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