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Find the integral $\int\frac{1}{x\left(x^2-36\right)^2}dx$

Step-by-step Solution

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Final answer to the problem

$7.72\times 10^{-4}\ln\left|x\right|+\frac{x^{2}}{-2592\left(x^2-36\right)}+\frac{1.54\times 10^{-3}}{2}\ln\left|\frac{6}{\sqrt{x^2-36}}\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate using trigonometric identities
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Rewrite the fraction $\frac{1}{x\left(x^2-36\right)^2}$ in $3$ simpler fractions using partial fraction decomposition

$\frac{7.72\times 10^{-4}}{x}+\frac{\frac{1}{36}x}{\left(x^2-36\right)^2}+\frac{-7.72\times 10^{-4}x}{x^2-36}$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\frac{7.72\times 10^{-4}}{x}+\frac{\frac{1}{36}x}{\left(x^2-36\right)^2}+\frac{-7.72\times 10^{-4}x}{x^2-36}$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(1/(x(x^2-36)^2))dx. Rewrite the fraction \frac{1}{x\left(x^2-36\right)^2} in 3 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{7.72\times 10^{-4}}{x}dx results in: 7.72\times 10^{-4}\ln\left|x\right|. The integral \frac{1}{36}\int\frac{x}{\left(x^2-36\right)^2}dx results in: \frac{x^{2}}{-2592\left(x^2-36\right)}.

Final answer to the problem

$7.72\times 10^{-4}\ln\left|x\right|+\frac{x^{2}}{-2592\left(x^2-36\right)}+\frac{1.54\times 10^{-3}}{2}\ln\left|\frac{6}{\sqrt{x^2-36}}\right|+C_0$

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Function Plot

Plotting: $7.72\times 10^{-4}\ln\left|x\right|+\frac{x^{2}}{-2592\left(x^2-36\right)}+\frac{1.54\times 10^{-3}}{2}\ln\left|\frac{6}{\sqrt{x^2-36}}\right|+C_0$

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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
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

How to improve your answer:

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 (5)

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