Question

11) Find the following indefinite integrals.
∫x/(x+9)^(1/2)dx

Answer 1

Let u^2 = x+9
Then √(x+9) = u
x = u^2-9
dx = 2u du

Then the integral becomes

∫(u^2-9)/u (2u du)
= ∫2(u^2-9) du
= 2/3 u^3 - 18u
= 2u/3 (u^2-27)
= 2/3 √(x+9) (x-18)

For other problems, you can check your results at

http://www.wolframalpha.com/input/?i=%E2%88%ABx%2F%28x%2B9%29^%281%2F2%29dx

Even if you have trouble with the solution, someimes seeing the answer can give you a hint where to start.