How do you integrate #int x^4/(x^4-1)# using partial fractions?
The answer is
Since the denominator is the same as the numerator, you need to do long division first:
Then, we started to do partial fraction.
Since the denominator is not a linear function, we need to check it if it is reducible. Therefore, the denominator is reduced to:
These factors are also not linear function. Therefore, we check again whether these funtion can be reduce and we find out:
So, overall the denominator is:
Then, we do partial fraction:
compare the coefficient of
compare the constant number on both side
use formula :
Sometimes we can obtain Partial fraction with simple adjustment methods, without using A, B, C..etc.The advantage of this method is : no need to solve for A,B ,C...etc
Integrating each term we get