If the integral `I=inte^(sinx)(cosx.x^(2)+2x)dx=e^(f(x))g(x)+C` (where, C is the constant of integration), then the number of solution(s) of `f(x)=g(x)` is/are

The integral I=int[xe^(x^(2))(sinx^(2)+cosx^(2))]dx =f(x)+c , (where, c is the constant of integration). Then, f(x) can be

The integral I=int[xe^(x^(2))(sinx^(2)+cosx^(2))]dx =f(x)+c , (where, c is the constant of integration). Then, f(x) can be

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

The integral I=int(e^((e^sinx+sinx)))cos x dx simpllifies to (where, c is the constant of integration)

The integral I=int(e^((e^sinx+sinx)))cos x dx simpllifies to (where, c is the constant of integration)

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to

The integral I=inte^(x)((1+sinx)/(1+cosx))dx=e^(x)f(x)+C (where, C is the constant of integration). Then, the range of y=f(x) (for all x in the domain of f(x) ) is

The integral I=inte^(x)((1+sinx)/(1+cosx))dx=e^(x)f(x)+C (where, C is the constant of integration). Then, the range of y=f(x) (for all x in the domain of f(x) ) 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