Fill `int 1/(x^2-a^2)dx=....log((x-a)/(x+a))`

int 1/(x(log x)^2)dx

int ln(x^(2)+x+2)dx

1) int x log x^(2)dx

int x^(2)(log x)^(2)dx

The value of ({int_(-1//2)^(1//2) cos2x.log((1+x)/(1-x))dx})/({int_(0)^(1//2)cos2x.log((1+x)/(1-x))dx}) is

int(1)/(x(log x)^(2))dx

int(x log(x+1)^(2)dx)

int(1)/(x(2+log x^(2)))dx

int (1)/(x(1+log x)^(2))dx

If int x log(1+(1)/(x))dx=f(x)log(x+1)+g(x)x^(2)+dx+C, then