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d/(dx)[atan^(-1)x+blog((x-1)/(x+1))]=1/(...

`d/(dx)[atan^(-1)x+blog((x-1)/(x+1))]=1/(x^4-1)=>a-2b=`

A

1

B

`-1`

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Given `(d)/(dx)[ a tan^(-1)x+b log((x-1)/(x+1))]=(1)/(x^(4)+1)`
On intergrating both sides, we get
`a tan^(-1)x+b log((x-1)/(x+1))=(1)/(2)int[(1)/(x^(2)-1)-(1)/(x^(2)+1)]dx`
`rArr" " a tan^(-1)x+b log((x-1)/(x+1))=(1)/(4)log((x-1)/(x+1))-(1)/(2)tan^(-1)x`
`rArr" "A=-(1)/(2), b=(1)/(4)`
`therefore" "a-2b=-(1)/(2)-2((1)/(4))=-1`
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