Homework Help: Calc II Integral

1. Jun 21, 2010

brushman

1. The problem statement, all variables and given/known data
Solve.

$$\int \frac{xdx}{\sqrt{x^2 + 4x}}$$

3. The attempt at a solution

First I added and subtracted 2, then let $u = x^2 + 4x$

After that I fiddled around with it to no success. What's my problem?

$$\int \frac{xdx}{\sqrt{x^2 + 4x}} \Rightarrow \int \frac{(x+2)dx}{\sqrt{x^2 + 4x}} - \int \frac{2dx}{\sqrt{x^2 + 4x}} \Rightarrow \int \frac{u^{-1/2}}{2} - \int \frac{2dx}{\sqrt{x^2 + 4x}} = (x^2 + 4x)^{1/2} - \int \frac{2dx}{\sqrt{x^2 + 4x}}$$

Thanks.

edit: got it thanks guys

Last edited: Jun 22, 2010
2. Jun 21, 2010

Tedjn

I would try trig substitution. Have you learned it?

3. Jun 21, 2010

brushman

oh. the 4x was throwing me off, but I guess I can just make it $(\sqrt{x})^2$.

Thanks.

4. Jun 21, 2010

Staff: Mentor

x2 + 4x = x2 + 4x + 4 - 4 = (x + 2)2 - 4

Now you're ready for a substitution.

5. Jun 22, 2010

Gib Z

Maybe it was his trap. If the OP were to use his solution he would have to write and still do much much more than if he listened to Mark44 and Tedjn. And his teacher might mention in his feedback how unnecessary that was.