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

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lfryerda's profile pic

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's profile pic

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.

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