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Find the integral $\int\frac{2}{x\left(x+3\right)}dx$

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Solution

Formulas

Videos

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$

Integrals of Rational Functions

$\int\frac{n}{x+b}dx=nsign\left(x\right)\ln\left(x+b\right)+C$

Function Plot

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

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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
D□x
∫
∫◻
|◻|
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:

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$\int\frac{1}{\left(x^4+1\right)}dx$

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

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