E / | | / ___ \ | |\/ 1 2 | | |----- - log (x)| dx | \ x / | / 1
Integral(sqrt(1)/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:
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | | / ___ \ | |\/ 1 2 | 2 | |----- - log (x)| dx = C - 2*x - x*log (x) + 2*x*log(x) + log(x) | \ x / | /
Use the examples entering the upper and lower limits of integration.