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Find the integral $\int\frac{5x-2}{x^2-4}dx$

Step-by-step Solution

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Final Answer

$2\ln\left(x-2\right)+3\ln\left(x+2\right)+C_0$
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Step-by-step Solution

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Expand the fraction $\frac{5x-2}{x^2-4}$ into $2$ simpler fractions with common denominator $x^2-4$

$\int\left(\frac{5x}{x^2-4}+\frac{-2}{x^2-4}\right)dx$

Learn how to solve integrals of rational functions problems step by step online.

$\int\left(\frac{5x}{x^2-4}+\frac{-2}{x^2-4}\right)dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((5x-2)/(x^2-4))dx. Expand the fraction \frac{5x-2}{x^2-4} into 2 simpler fractions with common denominator x^2-4. Simplify the expression inside the integral. The integral 5\int\frac{x}{x^2-4}dx results in: \frac{5}{2}\ln\left(x+2\right)+\frac{5}{2}\ln\left(x-2\right). Gather the results of all integrals.

Final Answer

$2\ln\left(x-2\right)+3\ln\left(x+2\right)+C_0$

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Function Plot

Plotting: $2\ln\left(x-2\right)+3\ln\left(x+2\right)+C_0$

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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 of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

Used Formulas

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