# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{1}{\left(x+2\right)\left(x-3\right)}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\frac{1}{\left(x+2\right)\left(x-3\right)}=\frac{A}{x+2}+\frac{B}{x-3}$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of 1/((x+2)(x-3)) with respect to x. Rewrite the fraction \frac{1}{\left(x+2\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by \left(x+2\right)\left(x-3\right). Multiplying polynomials. Simplifying.

$-\frac{1}{5}\ln\left|x+2\right|+\frac{1}{5}\ln\left|x-3\right|+C_0$

### Problem Analysis

$\int\frac{1}{\left(x+2\right)\left(x-3\right)}dx$

### Main topic:

Integrals by partial fraction expansion

~ 0.09 seconds