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# Find the integral $\int\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}dx$

## Step-by-step Solution

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###  Solution

$4\ln\left(x+1\right)+\ln\left(x-3\right)-5\ln\left(x-2\right)+C_0$
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##  Step-by-step Solution 

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Rewrite the expression $\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}$ inside the integral in factored form

$\int\frac{37-11x}{\left(x+1\right)\left(x-3\right)\left(x-2\right)}dx$

Learn how to solve problems step by step online.

$\int\frac{37-11x}{\left(x+1\right)\left(x-3\right)\left(x-2\right)}dx$

Learn how to solve problems step by step online. Find the integral int((37-11x)/((x^2-x+-2)(x-3)))dx. Rewrite the expression \frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)} inside the integral in factored form. Rewrite the fraction \frac{37-11x}{\left(x+1\right)\left(x-3\right)\left(x-2\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 \left(x+1\right)\left(x-3\right)\left(x-2\right). Multiply both sides of the equality by 1 to simplify the fractions.

$4\ln\left(x+1\right)+\ln\left(x-3\right)-5\ln\left(x-2\right)+C_0$

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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