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Find the integral $\int\frac{32x-20}{\left(x-1\right)\left(5x-3\right)}dx$

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Solution

Formulas

Videos

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

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

_-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

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

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Function Plot

Plotting: $6\ln\left(x-1\right)+\frac{2}{5}\ln\left(5x-3\right)+C_0$

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a
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m
n
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻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 (4)

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