Question

find the antiderivative for each function when c equals 0.
a. ( f(x)=e^{7x} ) b. ( g(x)=e^{-8x} ) c. ( h(x)=e^{\frac{x}{9}} )
a. the antiderivative of ( e^{7x} ) is ( \frac{1}{7}e^{7x} )
b. the antiderivative of ( e^{-8x} ) is

Explanation:

Step1: Recall the antiderivative formula

The antiderivative of \(e^{ax}\) is \(\frac{1}{a}e^{ax}+C\). Here \(a=-8\) and \(C = 0\).

Step2: Substitute \(a=-8\) into the formula

When \(a=-8\), the antiderivative of \(e^{-8x}\) is \(\frac{1}{-8}e^{-8x}\).

Answer:

\(-\frac{1}{8}e^{-8x}\)