Evaluate: `intsqrt((1+x)/x)\ dx`

Explanation

`int sqrt(1+x)/(x) dx=int sqrt((1+x)/(x))sqrt((1+x)/(1+x))dx`
`=int(1+x)/(sqrt(x(1+x)))dx`
`=int(1+x)/(sqrt(x^(2)+x))dx`
`=(1)/(2)int(2x+1)/(sqrt(x^(2)+x))dx+(1)/(2)int(1)/(sqrt(x^(2)+x))dx`
`=(1)/(2)int(1)/(sqrt(t))dt +(1)/(2)int(1)/(sqrt((x+(1)/(2))^(2)-((1)/(2))^(2)))dx`,
` " where "t=x^(2)+x`
`=sqrt(t)+(1)/(2)log|(x+(1)/(2))+sqrt(x^(2)+x)|+C`
`=sqrt(x^(2)+x)+(1)/(2)log|(x+(1)/(2))+sqrt(x^(2)+x)|+C`