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Gold Member

## u substitution

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
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 your first choice on a u-substitution with a rational number should always be the entire thing under the square root. try u=7*t^2+12 instead
 let u be the radican (is that the proper term? i forget) :D

Recognitions:
Gold Member

## u substitution

 Quote by rocophysics let u be the radican (is that the proper term? i forget) :D
do you mean like this?
 Quote by bob1182006 your first choice on a u-substitution with a rational number should always be the entire thing under the square root. try u=7*t^2+12 instead

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

I think I am confused...
 no just the 7t^2+12 if u=7t^2+12 what is dt=??
 Recognitions: Gold Member Oh..one sec...
 Recognitions: Gold Member Brain Cramp!$$u=7t^2+12$$ so $$du=14tdt$$ $$\int t u^{1/2} dt *14*\frac{1}{14}$$ $$=\frac{1}{14}\int \sqrt{u}* du$$ and I got it from here.. Thanks guys, Casey

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