1 / | | 4 | / 2 \ | (8*x - 12)*\4*x - 12*x/ dx | / 0
Integral((8*x - 12)*(4*x^2 - 12*x)^4, (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:
Rewrite the integrand:
Integrate term-by-term:
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:
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:
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:
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:
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:
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:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 5 | 4 / 2 \ | / 2 \ \4*x - 12*x/ | (8*x - 12)*\4*x - 12*x/ dx = C + -------------- | 5 /
Use the examples entering the upper and lower limits of integration.