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int(0)^(5) 1/((x-1)(x-2))dx is equal to...

` int_(0)^(5) 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 `l = 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+2log 2-log 3`
`=-3 log 3 + 5 log 2 = -log 2 = - log 27 + log 32`
`= log (32)/(27)`
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