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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of -15x^2
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Integral of x*ln((1-x)/(1+x))
- Integral of xcoskx
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Integral of xe^(1-x)
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Identical expressions
- xln((one -x)/(one +x))
- xln((1 minus x) divide by (1 plus x))
- xln((one minus x) divide by (one plus x))
- xln1-x/1+x
- xln((1-x) divide by (1+x))
- xln((1-x)/(1+x))dx
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Similar expressions
- x*ln((1-x)/(1+x))
- xln((1+x)/(1+x))
- x*(ln((1-x)/(1+x)))
- xln((1-x)/(1-x))
Integral of xln((1-x)/(1+x)) dx
The solution
You have entered
[src]
1 / | | /1 - x\ | x*log|-----| dx | \1 + x/ | / 0
$$\int\limits_{0}^{1} x \log{\left(\frac{1 - x}{x + 1} \right)}\, dx$$
Integral(x*log((1 - x)/(1 + x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ 2 / 1 x \ | x *log|----- - -----| | /1 - x\ log(1 + x) log(-1 + x) \1 + x 1 + x/ | x*log|-----| dx = C + ---------- - x - ----------- + --------------------- | \1 + x/ 2 2 2 | /
$$\int x \log{\left(\frac{1 - x}{x + 1} \right)}\, dx = C + \frac{x^{2} \log{\left(- \frac{x}{x + 1} + \frac{1}{x + 1} \right)}}{2} - x - \frac{\log{\left(x - 1 \right)}}{2} + \frac{\log{\left(x + 1 \right)}}{2}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.