Evaluate: `int(sqrt(x))/(x+1)\ dx`

Explanation

Assume `sqrt x=t=>1/2 x(-1/2)dx=dt`

`dx=2 sqrt x dt`

`=int t/(t^2+1) xx 2 sqrt x dt`

`=2 int frac{t^2}{t^2+1}dt=2 int frac{t^2+1-1}{t^2+1}dt `

`2 int dt-2 int frac{1}{t^2+1}dt`

`2t-2tan^(-1)t+C`

`2 sqrt x-2 tan^(-1)sqrt x+C`