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# Find the integral $\int\frac{1}{x\left(x^2+x+1\right)}dx$

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sinh
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asinh
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## Basic Integrals

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

## Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

## Integrals of Rational Functions

$\int\frac{n}{a+b}dx=n\int\frac{1}{a+b}dx$

## Trigonometric Integrals

$\int\tan\left(\theta \right)dx=-\ln\left(\cos\left(\theta \right)\right)+C$

SnapXam A2

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0
a
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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: 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.