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int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=alo...

`int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=alog((x+1)/(x-1))+b"tan"^(-1)(x)/(2)` , then (a,b) is

A

`(1, -1)`

B

`(-1, 1)`

C

`((1)/(2),-(1)/(2))`

D

`((1)/(2),(1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=int(dx)/(x^(2)-1)+int(dx)/(x^(2)+4)`
`" "[because (2x^(2)+3)/((x^(2)-1)(x^(2)+4))=(1)/(x^(2)-1)+(1)/(x^(2)+4)]`
`rArr" "l=(1)/(2)log((x-1)/(x+1))+(1)/(2)tan^(-1).(x)/(2)+C`
`But" "l=a log((x-1)/(x+1))+b tan^(-1)((x)/(2))+C`
`therefore" "a=(1)/(2), b=(1)/(2)`
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