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# Find the integral $\int\frac{x^4+81}{x\left(x^2+9\right)^2}dx$

## Step-by-step Solution

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### Videos

$\ln\left(x\right)+\frac{9}{x^2+9}+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\frac{x^4+81}{x\left(x^2+9\right)^2}dx$

Specify the solving method

1

Rewrite the fraction $\frac{x^4+81}{x\left(x^2+9\right)^2}$ in $3$ simpler fractions using partial fraction decomposition

$\frac{x^4+81}{x\left(x^2+9\right)^2}=\frac{A}{x}+\frac{Bx+C}{\left(x^2+9\right)^2}+\frac{Dx+F}{x^2+9}$

Learn how to solve integrals of rational functions problems step by step online.

$\frac{x^4+81}{x\left(x^2+9\right)^2}=\frac{A}{x}+\frac{Bx+C}{\left(x^2+9\right)^2}+\frac{Dx+F}{x^2+9}$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^4+81)/(x(x^2+9)^2))dx. Rewrite the fraction \frac{x^4+81}{x\left(x^2+9\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D, F. The first step is to multiply both sides of the equation from the previous step by x\left(x^2+9\right)^2. Multiplying polynomials. Simplifying.

$\ln\left(x\right)+\frac{9}{x^2+9}+C_0$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
5
6
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

$\int\frac{x^4+81}{x\left(x^2+9\right)^2}dx$

### Main topic:

Integrals of Rational Functions

~ 0.21 s