1 / | | 4 | log (x - 3) | ----------- dx | x - 3 | / 0
Integral(log(x - 3)^4/(x - 3), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
Let .
Then let and substitute :
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:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 4 5 | log (x - 3) log (x - 3) | ----------- dx = C + ----------- | x - 3 5 | /
5 5 (pi*I + log(3)) (pi*I + log(2)) - ---------------- + ---------------- 5 5
=
5 5 (pi*I + log(3)) (pi*I + log(2)) - ---------------- + ---------------- 5 5
-(pi*i + log(3))^5/5 + (pi*i + log(2))^5/5
(-20.1841274313655 + 41.2006194702006j)
(-20.1841274313655 + 41.2006194702006j)
Use the examples entering the upper and lower limits of integration.