# Find the most general form of the antiderivative of f(x)= 2x + e.

lfryerda | High School Teacher | (Level 2) Educator

Posted on

Although the integral \int(2x+e)dx looks like it may be complicated, the integrand is really just a polynomial, which means we can separate it into two different integrals, each of which is just a power rule.

\int 2xdx+\int edx

=2 1/2 x^2+ex+C   notice that e is just a number, so this is the integral of a constant

=x^2+ex+C

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

Antiderivative means the integration.

f(x) = 2x+e

intf(x)dx = int(2x+e)dx

=int2xdx+intedx

= x^2+ex+C

Therefore antiderivative f(x) = x^2+ex+C  where C is a constant.