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Find the integral $\int\frac{x^2+6x-4}{x^3-6x^2+12x-8}dx$

Step-by-step Solution

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Final Answer

$\ln\left(x-2\right)+\frac{-10}{x-2}+\frac{-6}{\left(x-2\right)^{2}}+C_0$
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Step-by-step Solution

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Rewrite the expression $\frac{x^2+6x-4}{x^3-6x^2+12x-8}$ inside the integral in factored form

$\int\frac{x^2+6x-4}{\left(x-2\right)^{3}}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{x^2+6x-4}{\left(x-2\right)^{3}}dx$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x^2+6x+-4)/(x^3-6x^212x+-8))dx. Rewrite the expression \frac{x^2+6x-4}{x^3-6x^2+12x-8} inside the integral in factored form. Rewrite the fraction \frac{x^2+6x-4}{\left(x-2\right)^{3}} 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-2\right)^{3}. Multiply both sides of the equality by 1 to simplify the fractions.

Final Answer

$\ln\left(x-2\right)+\frac{-10}{x-2}+\frac{-6}{\left(x-2\right)^{2}}+C_0$

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Plotting: $\ln\left(x-2\right)+\frac{-10}{x-2}+\frac{-6}{\left(x-2\right)^{2}}+C_0$

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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

How to improve your answer:

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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