3 / | | x*log(x - 1) dx | / 2
Integral(x*log(x - 1*1), (x, 2, 3))
Use integration by parts:
Let and let .
Then .
To find :
The integral of is when :
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Integrate term-by-term:
The integral of is when :
The integral of a constant is the constant times the variable of integration:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
The result is:
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 2 2 | x log(-1 + x) x x *log(x - 1) | x*log(x - 1) dx = C - - - ----------- - -- + ------------- | 2 2 4 2 /
-7/4 + 4*log(2)
=
-7/4 + 4*log(2)
Use the examples entering the upper and lower limits of integration.