This integral is confusing: (1/x+1)*(1/sqrt(x))?

Question

This problem looks like one for u substitution but I have tried to use that and cant figure out a way!

Answer 1

int [(1/x+1)*(1/sqrt(x)) dx]
set
u = sqrt x
du = dx/(2*sqrtx)
2 * du = dx/sqrtx
But:
u^2 = x
u^2 + 1 = x + 1
so we get:
int [2 du/(u^2+1)] =
= 2 int [1/(u^2+1) du]
= 2 * tan u + c
= 2 * tan (sqrtx) + c

Answer 2

let u = sqrt(x)
du = (1/2) x^(-1/2)dx

the integral becomes
(u^-2 + 1) 2 du

Answer 3

2 arctg(sqrt(x)) + constant