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