# [SOLVED] Integration

• Feb 25th 2009, 01:01 PM
swensonm
[SOLVED] Integration
I am integrating by parts. I do not know what let u and v be. I am also stuck on the radical.

e^{sqre rt} 3s+9 ds

I want to let u = 3s+9 and v = e^rt x

can it be done or am i just lost?
• Feb 25th 2009, 03:02 PM
skeeter
$\int e^{\sqrt{3s+9}} \, ds
$

$t = \sqrt{3s+9}$

$dt = \frac{3}{2\sqrt{3s+9}} \, ds = \frac{3}{2t} \, ds$

$ds = \frac{2t}{3} \, dt$

$\int e^t \cdot \frac{2t}{3} \, dt$

$\frac{2}{3} \int t \cdot e^t \, dt$

now do parts ... let $u = t$ and $dv = e^t \, dt$
• Feb 25th 2009, 04:36 PM
swensonm
Why did you solve for ds?
• Feb 25th 2009, 04:44 PM
skeeter
because one cannot integrate a function of t w/respect to s.
• Feb 25th 2009, 06:55 PM
swensonm
Thank You
Thanks skeeter. (Rofl)