Natural Logs and Anit-Derivatives are kicking me

Question

I am given a problem involving rates of flow, $F(t)=\frac{t+7}{2+t}$ is the rate at which a bucket is being filled. The same bucket is being emptied at a rate given by $E(t)=\frac{\ln(t+4)}{t+2}$. My job is to find the number of pints left in the bucket after five minutes, yes t is in minutes. I know the equation looks something like... $\int_0^5{F(t)dt}-\int_0^5{E(t)dt}$ and maybe it would look like this... $\int_0^5{F(t)-E(t)dt}$. But I don't know how to get the anti-derivative of E(t). I have worked it down further to exclude the theory that my problem involves polylogarithms. It is now $\int_0^5{\frac{t+7-\ln(t+4)}{t+2}}$

Answer 1

For problems like this, I think the convention is to use numerical integration, approximations using Simpson's rule in your calculator, the part you're responsible for is setting up the integrals. I attempted to integrate E(t) and I'm fairly certain the answer would require some special function like polylogarithms.