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Find the integral $\int\frac{5x^2-11x+5}{x^3-4x^2+5x-2}dx$

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Solution

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Videos

Definite integral of rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=4WJUEXIksH0

Algebra 2 - Learning to solve rational equations in math class ((x+3)/(x‐2)) + (5/(x^2‐4)) = 1

https://www.youtube.com/watch?v=y8p0Tpn3BcI

Algebra 2 - Learn to solve a rational equation by multiplying by the LCD (15/x)+((9x-7)/(x+2))=9

https://www.youtube.com/watch?v=BMSmvkWcVTU

Algebra 2 - How to divide the cube root of a rational expression by rationalizing the denominator

https://www.youtube.com/watch?v=zfKL1_DzUBk

Algebra 2 - Simplify by dividing two rational expressions using factoring (32/n‐8)/(1/n‐8)

https://www.youtube.com/watch?v=wFy0p8Jo6pQ

Algebra 1 - Solve an equation with a rational term 1/x= 3+ 7/x^2+7x ex 2

https://www.youtube.com/watch?v=OjNDpBeMpxI

Function Plot

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

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0
a
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d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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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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.

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