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Find the integral $\int\frac{8x-1}{\left(x-2\right)\left(x+3\right)}dx$

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Solution

Formulas

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

Finding specific antiderivatives: rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=bjdOWH43-9s

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Linear approximation of a rational function | Derivative rules | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=vRw4ovZK1CQ

Function Plot

Plotting: $3\ln\left(x-2\right)+5\ln\left(x+3\right)+C_0$

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0
a
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c
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.

Used Formulas

See formulas (3)

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