Evaluate: `int(x^3)/((x-1)(x-2))\ dx`

Answer

`(x^(2))/(3)+3x-log|x-1|+8log|x-2|+C`

Explanation

Here, the degree of numerator is greater than that of denominator.
So, we divide the numerator by denominator to obtain
`int(x^(3))/((x-1)(x-2))dx=int(x+3 +(7x-6)/((x-1)(x-2)))dx`
`=(x^(2))/(3)+3x+int((-1)/((x-1))+(8)/((x-2)))dx`
`=(x^(2))/(3)+3x-log|x-1|+8log|x-2|+C`