Find an antiderivative of $e^{t}+e^{7}$ .
A) $\frac{e^{t+1}}{t+1}+e^{7} t+C$
B) $\frac{e^{t}}{t}+e^{7} t+C$
C) $e^{t}+C$
D) $e^{t}+e^{7} t+C$

Question

Quizplus · Accepted Answer

The antiderivative of $e^{t}$ is $e^{t}$ because the derivative of $e^{t}$ is $e^{t}$. The antiderivative of a constant $e^{7}$ with respect to $t$ is $e^{7}t$ because the derivative of $e^{7}t$ with respect to $t$ is $e^{7}$. The constant of integration $C$ is added to account for the indefinite integral.

Find an Antiderivative Of et+e7e^{t}+e^{7}et+e7 A) et+1t+1+e7t+C\frac{e^{t+1}}{t+1}+e^{7} t+Ct+1et+1​+e7t+C B) ett+e7t+C\frac{e^{t}}{t}+e^{7} t+Ctet​+e7t+C C) et+Ce^{t}+Cet+C

Find an Antiderivative Of $e^{t}+e^{7}$
A) $\frac{e^{t+1}}{t+1}+e^{7} t+C$ B) $\frac{e^{t}}{t}+e^{7} t+C$ C) $e^{t}+C$