Question

What is the integral of e^-4x?

Answer 1

did u mean
\[\int e^{-4x}dx\]

Answer 2

in this case, you can set
\(u=-4x\).
\(du=-4dx\)
\[dx=-\frac{du}{4}\]
hence, your question become:
\[-\frac{1}{4}\int e^u du = -\frac{1}{4}e^u+C = -\frac{1}{4}e^{-4x}+C\]