U- sub check.

**Bushy** · October 31st 2009, 02:35 PM

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?

**skeeter** · October 31st 2009, 02:43 PM

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.

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