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