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**Jason76** $\displaystyle \int \dfrac{dx}{2\sqrt{x} + 2x}$. - The key here is pulling the constant out, before doing u substitution.

$\displaystyle \int (\dfrac{1}{2})\dfrac{dx}{\sqrt{x} + x}$.

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

$\displaystyle u = \sqrt{x} + x$.

$\displaystyle du = \dfrac{1}{2\sqrt{x}} + 1dx $. ?? What is the next step? Somehow we need to get rid of that constant of 1, and $\displaystyle \dfrac{1}{x}$

Note: The answer to this problem is $\displaystyle \ln(\sqrt{x} + x) + C$ But do we get there?