1 / | | 1 | 1*-*(1 + log(x)) dx | x | / 0
Integral(1*(1 + log(x))/x, (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
Now substitute back in:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
The integral of is .
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 2 | 1 (-1 - log(x)) | 1*-*(1 + log(x)) dx = C + -------------- | x 2 | /
Use the examples entering the upper and lower limits of integration.