# Homework Help: Integration: Rationalizing and then Partial Fractions

1. Jul 15, 2010

### mickellowery

1. The problem statement, all variables and given/known data
$$\int$$$$\frac{e^xcos(log_7(e^x+9))}{(e^x+9)ln(7)}$$dx

2. Relevant equations

3. The attempt at a solution
Let u= (ex+9)
du= exdx
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.

2. Jul 15, 2010

### losiu99

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