indefinite intergral

[abby_07]

I would appreciate if you can help me with this problem. I do not know how to start the problem. Can you please help me?

Find the indefinite intergral
1/1+(2x)^(1/2) dx

and

x(x-2)/(x-2)^2 dx

 

[galactus]

Find the indefinite integral
\(\displaystyle \L\\\frac{1}{1+\sqrt{2x}}dx\)

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

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