D doguden New member Joined Oct 27, 2007 Messages 5 Oct 27, 2007 #1 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)
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)
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Oct 27, 2007 #2 \(\displaystyle \L\\\int\frac{1}{2\sqrt{x}+1}dx\) 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?.
\(\displaystyle \L\\\int\frac{1}{2\sqrt{x}+1}dx\) 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?.
