Let `int(dx)/((x^(2)+1)(x^(2)+9))=f(x)+C,` (where `C` is constant of integration) such that `f(0)=` 0.If `f(sqrt(3))=(5)/(36)k,` then `k` is

Let int(dx)/(sqrt(x^(2)+1)-x)=f(x)+C such that f(0)=0 and C is the constant of integration, then the value of f(1) is

If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C , where C is a constant of integration, then f(x) is equal to

If I=int(dx)/(x^(2)sqrt(1+x^(2)))=(f(x))/(x)+C, (AA x gt0) (where, C is the constant of integration) and f(1)=-sqrt2 , then the value of |f(sqrt3)| 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

Let I=int(dx)/((cosx-sinx)^(2))=(1)/(f(x))+C (where, C is the constant of integration). If f((pi)/(3))=1-sqrt3 , then the number of solution(s) of f(x)=2020 in x in ((pi)/(2), pi) is/are

If I=int(1+x^(4))/((1-x^(4))^((3)/(2)))dx=(1)/(sqrt(f(x)))+C (where, C is the constant of integration) and f(2)=(-15)/(4) , then the value of 2f((1)/(sqrt2)) is

Let I=int(dx)/(1+3sin^(2)x)=(1)/(2)tan^(-1)(2f(x))+C (where, C is the constant of integration). If f((pi)/(4))=1 , then the fundamental period of y=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

The value of int(1)/((2x-1)sqrt(x^(2)-x))dx is equal to (where c is the constant of integration)

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