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

## Step-by-step Solution

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###  Videos

$-\ln\left(\frac{3}{\sqrt{x^2+9}}\right)+C_0$
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##  Step-by-step Solution 

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We can solve the integral $\int\frac{x}{x^2+9}dx$ by applying integration method of trigonometric substitution using the substitution

$x=3\tan\left(\theta \right)$

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

$x=3\tan\left(\theta \right)$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(x/(x^2+9))dx. We can solve the integral \int\frac{x}{x^2+9}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Simplifying.

$-\ln\left(\frac{3}{\sqrt{x^2+9}}\right)+C_0$

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

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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

### Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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