integration of 1 / (2*x^(1/2) + 1)

[doguden]

I can't integrate this one, could someone please show me the steps of integration? I can find the result by a program but I can't do it myself:

1 / (2*x^(1/2) + 1)

 

[galactus]

\(\displaystyle \L\\\int\frac{1}{2\sqrt{x}+1}dx\)

Let \(\displaystyle \L\\u=\sqrt{x}, \;\ u^{2}=x, \;\ 2udu=dx\)

Then you get:

\(\displaystyle \L\\\int\frac{2u}{2u+1}du=\int{1-\frac{1}{2u+1}}du=\int{du}-\int\frac{1}{2u+1}du\)

Finish?.

 

[doguden]

Thank you!
sometimes I can't see