Solving Calc II Integral Homework Problem

[brushman]

Homework Statement

Solve.

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

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?

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

edit: got it thanks guys

 

[Tedjn]

I would try trig substitution. Have you learned it?

 

[brushman]

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

Thanks.

 

[Mark44]

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

Now you're ready for a substitution.

 

[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.