Beräkna integral

Jag ska beräkna integralen:

Såhär räknar jag den:

$$\begin{gathered} \int e^{ax}\sin \left(bx\right)dx \\ u = \sin \left(bx\right) du = b*\cos \left(bx\right)*dx \\ v =\frac{e^{ax}}{a}, dv =e^{ax} \\ \int e^{ax}\sin \left(bx\right)dx = \sin \left(bx\right) *\frac{e^{ax}}{a}- \int \frac{e^{ax}}{a}*\frac{du}{b*\cos \left(bx\right)} \\ =\frac{\sin \left(bx\right) *e^{ax}}{a}-\int \frac{e^{ax}du}{ab*\cos \left(bx\right)} \\ =\frac{\sin \left(bx\right) *e^{ax}}{a} - \frac{1}{ab}\int \frac{e^{ax}du}{\cos \left(bx\right)} \end{gathered}$$

men sen fastnar jag, vad kan jag göra?