Question

The value of `int(x^(2)+1)/(x^(4)-x^(2)+1)dx` is
A. `tan^(-1)(2x^(2)-1)+C`
B. `tan^(-1)(x^(2)+1)/(x)+C`
C. `sin^(-1)(x-(1)/(x))+C`
D. `tan^(-1)((x^(2)-1)/(x))+C`

Answer 1

Correct Answer - D
Let `l=int(x^(2)+1)/(x^(4)-x^(2)+1)dx=int(1+(1)/(x^(2)))/(x^(2)+(1)/(x^(2))-1)dx`
`l=((1+(1)/(x^(2))))/((x-(1)/(x))^(2)+1)dx`
`"Put "x-(1)/(x)=t rArr (1+(1)/(x^(2)))dx=dt`
`therefore" "l=int(dt)/(t^(2)+1)tan^(-1)t+C = tan^(-1)(x-(1)/(x))+C`
`=tan^(-1)((x^(2)-1)/(x))+C`