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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of -x+4
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Integral of cos^2(x)dx
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Integral of e^x*dx/(1+e^(2*x))
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Integral of dx/x+√x
- Graphing y =:
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(x)/(x^2-4)
- Derivative of:
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(x)/(x^2-4)
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Identical expressions
- (x)/(x^ two - four)
- (x) divide by (x squared minus 4)
- (x) divide by (x to the power of two minus four)
- (x)/(x2-4)
- x/x2-4
- (x)/(x²-4)
- (x)/(x to the power of 2-4)
- x/x^2-4
- (x) divide by (x^2-4)
- (x)/(x^2-4)dx
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Similar expressions
- dx/(x^2-4*x+3)
- (x)/(x^2+4)
- x/(x^2-4)^(1/4)
- dx/x^2-4*x+3
- x/(x^2-4)^(1/3)
Integral of (x)/(x^2-4) dx
The solution
You have entered
[src]
-3 / | | x | ------ dx | 2 | x - 4 | / -oo
$$\int\limits_{-\infty}^{-3} \frac{x}{x^{2} - 4}\, dx$$
Integral(x/(x^2 - 4), (x, -oo, -3))
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 graph
Use the examples entering the upper and lower limits of integration.