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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
-
Integral of x*cos(x/2)
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Integral of x*dx/(x^2-1)
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Integral of x^5/(x^2+1)
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Integral of x/(2*x+1)
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Identical expressions
- x*dx/(x^ two - one)
- x multiply by dx divide by (x squared minus 1)
- x multiply by dx divide by (x to the power of two minus one)
- x*dx/(x2-1)
- x*dx/x2-1
- x*dx/(x²-1)
- x*dx/(x to the power of 2-1)
- xdx/(x^2-1)
- xdx/(x2-1)
- xdx/x2-1
- xdx/x^2-1
- x*dx divide by (x^2-1)
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Similar expressions
- x*dx/(x^2+1)
Integral of x*dx/(x^2-1) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{2} - 1}\, dx$$
Integral(x/(x^2 - 1), (x, 0, 1))
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
The answer
[src]
pi*I
-oo - ----
2
$$-\infty - \frac{i \pi}{2}$$
=
=
pi*I
-oo - ----
2
$$-\infty - \frac{i \pi}{2}$$
-oo - pi*i/2
The graph
Use the examples entering the upper and lower limits of integration.