`int \ x/(x^4-1)dx`

Options

A. `1/(6).log|(x^(2)+1)/(x^(2)-1)|+C`
B. `1/(6).log|(x^(2)-1)/(x^(2)+1)|+C`
C. `log|(x^(2)-1)/(x^(2)+1)|+C`
D. `1/(4).log|(x^(2)-1)/(x^(2)+1)|+C`

Answer

D

Explanation

Let `I = int(x)/(x^(4)-1)dx`
Put `x^(2)=trArr 2xdx = dt rArr xdx = 1/2 dt`
`:. I = 1/2int(dt)/(t^(2)-1)= 1/(2).(1)/(2)log|(t-1)/(t+1)|+C , [:' int(dx)/(x^(2)-a^(2))= 1/2a log |(x-a)/(x+a)|+C]`
`= log[log|x^(2)-1|-log|x^(2)+1|]+C`
=`1/(4).log|(x^(2)-1)/(x^(2)+1)|+C`