# U substitution

1. Sep 10, 2007

First day of u subs...

$$\int t \sqrt{7t^2+12}dt$$

I am assuming that u=t, but It is maiking a mess when I do that.

Casey

2. Sep 10, 2007

### bob1182006

your first choice on a u-substitution with a rational number should always be the entire thing under the square root.

3. Sep 10, 2007

### rocomath

let u be the radican (is that the proper term? i forget) :D

4. Sep 10, 2007

do you mean like this?

If I do this, I get $$\int tudt$$ and $$du=\frac{dt}{2\sqrt{7t^2+12}}$$ ...right?

I think I am confused...

5. Sep 10, 2007

### bob1182006

no just the 7t^2+12

if u=7t^2+12
what is dt=??

6. Sep 10, 2007

Oh..one sec...

7. Sep 10, 2007

Brain Cramp!$$u=7t^2+12$$
$$du=14tdt$$
$$\int t u^{1/2} dt *14*\frac{1}{14}$$
$$=\frac{1}{14}\int \sqrt{u}* du$$