Find the integral $\int\frac{2x}{x^2-4}dx$

Step-by-step Solution

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Final answer to the problem

$\ln\left|x+2\right|+\ln\left|x-2\right|+C_0$
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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
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Rewrite the expression $\frac{2x}{x^2-4}$ inside the integral in factored form

$\int\frac{2x}{\left(x+2\right)\left(x-2\right)}dx$

Learn how to solve integral calculus problems step by step online.

$\int\frac{2x}{\left(x+2\right)\left(x-2\right)}dx$

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Learn how to solve integral calculus problems step by step online. Find the integral int((2x)/(x^2-4))dx. Rewrite the expression \frac{2x}{x^2-4} inside the integral in factored form. Take out the constant 2 from the integral. Rewrite the fraction \frac{x}{\left(x+2\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2\left(x+2\right)}+\frac{1}{2\left(x-2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

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

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Function Plot

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

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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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