/(root3(z^2+1))`

Explanation

Method 1
Let `I=int(2zdz)/(root3(z^2+1))`.
Let `u=z^2+1`, then `du=2zdz`.
`I=intu^(-1//3)du` [In the form of `u^ndu`]
`=(u^(2//3))/(2//3)+C` [Integrate with respect to u]
`=3/2u^(2//3)+C`
`=(z^2+1)^(2//3)+C` [Replace `u` by `z^2+1`]
Method 2
Let `u=root3(z^2+1)impliesu^3=z^2+1`
Then `3u^2du=2zdz`
`I=int(2zdz)/(root3(z^2+1))`
`=int(3u^2du)/(u)`
`=3*intudu`
`=3*u^2/2+C` [Integrate with respect to u]
`=3/2(z^2+1)^(2//3)+C` [Replace u by `(z^2+1)^(1//3)`]