Determine the integrand f(x) if F(x) = x^2+cosx+1

F(x) = x^2+cosx+1.

To find
the integrand f(x).

Since the integrand is
f(x),

F(x) = integral f(x)
dx

Threfore Integral f(x) =
F(x),

Integral f(x) dx =
x^2+cosx+1.

Differentiating both sides, we
get:

f(x) = d/dx
{x^2+cosx+1}

f(x) = d/dx (x^2) + d/dx(cosx) +d/dx
(1)

f(x) = 2x -sinx +0 , as d/dx(x^n) = nx^(n-1) ,
d/dx(cosx) = -sinx.

f(x) = 2x-sinx.