Let (3x + 5)/((x - 1)(x + 3)) = A/(x - 1) + B/(x + 3)…

Step 1. Constants. At $x = 1$: $A = \dfrac{3 + 5}{1 + 3} = 2$. At $x = -3$: $B = \dfrac{-9 + 5}{-3 - 1} = 1$.

Step 2. The antiderivative. $F(x) = 2\ln(x - 1) + \ln(x + 3)$ for $x > 1$.

Step 3. The difference. $F(3) = 2\ln 2 + \ln 6$ and $F(2) = 2\ln 1 + \ln 5 = \ln 5$. So $F(3) - F(2) = 2\ln 2 + \ln\dfrac{6}{5} = 1.3863 + 0.1823 = 1.5686$.