Find the integral of (x+4)/x(2-x) .dx

In order to integrate the expression we must first rewrite it in terms of Partial Fractions i.e. A/x and B/(2-x), so that when multiplied together we have a fraction with same denominator as the expression we want to integrate. The numerator is then A(2-x)+B(x). We compare this to (x+4) and determine our values for A and B by equating the coefficients. 2A=4 therefore A=2. -A+B=1 therefor B=3. We now have a new integrand which is easier to solve, 2/x + 3/(2-x). Using our standard examples of integrals we see that the solution is 2ln|x|-3ln|2-x|. Be careful of the -x in 3/(2-x) as this affects the sign of ln when we integrate.