[SOLVED] Integration

**swensonm** · February 25th 2009, 12:01 PM

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?

**skeeter** · February 25th 2009, 02:02 PM

$\int e^{\sqrt{3s+9}} \, ds<br />$

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

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

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

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

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

now do parts ... let $u = t$ and $dv = e^t \, dt$

**swensonm** · February 25th 2009, 03:36 PM

Why did you solve for ds?

**skeeter** · February 25th 2009, 03:44 PM

because one cannot integrate a function of t w/respect to s.

**swensonm** · February 25th 2009, 05:55 PM

Thanks skeeter.

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