What is the integral of 2^{x-3} ?

The integral of 2^{x-3} is (2^{x-3})/(ln(2))+C

integral of 2^{x-3}

\int 2^{x - 3} d x

\frac{2 ^{x - 3}}{ln ( 2 )} + C

Solution steps

\int 2^{x - 3} d x

Simplify

2^{x - 3} : 2^{x} \cdot 2^{- 3}

= \int 2^{x} \cdot 2^{- 3} d x

Take the constant out:

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

= 2^{- 3} \cdot \int 2^{x} d x

2^{- 3} = \frac{1}{8}

= \frac{1}{8} \cdot \int 2^{x} d x

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

= \frac{1}{8} \cdot \frac{2 ^{x}}{ln ( 2 )}

Simplify

\frac{1}{8} \cdot \frac{2 ^{x}}{ln ( 2 )} : \frac{2 ^{x - 3}}{ln ( 2 )}

= \frac{2 ^{x - 3}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{x - 3}}{ln ( 2 )} + C

\int \frac{1}{x} \cdot e^{x} d x

\int \frac{1}{2} x + 4 d x

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

\int \frac{2 x ^{2} + x - 1}{1 + x ^{2}} d x

\int x^{2} \frac{2}{1 + x ^{3}} d x

What is the integral of 2^{x-3} ?
The integral of 2^{x-3} is (2^{x-3})/(ln(2))+C