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.