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- Improper integral
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-
How to use it?
- Integral of d{x}:
-
Integral of 1/(2+x^2)
- Integral of x/(x^3-3x+2)
-
Integral of -x+4
-
Integral of (x-2)^2dx
- Graphing y =:
- x/(x²-4)
-
Identical expressions
- x/(x²- four)
- x divide by (x² minus 4)
- x divide by (x² minus four)
- x/x²-4
- x divide by (x²-4)
- x/(x²-4)dx
-
Similar expressions
- x/(x²+4)
Integral of x/(x²-4) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | x - 4 | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{2} - 4}\, dx$$
Integral(x/(x^2 - 4), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | x - 4 | /
Rewrite the integrand
/ 2*x \
|------------|
| 2 |
x \x + 0*x - 4/
------ = --------------
2 2
x - 4 or
/ | | x | ------ dx | 2 = | x - 4 | /
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 4
|
/
------------------
2 In the integral
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 4
|
/
------------------
2 do replacement
2 u = x
then
the integral =
/
|
| 1
| ------ du
| -4 + u
|
/ log(-4 + u)
------------ = -----------
2 2 do backward replacement
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 4
| / 2\
/ log\-4 + x /
------------------ = ------------
2 2 Solution is:
/ 2\
log\-4 + x /
C + ------------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\-4 + x / | ------ dx = C + ------------ | 2 2 | x - 4 | /
$$\int \frac{x}{x^{2} - 4}\, dx = C + \frac{\log{\left(x^{2} - 4 \right)}}{2}$$
The graph
The answer
[src]
log(3) log(4) ------ - ------ 2 2
$$- \frac{\log{\left(4 \right)}}{2} + \frac{\log{\left(3 \right)}}{2}$$
=
=
log(3) log(4) ------ - ------ 2 2
$$- \frac{\log{\left(4 \right)}}{2} + \frac{\log{\left(3 \right)}}{2}$$
log(3)/2 - log(4)/2
The graph
Use the examples entering the upper and lower limits of integration.