1. ## U- sub check.

I have

$\int (3x+1) \sqrt{3x-1}~dx$

$u = 3x-1$

$\frac{du}{du} = 3$

which gives $\frac{1}{3}\int \frac{du}{dx} (u+2)\sqrt{u}~dx = \frac{1}{3}\int (u+2)\sqrt{u}~du$

Is this correct so far?

2. Originally Posted by Bushy
I have

$\int (3x+1) \sqrt{3x-1}~dx$

$u = 3x-1$

$\frac{du}{du} = 3$

which gives $\frac{1}{3}\int \frac{du}{dx} (u+2)\sqrt{u}~dx = \frac{1}{3}\int (u+2)\sqrt{u}~du$

Is this correct so far?
I'll buy that substitution, although I think you meant $\frac{du}{dx} = 3$ ... continue and finish it.