Answer
$-\displaystyle \frac{4^{-2x}}{2\ln 4}+C$
Work Step by Step
$\displaystyle \int 4^{-2x}dx$=
Shortcut formula:
$\displaystyle \qquad\int c^{ax+b}dx=\frac{\mathrm{l}}{a\ln c}\cdot c^{ax+b}+C$
Apply with $ \left[\begin{array}{l}
c=4\\
a=-2\\
b=0
\end{array}\right]$
$=\displaystyle \frac{1}{-2\ln 4}\cdot 4^{-2x}$
= $-\displaystyle \frac{4^{-2x}}{2\ln 4}+C$
