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int(8)^(15)(dx)/((x-3)sqrt(x+1)) is equa...

`int_(8)^(15)(dx)/((x-3)sqrt(x+1))` is equal to

A

`(1)/(2)"log"(5)/(3)`

B

`(1)/(3)"log"(5)/(3)`

C

`(1)/(5)"log"(3)/(5)`

D

`(1)/(2)"log"(3)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
Put x+1=`t^(2)`
`impliesdx=2tdt`
At x=8,t=3
and x=15,t=4
`thereforel=int_(3)^(4)(2tdt)/((t^(2)-1-3)t)`
`=int_(3)^(4)(2dt)/((t^(2)-4))=2*(1)/(4)["log"(t-2)/(t+2)]_(0)^(4)`
`=(1)/(2)["log"(1)/(3)-"log"(1)/(5)]`
`=(1)/(2)"log"(5)/(3)`
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