Originally Posted by

**Furyan** Hello,

I have to solve the following using the given substitution:

$\displaystyle \int\dfrac{1}{1 + \sqrt{x - 1}} dx$

Using the substitution:

$\displaystyle u^2 = x - 1$

Which differentiating implicitly gives me:

$\displaystyle \dfrac{dx}{du} = 2u$

Substituting into to

$\displaystyle \int\dfrac{1}{1 + \sqrt{x - 1}} \dfrac{dx}{du}du$

I get

$\displaystyle \int\dfrac{1}{1 + u}(2u) du$

$\displaystyle 2\int\dfrac{u}{1 + u} du$

Would someone please tell me if this is correct so far and if so how to proceed from here.

Thank you.