`f(x)=tan^(-1){log(e/x^2)/log(ex^2)}+tan^(-1)((3+2logx)/(1-6logx))` then find `(d^ny)/(dx^n)`

int(1)/(x(logx)log(logx))dx=

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

Column I: Function, Column II: Value of x for which both the functions in any option of column I are identical f(x)=tan^(-1)((2x)/(1-x^2)),g(x)=2tan^(-1)x , p. x in {-1,1} f(x)=(log)_(x2)25a n dg(x)=(log)_x5 , q. x in (-1,1) f(x)=sec^(-1)x+cos e c^(-1)x ,g(x)=sin^(-1)x+cos^(-1)x , r. x in (0,1)

Evaluate int(logx)/((1+logx)^(2))dx .

Evaluate int_(-1)^(1) log ((2-x)/( 2+x)) dx

Evaluate int_(1)^(e)(1)/(x(1+logx))dx

If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

If f(x)=(log)_e((x^2+e)/(x^2+1)) , then the range of f(x)