Question

Integration!
\[\int x^2\sqrt{x-2} dx\]

Answer 1

So I think I have to \(u = x - 2\)
However that leads to \(u + 2 = x\)
\[\int (u+2)^2\sqrt{u} du\]
I just wonder if anyone had a faster way before I dove headlong into that mess. :D

Answer 2

It works doesn't it?

Answer 3

Well, yes. :D

Answer 4

So don't sweat it.

Answer 5

\[\int (u^2 + 4u + 4)\sqrt{u}\]\[\int u^{5/2} + 4u^{3/2} + 4u^{1/2}\]

Answer 6

\[\frac{2u^{7/2}}{7} + \frac{8u^{5/2}}{5} + \frac{8u^{3/2}}{3} + C \]
\[\frac{2(x-2)^{7/2}}{7} + \frac{8(x-2)^{5/2}}{5} + \frac{8(x-2)^{3/2}}{3} + C \]

Answer 7

Oh well, I guess there's another way, but, there you go.

Answer 8

What's the other way? :O

Answer 9

i remember seeing a question like this

Answer 10

You asked for it.

Answer 11

Forget it; it's much longer. Stick with that.

Answer 12

Thanks!

Answer 13

It's all you. Good job.