Integration: Rationalizing and then Partial Fractions

[mickellowery]

Homework Statement

$$\int$$$$\frac{e^xcos(log_7(e^x+9))}{(e^x+9)ln(7)}$$dx

Homework Equations

The Attempt at a Solution

Let u= (e^x+9)
du= e^xdx
New integral $$\int$$$$\frac{cos(log_7(u))}{(u)ln(7)}$$du
This is where I got l little lost. Should I let log₇(u)=$$\frac{ln(u)}{ln(7)}$$? Or is this just a waste of time. I was thinking after that I would use log rules to make it ln(u)-ln(7) and then split it into two separate integrals and follow that by partial fractions. I'm just curious if I'm on the right track.

 

[losiu99]

Just let $$t=\log_7 u$$. Then only constant times integral of cosine is left.