Mathematics

Problem

Consider the integral

J=\int \frac{x^{2}+3x+2}{x\left(x^{2}+4\right)}\,dx.

(a) Express the integrand as a sum of simpler rational functions whose denominators are

x

and

x^{2}+4

. (b) Hence evaluate

J

, writing your final answer as a combination of logarithmic and inverse–trigonometric terms.