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# Find the integral $\int\frac{5x+3}{x^3-2x^2-3x}dx$

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##  Final Answer

$-\ln\left(x\right)+\frac{3}{2}\ln\left(x-3\right)-\frac{1}{2}\ln\left(x+1\right)+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{5x+3}{x^3-2x^2-3x}dx$

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1

Rewrite the expression $\frac{5x+3}{x^3-2x^2-3x}$ inside the integral in factored form

$\int\frac{5x+3}{x\left(x-3\right)\left(x+1\right)}dx$

Learn how to solve problems step by step online.

$\int\frac{5x+3}{x\left(x-3\right)\left(x+1\right)}dx$

Learn how to solve problems step by step online. Find the integral int((5x+3)/(x^3-2x^2-3x))dx. Rewrite the expression \frac{5x+3}{x^3-2x^2-3x} inside the integral in factored form. The integral \int\frac{-1}{x}dx results in: -\ln\left(x\right). The integral \int\frac{3}{2\left(x-3\right)}dx results in: \frac{3}{2}\ln\left(x-3\right). The integral \int\frac{-1}{2\left(x+1\right)}dx results in: -\frac{1}{2}\ln\left(x+1\right).

##  Final Answer

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

##  Explore different ways to solve this problem

SnapXam A2

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3
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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

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