How to find the function if the derivative is given? Given f'(x)=36x^5+3x^2 determine f(x).

The problem
provides the derivative of the function, hence, you need to evaluate the function using
anti-derivatives, such that:

f(x)

You need to use the linearity of integral, hence, you need to split the
integral in two simpler integrals, such that:

= 36 int x^5 dx + 3 int x^2 dx

x^3/3 + c

Reducing duplicate factors yields:

dx + int (3x^2)dx = 6x^6 + x^3 + c

Hence, evaluating the
function f(x) using anti-derivatives, yields