Find the intgral of f(x) = 1/(1+ sqrtx)

f(x) = 1/(1+ sqrtx)

Let us
use the substitution method to solve:

let x=
u^2

==> dx = 2u du

Now
we will substitute:

intg f(x) = intg (1/(1+u)
2udu

              = intg (2u/(1+u) 
du

  Now simplify using polynomial
division:

=> intg f(x) = intg ( 2 - 2/(u+1) 
du

                       = intg 2 du - 2 intg (1/u+1)
du

                         = 2u - 2 ln(u+1) +
C

Now subsitute with u=
sqrtx

==> intg f(x) = 2sqrtx -
2ln(sqrtx + 1) + C