1 / | | / x \ | x*log|1 + - - x| dx | \ 1 / | / 0
Integral(x*log(1 + x/1 - x), (x, 0, 1))
Use integration by parts, noting that the integrand eventually repeats itself.
For the integrand :
Let and let .
Then .
Notice that the integrand has repeated itself, so move it to one side:
Therefore,
Now simplify:
Add the constant of integration:
The answer is:
/ 2 / x \ | x *log|1 + - - x| | / x \ \ 1 / | x*log|1 + - - x| dx = C + ----------------- | \ 1 / 2 | /
Use the examples entering the upper and lower limits of integration.