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(sqrt3)= 5/36 k`, then k is.

If int e^(x)((3-x^(2))/(1-2x+x^(2)))dx=e^(x)f(x)+c , (where c is constant of integration) then f(x) is equal to

If intxe^(2x)dx is equal to e^(2x)f(x)+c , where c is constant of integration, then f(x) is

If f (x) = k, where k is constant then int k dx =0

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

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(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 intf(x)dx=3[f(x)]^(2)+c (where c is the constant of integration) and f(1)=(1)/(6) , then f(6pi) is equal to

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 intsin(2x)ln(cosx)dx=f(x)cos^(2)x+C , (where, C is the constant of integration) and f(0)=(1)/(2) , If f((pi)/(3)) is equal to (1)/(a)+lnb, then the value of a+b 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