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# Find the integral $\int\frac{9-4x^2}{x}dx$

## Step-by-step Solution

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###  Videos

$9\ln\left(x\right)-2x^2+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{9-4x^2}{x}dx$

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Expand the fraction $\frac{9-4x^2}{x}$ into $2$ simpler fractions with common denominator $x$

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

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

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

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((9-4x^2)/x)dx. Expand the fraction \frac{9-4x^2}{x} into 2 simpler fractions with common denominator x. Simplify the resulting fractions. Expand the integral \int\left(\frac{9}{x}-4x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{9}{x}dx results in: 9\ln\left(x\right).

$9\ln\left(x\right)-2x^2+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int((9-4x^2)/x)dx using partial fractionsSolve int((9-4x^2)/x)dx using basic integralsSolve int((9-4x^2)/x)dx using u-substitutionSolve int((9-4x^2)/x)dx using integration by partsSolve int((9-4x^2)/x)dx using trigonometric substitution

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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

### Main topic:

Integrals of Rational Functions

~ 0.05 s

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