Question

13 mark for review
$int (e^{x}+e)dx =$
a $e^{x}+c$
b $2e^{x}+c$
c $e^{x}+e+c$
d $e^{x+1}+ex+c$
e $e^{x}+ex+c$

Explanation:

Step1: Split the integral

$$\int (e^x + e)dx = \int e^x dx + \int e dx$$

Step2: Integrate each term

• For $\int e^x dx$, the antiderivative is $e^x$.
• For $\int e dx$, since $e$ is a constant, the antiderivative is $ex$.

Add the constant of integration $C$ to the sum.
$$\int e^x dx + \int e dx = e^x + ex + C$$

Answer:

E. $e^x+ex+C$