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Find the integral $\int\frac{x^3}{5x^4-5}dx$

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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

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

https://www.youtube.com/watch?v=urYZhqwUTI0

Calculus - Derivative of inverse function given an equation, f(x) = x^3 + 7x; Find g'(8)

https://www.youtube.com/watch?v=cPvUjcS7N9w

Pre-Calculus - Graphing rational functions using 5 steps, g(x) = (-3x^2 + x + 12) / (x^2 - 4)

https://www.youtube.com/watch?v=fG2HAWBNVNE

Definite integral of rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=4WJUEXIksH0

Calculus - Learn how to take the fourth derivative of a polynomial, dy/dx = 5x^4 - 3x

https://www.youtube.com/watch?v=OjQG3EnZ-Mc

Function Plot

Plotting: $\frac{1}{20}\ln\left|1+x^2\right|+\frac{1}{20}\ln\left|x+1\right|+\frac{1}{20}\ln\left|-x+1\right|+C_0$

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7
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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

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Similar Problems Solved

Find the integral

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

Find the integral

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

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

$\int\frac{4x+12}{\left(x-2\right)\left(x^2+4x+8\right)}dx$

Find the integral

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

Find the integral

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

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

See formulas (4)

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