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Find the integral $\int\frac{5x^3-4x}{\left(9x^2+5\right)\left(3x+2\right)\left(3x-2\right)}dx$

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Solution

Formulas

Videos

Algebra 2 - Learning to solve rational equations in math class ((x+3)/(x‐2)) + (5/(x^2‐4)) = 1

https://www.youtube.com/watch?v=y8p0Tpn3BcI

Algebra 2 - How to write a polynomial in standard form when divided by a number, (2x^4 + 4x - 5) / 4

https://www.youtube.com/watch?v=nSzTK9_lYZw

Algebra 2 - Finding all the roots of a cubic polynomial by factoring, f(x) = 5x^3 + 6x^2 + x

https://www.youtube.com/watch?v=U0KxodjH624

Algebra 2 - How to graph a quadratic using a table y = x^2 + 4x -1

https://www.youtube.com/watch?v=SQGShfsW4tk

Algebra 2 - Learn to solve a rational equation by multiplying by the LCD (15/x)+((9x-7)/(x+2))=9

https://www.youtube.com/watch?v=BMSmvkWcVTU

Algebra 2 - Learn how solve a quadratic by completing the square with fractions, x^2 + 3x + 6 = 0

https://www.youtube.com/watch?v=KWBr5zM3tXs

Function Plot

Plotting: $\frac{61}{729}\ln\left(\sqrt{9x^2+5}\right)-\frac{8}{729}\ln\left(3x+2\right)-\frac{8}{729}\ln\left(3x-2\right)+C_1$

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5
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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
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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Similar Problems Solved

Find the integral

$\int\frac{\left(3x-5\right)}{\left(x-1\right)\left(x^2-1\right)}dx$

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Find the integral

$\int \frac { 32 x - 20 } { ( x - 1 ) ( 5 x - 3 ) } d x$

Find the integral

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Find the integral

$\int\frac{x+7}{x^2+2x-3}dx$

Find the integral

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

Find the integral

$\int\frac{3x-5}{\left(x-1\right)\left(x^2-1\right)}dx$

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

See formulas (3)

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