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Integral of x*ln(1+x/1-x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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  /                    
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 |       /    x    \   
 |  x*log|1 + - - x| dx
 |       \    1    /   
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$$\int\limits_{0}^{1} x \log{\left(- x + \left(\frac{x}{1} + 1\right) \right)}\, dx$$
Integral(x*log(1 + x/1 - x), (x, 0, 1))
Detail solution
  1. Use integration by parts, noting that the integrand eventually repeats itself.

    1. For the integrand :

      Let and let .

      Then .

    2. Notice that the integrand has repeated itself, so move it to one side:

      Therefore,

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                           2    /    x    \
 |                           x *log|1 + - - x|
 |      /    x    \                \    1    /
 | x*log|1 + - - x| dx = C + -----------------
 |      \    1    /                  2        
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$$\int x \log{\left(- x + \left(\frac{x}{1} + 1\right) \right)}\, dx = C + \frac{x^{2} \log{\left(- x + \left(\frac{x}{1} + 1\right) \right)}}{2}$$
The graph
The answer [src]
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.