# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{x-2}{x\left(x^2+5x-14\right)}dx$

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

$\begin{matrix}\left(-2\right)\left(7\right)=-14\\ \left(-2\right)+\left(7\right)=5\end{matrix}$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (x-2)/(x(x^2+5x-14)) with respect to x. Factor the trinomial \left(x^2+5x-14\right) finding two numbers that multiply to form -14 and added form 5. Thus. Simplifying. Rewrite the fraction \frac{1}{x\left(x+7\right)} in 2 simpler fractions using partial fraction decomposition.

$\frac{1}{7}\ln\left|x\right|-\frac{1}{7}\ln\left|x+7\right|+C_0$

### Problem Analysis

$\int\frac{x-2}{x\left(x^2+5x-14\right)}dx$

### Main topic:

Integrals by partial fraction expansion

~ 0.09 seconds