Match the following lists:

Answer

` a to p, q, r; b to p, q, r; c to p, q, r, s; d to p, q, r, s`

Explanation

a. `int(x^(2)-x+1)/(x^(3)-4x^(2)+4x)dx=int[(A)/(x)+(B)/(x-2)+(C)/((x-2)^(2))]dx`
b. `int(x^(2)-1)/(x(x-2)^(3))dx=int[(A)/(x)+(B)/(x-2)+(C)/((x-2)^(2))+(D)/((x-2)^(3))]dx`
c. `int(x^(3)+1)/(x(x-2)^(2))dx=int[((x^(3)+1)/(x(x-2)^(2))-1)+1]dx`
`=int[((x^(3)+1-x(x-2)^(2))/(x(x-2)^(2)))+1]dx`
`=int[((A)/(x)+(B)/(x-2)+(C)/((x-2)^(2)))+1]dx`
d. `int(x^(5)+1)/(x(x-2)^(3))dx=int[x+k+(g(x))/(x(x-2)^(3))]dx, `
where k is constant ` ne 0 ` and `g(x)` is a polynomial of degree less than 4.