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- Improper integral
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-
How to use it?
- Integral of d{x}:
-
Integral of x^(4/5)
-
Integral of 1/(x^2-2)
-
Integral of sin³xcosx
-
Integral of dx/(x^2+4x+5)
- Graphing y =:
- x/(x-x^2)
- Limit of the function:
-
x/(x-x^2)
-
Identical expressions
- x/(x-x^ two)
- x divide by (x minus x squared )
- x divide by (x minus x to the power of two)
- x/(x-x2)
- x/x-x2
- x/(x-x²)
- x/(x-x to the power of 2)
- x/x-x^2
- x divide by (x-x^2)
- x/(x-x^2)dx
-
Similar expressions
- x/(x+x^2)
Integral of x/(x-x^2) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | x - x | / 0
$$\int\limits_{0}^{1} \frac{x}{- x^{2} + x}\, dx$$
Integral(x/(x - x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | x - x | /
Rewrite the integrand
-2*x + 1
- --------
2
x - x + x
------ = -----------
2 2
x - x or
/ | | x | ------ dx | 2 = | x - x | /
/
|
| -2*x + 1
- | -------- dx
| 2
| - x + x
|
/
----------------
2 In the integral
/
|
| -2*x + 1
- | -------- dx
| 2
| - x + x
|
/
----------------
2 do replacement
2 u = x - x
then
the integral =
/
|
| 1
- | - du
| u
|
/ -log(u)
--------- = --------
2 2 do backward replacement
/
|
| -2*x + 1
- | -------- dx
| 2
| - x + x
| / 2 \
/ -log\x - x/
---------------- = -------------
2 2 Solution is:
C - log(-1 + x)
The answer (Indefinite)
[src]
/ | / 2\ | x log(2*x) log(-2 + 2*x) log\x - x / | ------ dx = C + -------- - ------------- - ----------- | 2 2 2 2 | x - x | /
$$\int \frac{x}{- x^{2} + x}\, dx = C + \frac{\log{\left(2 x \right)}}{2} - \frac{\log{\left(2 x - 2 \right)}}{2} - \frac{\log{\left(- x^{2} + x \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.