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- Improper integral
- Double Integral
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- Derivative Step by Step
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-
How to use it?
- Integral of d{x}:
-
Integral of x^(-1/2)
-
Integral of sin²xcos²x
-
Integral of x*2^(-x)
-
Integral of y^(-2/3)
- Graphing y =:
- x/(x²-1)
- Derivative of:
-
x/(x²-1)
-
Identical expressions
- x/(x²- one)
- x divide by (x² minus 1)
- x divide by (x² minus one)
- x/x²-1
- x divide by (x²-1)
- x/(x²-1)dx
-
Similar expressions
- x/(x²+1)
Integral of x/(x²-1) dx
The solution
You have entered
[src]
4 / | | x | ------ dx | 2 | x - 1 | / 0
$$\int\limits_{0}^{4} \frac{x}{x^{2} - 1}\, dx$$
Integral(x/(x^2 - 1), (x, 0, 4))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | x - 1 | /
Rewrite the integrand
/ 2*x \
|------------|
| 2 |
x \x + 0*x - 1/
------ = --------------
2 2
x - 1 or
/ | | x | ------ dx | 2 = | x - 1 | /
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 1
|
/
------------------
2 In the integral
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 1
|
/
------------------
2 do replacement
2 u = x
then
the integral =
/
|
| 1
| ------ du
| -1 + u
|
/ log(-1 + u)
------------ = -----------
2 2 do backward replacement
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x - 1
| / 2\
/ log\-1 + x /
------------------ = ------------
2 2 Solution is:
/ 2\
log\-1 + x /
C + ------------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\-1 + x / | ------ dx = C + ------------ | 2 2 | x - 1 | /
$$\int \frac{x}{x^{2} - 1}\, dx = C + \frac{\log{\left(x^{2} - 1 \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.