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?
$\displaystyle \int e^{\sqrt{3s+9}} \, ds
$
$\displaystyle t = \sqrt{3s+9}$
$\displaystyle dt = \frac{3}{2\sqrt{3s+9}} \, ds = \frac{3}{2t} \, ds$
$\displaystyle ds = \frac{2t}{3} \, dt$
$\displaystyle \int e^t \cdot \frac{2t}{3} \, dt$
$\displaystyle \frac{2}{3} \int t \cdot e^t \, dt$
now do parts ... let $\displaystyle u = t$ and $\displaystyle dv = e^t \, dt$