Question

Find `int dx/(sqrt(x) + x)`

Answer 1

`int dx/(sqrt(x) + x) dx = int 1/(sqrt(x) (1 + sqrt(x))) dx`

Let, `1 + sqrt(x) = t`

`0 + 1/(2sqrt(x)) dx = dt`

`1/sqrt(x) dx = 2dt`

= `2 int 1/t dt`

= 2 log t + C

= `2 log (1 + sqrt(x)) + "C"`