u substitution

Saladsamurai

First day of u subs...

[tex]\int t \sqrt{7t^2+12}dt[/tex]

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

Just a hint please,
Casey

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

rocomath

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

Saladsamurai

do you mean like this?
If I do this, I get [tex]\int tudt[/tex] and [tex]du=\frac{dt}{2\sqrt{7t^2+12}}[/tex] ...right?

I think I am confused...

bob1182006

no just the 7t^2+12

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

Saladsamurai

Oh..one sec...

Saladsamurai

Brain Cramp![tex]u=7t^2+12[/tex]
so
[tex]du=14tdt[/tex]
[tex]\int t u^{1/2} dt *14*\frac{1}{14}[/tex]
[tex]=\frac{1}{14}\int \sqrt{u}* du[/tex]
and I got it from here..
Thanks guys,
Casey