How do you integrate #(x^3 - 5x + 2) / (x^2 - 8x + 15)# using partial fractions?
The answer is
Perform a polynomial division first
Perform the decomposition into partial fractions
The denominators are the same, compare the numerators
Observe that the integrand is an improper rational function,
i.e., the degree of the Nr. poly. is more than that of the Dr.
So, first of all we will have to make it proper. Usually, the
long division is performed, but, let us proceed as under :
N.B. : It will be an interesting exercise for the
Questioner to verify that this Answer is the
same as the one submitted by Respected Narad T.!