Asked by Anonymous
integral (x^3)/(x^2-2x+1) from -1 to 0
How do you get this integral? I was doing partial fractions and got A/(x-1)+B/(x-1), A+B=x^3, but that should equal 0 so where do I go from there?
How do you get this integral? I was doing partial fractions and got A/(x-1)+B/(x-1), A+B=x^3, but that should equal 0 so where do I go from there?
Answers
Answered by
Steve
Since (x-1) is a repeated factor, you need A/(x-1) + (Bx+C)/(x-1)^2
First, a little long division will yield
x+2 + (3x-2)/(x-1)^2
That further breaks down into
x + 2 + 3/(x-1) + 1/(x-1)^2
Now it's clear sailing.
First, a little long division will yield
x+2 + (3x-2)/(x-1)^2
That further breaks down into
x + 2 + 3/(x-1) + 1/(x-1)^2
Now it's clear sailing.
Answered by
Anonymous
For some reason I had completely overlooked the Bx+C and long division part. Thanks though!