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Integrate $\int\left(x+\frac{3}{x^2-9}\right)dx$

Step-by-step Solution

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Final Answer

$\frac{1}{2}x^2+\frac{1}{2}\ln\left(x-3\right)-\frac{1}{2}\ln\left(x+3\right)+C_0$
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Step-by-step Solution

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Expand the integral $\int\left(x+\frac{3}{x^2-9}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int xdx+\int\frac{3}{x^2-9}dx$

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

$\int xdx+\int\frac{3}{x^2-9}dx$

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Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(x+3/(x^2-9))dx. Expand the integral \int\left(x+\frac{3}{x^2-9}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2. The integral \int\frac{3}{x^2-9}dx results in: -\frac{1}{2}\ln\left(x+3\right)+\frac{1}{2}\ln\left(x-3\right). Gather the results of all integrals.

Final Answer

$\frac{1}{2}x^2+\frac{1}{2}\ln\left(x-3\right)-\frac{1}{2}\ln\left(x+3\right)+C_0$

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Function Plot

Plotting: $\frac{1}{2}x^2+\frac{1}{2}\ln\left(x-3\right)-\frac{1}{2}\ln\left(x+3\right)+C_0$

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1
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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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