What is the integral of 6*2^{-x}-3 ?

The integral of 6*2^{-x}-3 is -(3*2^{-x+1})/(ln(2))-3x+C

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integral of 6*2^{-x}-3

\int 6 \cdot 2^{- x} - 3 d x

- \frac{3 \cdot 2 ^{- x + 1}}{ln ( 2 )} - 3 x + C

Solution steps

\int 6 \cdot 2^{- x} - 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 \cdot 2^{- x} d x - \int 3 d x

\int 6 \cdot 2^{- x} d x = - \frac{3 \cdot 2 ^{- x + 1}}{ln ( 2 )}

\int 3 d x = 3 x

= - \frac{3 \cdot 2 ^{- x + 1}}{ln ( 2 )} - 3 x

Add a constant to the solution

= - \frac{3 \cdot 2 ^{- x + 1}}{ln ( 2 )} - 3 x + C

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What is the integral of 6*2^{-x}-3 ?
The integral of 6*2^{-x}-3 is -(3*2^{-x+1})/(ln(2))-3x+C