ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Find the integral $\int\frac{4x^2-14x-6}{x^3-2x^2-3x}dx$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
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

$2\ln\left(x\right)-\ln\left(x-3\right)+3\ln\left(x+1\right)+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

Rewrite the expression $\frac{4x^2-14x-6}{x^3-2x^2-3x}$ inside the integral in factored form

$\int\frac{4x^2-14x-6}{x\left(x-3\right)\left(x+1\right)}dx$

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

$\int\frac{4x^2-14x-6}{x\left(x-3\right)\left(x+1\right)}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((4x^2-14x+-6)/(x^3-2x^2-3x))dx. Rewrite the expression \frac{4x^2-14x-6}{x^3-2x^2-3x} inside the integral in factored form. Rewrite the fraction \frac{4x^2-14x-6}{x\left(x-3\right)\left(x+1\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by x\left(x-3\right)\left(x+1\right). Multiplying polynomials.

$2\ln\left(x\right)-\ln\left(x-3\right)+3\ln\left(x+1\right)+C_0$

##  Explore different ways to solve this problem

SnapXam A2

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main Topic: Integrals by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.