# Step-by-step Solution

## Integral of $\frac{6-x}{x^2\left(x^2-x\right)}$ 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

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

## Step-by-step explanation

Problem to solve:

$\int\frac{\left(6-x\right)}{x^2\left(x^2-x\right)}dx$
1

Factoring by $x$

$\int\frac{6-x}{x^2x\left(x-1\right)}dx$
2

When multiplying exponents with same base you can add the exponents

$\int\frac{6-x}{x^{3}\left(x-1\right)}dx$

$5\ln\left|x-1\right|+3x^{-2}-5\ln\left|x\right|+5x^{-1}+C_0$
$\int\frac{\left(6-x\right)}{x^2\left(x^2-x\right)}dx$