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# Find the integral $\int\frac{4x+12}{\left(x-2\right)\left(x^2+4x+8\right)}dx$

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##  Final answer to the problem

$\ln\left|x-2\right|-\frac{1}{2}\ln\left|x^2+4x+8\right|+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

Rewrite the fraction $\frac{4x+12}{\left(x-2\right)\left(x^2+4x+8\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{x-2}+\frac{-x-2}{x^2+4x+8}$

Learn how to solve trigonometric integrals problems step by step online.

$\frac{1}{x-2}+\frac{-x-2}{x^2+4x+8}$

Learn how to solve trigonometric integrals problems step by step online. Find the integral int((4x+12)/((x-2)(x^2+4x+8)))dx. Rewrite the fraction \frac{4x+12}{\left(x-2\right)\left(x^2+4x+8\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x-2}+\frac{-x-2}{x^2+4x+8}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x-2}dx results in: \ln\left|x-2\right|. The integral \int\frac{-x-2}{x^2+4x+8}dx results in: -\frac{1}{2}\ln\left|x^2+4x+8\right|.

##  Final answer to the problem

$\ln\left|x-2\right|-\frac{1}{2}\ln\left|x^2+4x+8\right|+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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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

###  Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.