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

Explanation:

Step 1: Recall the antiderivative formula for \(e^{ax}\)

The antiderivative of \(e^{ax}\) is \(\frac{1}{a}e^{ax}+C\). Here \(a = 7\) and \(C = 0\).

Step 2: Substitute \(a = 7\) into the formula

Substituting \(a = 7\) into \(\frac{1}{a}e^{ax}\), we get \(\frac{1}{7}e^{7x}+0\).

Answer:

\(\frac{1}{7}e^{7x}\)