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Evaluate: int((x-1)(x-2)(x-3))/((x-4)(x-...

Evaluate: `int((x-1)(x-2)(x-3))/((x-4)(x-5)(x-6))dx`

Text Solution

Verified by Experts

`int(overset(underset(darr)("Improper fraction"))((x-1))(x-2)(x-3))/((x-4)(x-5)(x-6))dx`
`int[1+((x-1)(x-2)overset(underset(darr)("Proper fraction"))((x-3))-(x-4)(x-5)(x-6))/((x-4)(x-5)(x-6))]dx`
` " " `(Adding and subtracting 1)
`=int[1+(3xx2xx1)/((x-4)(-1)(-2))+(4xx3xx2)/(1(x-5)(-1))+(5xx4xx3)/((2)(1)(x-6))]dx`
`=1+3log|x-4|-24 log|x-5|+30 log|x-6|+C`
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