`int{((logx-1)/(1+(logx)^2)}^2 dx` is equal to

Options

A. `(x)/((logx)^(2)+1)+C`
B. `(xe^(x))/(1+x^(2))+C`
C. `(x)/(x^(2)+1) +C`
D. `(log x)/((log x)^(2) +1)+C`

Answer

A

Explanation

Derivative of options should be equal to integrand i.e. `((log x-1)/(1+(logx)^(2)))^(2)`
Taking option (a)
`(d)/(dx)((x)/((logx)^(2) +1)+c)`
` = ((logx)^(2)+1-x(2logx(1)/(x)))/([(log x)^(2) +1]^(2))`
` = ((logx)^(2) +1-2logx)/([(log x)^(2)+1]^(2))`
` = [(log x-1)/(1+(log x)^(2))]^(2)`