`int(sin 2x+2)/(sin 2x+cos2x+1) dx=f(x)+C,` where `C` is integration constant and `f(0)=0,` then

int(sin2x+2)/(sin2x+cos2x+1)dx=f(x)+C where C is integration constant and f(0)=0, then

If I=int(dx)/(root(3)(x^((5)/(2))(1+x)^((7)/(2))))=kf(x)+c , where c is the integration constant and f(1)=(1)/(2^((1)/(6))) , then the value of f(2) is

If B=int(1)/(e^(x)+1)dx=-f(x)+C , where C is the constant of integration and e^(f(0))=2 , then the value of e^(f(-1)) is

If B=int(1)/(e^(x)+1)dx=-f(x)+C , where C is the constant of integration and e^(f(0))=2 , then the value of e^(f(-1)) is

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

If int (cos x-sin x + 1-x)/(e^(x)+sin x+x)dx=ln{f(x)}+g(x)+C , where C is the constant of integrating and f(x) is positive, then (f(x)+g(x))/(e^(x)+sin x) is equal to .......... .

If inte^(sinx)[(xcos^3x-sinx)/(cos^2x)]dx=e^(sinx)*f(x)+c , where c is constant of integration, then f(x)=

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