# Thread: Trig Integration Problem - # 3

1. ## Trig Integration Problem - # 3

Using Integration by parts $\displaystyle \int udv = uv - \int vdu$

$\displaystyle \int e^{8\theta} \sin(9\theta) d\theta$

$\displaystyle u = \sin(9\theta)$

$\displaystyle dv = e^{8\theta}$

$\displaystyle v = \dfrac{1}{8}e^{8\theta}$

$\displaystyle du = \dfrac{1}{9}\cos(9\theta)$

$\displaystyle [\sin(9\theta)][\dfrac{1}{8}e^{8\theta}] - \int[\dfrac{1}{8}e^{8\theta}][\dfrac{1}{9}\cos(9\theta)]$

?? What is the next step, and are the steps above right? I did try to do integration by parts again, but it still is an integration by parts situation. In fact, I think it would keep doing that over and over.

2. ## Re: Trig Integration Problem - # 3

If $\displaystyle u = \sin(9 \theta)$, then $\displaystyle du = 9 \cos(9 \theta)$

3. ## Re: Trig Integration Problem - # 3

Using Integration by Parts again IS what you do. You should find that you get a multiple of the original integral you're trying to find, which means you can use simple algebra to solve for it...