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Fill in the Blank.
`int ("x"^2 + "x" - 6)/(("x - 2")("x - 1")) "dx" = "x"` + ______ + c
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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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