First of all a "lawn" is area of grass with other plantings.

The trend in calculus textbooks is to use $\displaystyle \log(x)$ where we once would have used $\displaystyle \ln(x).$

Secondly, there is a

web recourse.

Click it and you will see it helps with partial fractions beautifully.

Now once you have the parts, I would make three different integrals.

In general $\displaystyle \int_a^b {\frac{{f'(x)}}{{f(x)}}} dx = \log (b) - \log (a) = \log \left( {\frac{b}{a}} \right)$, of course $\displaystyle a~\&~b>0$.