What is the integral of ((4^x)/(e^x)) ?

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

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integral of ((4^x)/(e^x))

\int (\frac{4 ^{x}}{e ^{x}}) d x

\frac{4 ^{x}}{( 2 ln ( 2 ) - 1 ) e ^{x}} + C

Solution steps

\int \frac{4 ^{x}}{e ^{x}} d x

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= \int (\frac{4}{e})^{x} d x

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

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

Simplify

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

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

Add a constant to the solution

= \frac{4 ^{x}}{( 2 ln ( 2 ) - 1 ) e ^{x}} + C

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What is the integral of ((4^x)/(e^x)) ?
The integral of ((4^x)/(e^x)) is (4^x)/((2ln(2)-1)e^x)+C