What is the integral of-4^x ?

The integral of-4^x is -(2^{2x-1})/(ln(2))+C

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integral of-4^x

\int - 4^{x} d x

- \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

Solution steps

\int - 4^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int 4^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - \frac{4 ^{x}}{ln ( 4 )}

Simplify

- \frac{4 ^{x}}{ln ( 4 )} : - \frac{2 ^{2 x - 1}}{ln ( 2 )}

= - \frac{2 ^{2 x - 1}}{ln ( 2 )}

Add a constant to the solution

= - \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

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