Partial Fraction Decomposition Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Decompose

\dfrac{5}{(x+1)(x-2)}

and integrate.

1
$\frac{5}{(x+1)(x-2)} = \frac{A}{x+1}+\frac{B}{x-2}$ .
2
$x=2$ : $B=5/3$ . $x=-1$ : $A=-5/3$ .
3
$\int = -\frac{5}{3}\ln|x+1| + \frac{5}{3}\ln|x-2| + C = \frac{5}{3}\ln\left|\frac{x-2}{x+1}\right|+C$ .

Answer

\frac{5}{3}\ln\left|\frac{x-2}{x+1}\right| + C

Strategic substitution: set

x

equal to each root of the denominator to isolate each constant.

About Partial Fraction Decomposition

Breaking a rational expression into a sum of simpler fractions whose denominators are the factors of the original denominator.

Integrate [formula].

Decompose [formula].

Integrate [formula].