Let `int(2x^2+2x+1)e^(x^(2))dx=f(x) +C` where C is integration constant and `f(0) =1,` then -

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

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)/((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

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 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 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

If the integral int(x^(4)+x^(2)+1)/(x^(2)-x+1)dx=f(x)+C, (where C is the constant of integration and x in R ), then the minimum value of f'(x) is

If the integral int(x^(4)+x^(2)+1)/(x^(2)x-x+1)dx=f(x)+C, (where C is the constant of integration and x in R ), then the minimum value of f'(x) is