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Question
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Solution
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + 4 log |x – 1| + c
Explanation:
`int (x^2 + x - 6)/((x - 2)(x - 1)) dx = int((x + 3)(x - 2))/((x - 2)(x - 1))`dx
= `int (x + 3)/(x - 1)`dx
= `int ((x - 1) + 4)/(x - 1)`dx
= `int ((1 + 4)/(x - 1))`dx
= x + 4 log |x – 1| + c
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