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