Question

Evaluate the integral

Integral (2x-1)^(1/2)/(2x+3)

Please just say how to start it off.

Answer 1

\[\int\limits_{}^{}\frac{\sqrt{2x-1}}{2x+3}dx\]

Answer 2

That is the integral, but how do you start solving it?

Answer 3

ok, one approach is to set u=sqrt(2x-1) so du=1/sqrt(2x-1)dx and dx=sqrt(2x-1)du or just dx=u du This gives:\[\int\limits_{}^{}\frac{u^2}{u^2+4} du\]

Answer 4

http://www.wolframalpha.com/input/?i=integrate+%282x-1%29%5E%281%2F2%29%2F%282x%2B3%29

Answer 5

That gets rid of you peskey radical

Answer 6

So, do you get \[\sqrt{2x-1}-2\tan^{-1} (\sqrt{2x-1}/2) +C\]