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Find the integral $\int\frac{6}{\left(x+4\right)\left(x-2\right)}dx$

Step-by-step Solution

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Final answer to the problem

$-\ln\left|x+4\right|+\ln\left|x-2\right|+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
  • Integrate by substitution
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  • Integrate using tabular integration
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  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Rewrite the fraction $\frac{6}{\left(x+4\right)\left(x-2\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{6}{\left(x+4\right)\left(x-2\right)}=\frac{A}{x+4}+\frac{B}{x-2}$

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

$\frac{6}{\left(x+4\right)\left(x-2\right)}=\frac{A}{x+4}+\frac{B}{x-2}$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(6/((x+4)(x-2)))dx. Rewrite the fraction \frac{6}{\left(x+4\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(x+4\right)\left(x-2\right). Multiplying polynomials. Simplifying.

Final answer to the problem

$-\ln\left|x+4\right|+\ln\left|x-2\right|+C_0$

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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

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Function Plot

Plotting: $-\ln\left|x+4\right|+\ln\left|x-2\right|+C_0$

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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.

Used Formulas

See formulas (2)

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