For the following exercises, show that F(x)F(x) are antiderivatives of f(x). F(x) = 5x3 +2x2+ 3x+1, f(x) =15x2+4x+3 For the following exercises, find the antiderivative of the function. f (x ) = +x f(x) = ex - 3x2+ sinx For the following exercises, find the antiderivative F(x)F(x) of each function f(x). f (x) = (Vx)3 For the following exercises, evaluate the integral. ( AVI + (x )dx / (x-113 -x213 )dx For the following exercises, solve the initial value problem. f' (x) = x 3, f(1) =1 f' (x) = Vx+x2, f(0) =2 f' (x) = cosx + sec2 (x), f(#) =2+1/2