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Find the integral $\int\frac{x^2+1}{x^3-6x^2+12x-8}dx$

Used Formulas

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Solution

Formulas

Videos

Special Products

· Perfect Square Trinomial
$a^2+2ab+b^2=(a+b)^2$
· Perfect Square Trinomial
$ a^2-2ab+b^2= (a-b)^2$

Integration Techniques

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

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Constant factor Rule
$\int cxdx=c\int xdx$
· Power Rule of Integration
$\int x^ndx=\frac{x^{\left(n+1\right)}}{n+1}+C$

Function Plot

Plotting: $\frac{-2}{\left(x-2\right)^{2}}+\frac{-4}{x-2}+\ln\left(x-2\right)+\frac{1}{-2\left(x-2\right)^{2}}+C_0$

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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
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

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Main Topic: Integrals of Rational Functions

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

Used Formulas

See formulas (5)

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