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

## Step-by-step Solution

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asin
acos
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sinh
cosh
tanh
coth
sech
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asinh
acosh
atanh
acoth
asech
acsch

###  Videos

$\frac{x^2}{\left(x+3\right)\left(x-3\right)}+C_0$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

Rewrite the expression $\frac{x}{x^2-9}$ inside the integral in factored form

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

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{x^2}{\left(x+3\right)\left(x-3\right)}+C_0$

$\frac{x^2}{\left(x+3\right)\left(x-3\right)}+C_0$

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

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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

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