# Step-by-step Solution

## Integral of $\frac{x-2}{x\left(x^2+5x-14\right)}$ with respect to x

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

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

## Step-by-step explanation

Problem to solve:

$\int\frac{x-2}{x\cdot\left(x^2+5x-14\right)}dx$
1

Factor the trinomial $\left(x^2+5x-14\right)$ finding two numbers that multiply to form $-14$ and added form $5$

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

Thus

$\int\frac{x-2}{x\left(x-2\right)\left(x+7\right)}dx$

$-\frac{1}{7}\ln\left|x+7\right|+\frac{1}{7}\ln\left|x\right|+C_0$
$\int\frac{x-2}{x\cdot\left(x^2+5x-14\right)}dx$

### Main topic:

Integrals of Rational Functions

~ 1.0 seconds

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!