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

The integral of ((2^x))/(ln(2)) is (2^x)/(ln^2(2))+C

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

\int \frac{( 2 ^{x} )}{ln ( 2 )} d x

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

Solution steps

\int \frac{2 ^{x}}{ln ( 2 )} d x

Take the constant out:

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

= \frac{1}{ln ( 2 )} \cdot \int 2^{x} d x

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

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

Simplify

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

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

Add a constant to the solution

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

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