If `I=int(tan^(-1)(e^(x)))/(e^(x)+e^(-x))dx=([tan^(-1)(f(x))]^(2))/(2)+C` (where C is the constant of integration), then the range of `y=f(x) AA x in R` is

If int(dx)/(x^(2)+x)=ln|f(x)|+C (where C is the constant of integration), then the range of y=f(x), AA x in R-{-1, 0} is

If int(dx)/(x^(2)+x)=ln|f(x)|+C (where C is the constant of integration), then the range of y=f(x), AA x in R-{-1, 0} is

If int(dx)/(sqrt(e^(x)-1))=2tan^(-1)(f(x))+C , (where x gt0 and C is the constant of integration ) then the range of f(x) is

If int(dx)/(sqrt(e^(x)-1))=2tan^(-1)(f(x))+C , (where x gt0 and C is the constant of integration ) then the range of f(x) is

If I=int(dx)/(x^(2)-2x+5)=(1)/(2)tan^(-1)(f(x))+C (where, C is the constant of integration) and f(2)=(1)/(2) , then the maximum value of y=f(sinx)AA x in R is

If I=int(dx)/(x^(2)-2x+5)=(1)/(2)tan^(-1)(f(x))+C (where, C is the constant of integration) and f(2)=(1)/(2) , then the maximum value of y=f(sinx)AA x in R is

If int(e^(9x)+e^(11x))/(e^(x)+e^(-x))dx=(e^(k_(1)x))/(k_(2))+c , where c denotes the constant of integration,then k_(1)+k_(2)=

If int(e^(9x)+e^(11x))/(e^(x)+e^(-x))dx=(e^(k_(1)x))/(k_(2))+c where c denotes the constant of integration,then k_(1)+k_(2) =

int((f'(x)g(x)+f(x)g'(x)))/((1+(f(x)g(x))^(2)))dx is where C is constant of integration

if int xe^(2x) dx = e^(2x).f(x)+c , where c is the constant of integration, then f(x) is