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int(5)^(10) ""(1)/((x-1)(x-2))dx is equa...

`int_(5)^(10) ""(1)/((x-1)(x-2))dx` is equal to

A

`log""(27)/(32)`

B

`log""(32)/(27)`

C

`log""(8)/(9)`

D

`log""(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `I=int_(5)^(10)""(1)/((x-1)(x-2)) dx `
`=int_(5)^(10)[(-1)/(x-1)+(1)/(x-2)] dx `
`=[-log (x-1)+ log (x-2)]_(5)^(10)`
`=- log 9 +log 8 + log 4- log 3`
`= -2 log 3 + 3 log 2 + 2 log 2 - log 3 `
` =- 3 log 3 + 5 log 2 `
`=- log 27 + log 32`
`= log""(32)/(27)`
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