What is the integral of (e^x)/(2^x) ?

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

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integral of (e^x)/(2^x)

\int \frac{e ^{x}}{2 ^{x}} d x

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

Solution steps

\int \frac{e ^{x}}{2 ^{x}} d x

Apply exponent rule:

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

= \int (\frac{e}{2})^{x} d x

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

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

Simplify

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

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

Add a constant to the solution

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

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