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The value of overset(5)underset(3)int (...

The value of `overset(5)underset(3)int (x^(2))/(x^(2)-4)`dx, is

A

`2- log_(e) (15/7)`

B

`2+ log_(e) (15/7)`

C

`2+4 log_(e) 3 - 4 log_(e) 7 + 4 log _(e) 5`

D

`2 - tan^(-1) (15/7)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int_(3)^(5)(x^(2))/(x^(2)-4)dx=int_(3)^(5)((x^(2)-4)/(x^(2)-4)+(4)/(x^(2)-4))dx`
`=int_(3)^(5)(1+(4)/(x^(2)-4))dx=[x+(4)/(2xx2)log_(e)((x-2)/(x+2))]_(3)^(5)`
`=[5+log_(e)((5-2)/(5+2))-3-log_(e)((3-2)/(3+2))]`
`=2+log_(e)((3)/(7))-log_(e)((1)/(5))`
`=2+log_(e)((3)/(7)xx(5)/(1))=2+log_(e)((15)/(7))`
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