`intxsqrt(x+1)\ dx`

We could let `u=x` or `u=sqrt(x+1)`.

Once again, we choose the one that allows `(du)/(dx)` to be of a simpler form than `u`, so we choose `u=x`.

Therefore `du = dx`. With this choice, `dv` must be the "rest" of the integral: `dv=sqrt(x+1)\ dx`.

`u = x` so `du=dx`.

`dv=sqrt(x+1)\ dx`, and integrating gives:

`{: (v,=intsqrt(x+1) dx),(,=int(x+1)^(1//2)dx),(,=2/3(x+1)^(3//2)) :}`

Substituting into the integration by parts formula, we get: