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-
How to use it?
- Integral of d{x}:
-
Integral of 1/sqrt(1+u^2)
-
Integral of x*sin2x
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Integral of x*dx/(x^2-1)
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Integral of (x^2+x)dx
- Graphing y =:
-
x/(x^2-9)
- Derivative of:
-
x/(x^2-9)
- Canonical form:
- x/(x^2-9)
-
Identical expressions
- x/(x^ two - nine)
- x divide by (x squared minus 9)
- x divide by (x to the power of two minus nine)
- x/(x2-9)
- x/x2-9
- x/(x²-9)
- x/(x to the power of 2-9)
- x/x^2-9
- x divide by (x^2-9)
- x/(x^2-9)dx
-
Similar expressions
- x/(x^2+9)
Integral of x/(x^2-9) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | x - 9 | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{2} - 9}\, dx$$
Integral(x/(x^2 - 9), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | x - 9 | /
Rewrite the integrand
/ 2*x \
|------------|
| 2 |
x \x + 0*x - 9/
------ = --------------
2 2
x - 9 or
/ | | x | ------ dx | 2 = | x - 9 | /
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 9
|
/
------------------
2 In the integral
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 9
|
/
------------------
2 do replacement
2 u = x
then
the integral =
/
|
| 1
| ------ du
| -9 + u
|
/ log(-9 + u)
------------ = -----------
2 2 do backward replacement
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 9
| / 2\
/ log\-9 + x /
------------------ = ------------
2 2 Solution is:
/ 2\
log\-9 + x /
C + ------------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\-9 + x / | ------ dx = C + ------------ | 2 2 | x - 9 | /
$$\int \frac{x}{x^{2} - 9}\, dx = C + \frac{\log{\left(x^{2} - 9 \right)}}{2}$$
The graph
The answer
[src]
log(8) log(9) ------ - ------ 2 2
$$- \frac{\log{\left(9 \right)}}{2} + \frac{\log{\left(8 \right)}}{2}$$
=
=
log(8) log(9) ------ - ------ 2 2
$$- \frac{\log{\left(9 \right)}}{2} + \frac{\log{\left(8 \right)}}{2}$$
log(8)/2 - log(9)/2
The graph
Use the examples entering the upper and lower limits of integration.