What is the integral of 9-10e^{-0.3x} ?

The integral of 9-10e^{-0.3x} is 9x+33.33333…e^{-0.3x}+C

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integral of 9-10e^{-0.3x}

\int 9 - 10 e^{- 0.3 x} d x

9 x + 33.33333 \dots e^{- 0.3 x} + C

Solution steps

\int 9 - 10 e^{- 0.3 x} 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 9 d x - \int 10 e^{- 0.3 x} d x

\int 9 d x = 9 x

\int 10 e^{- 0.3 x} d x = - 33.33333 \dots e^{- 0.3 x}

= 9 x - (- 33.33333 \dots e^{- 0.3 x})

Simplify

= 9 x + 33.33333 \dots e^{- 0.3 x}

Add a constant to the solution

= 9 x + 33.33333 \dots e^{- 0.3 x} + C

What is the integral of 9-10e^{-0.3x} ?
The integral of 9-10e^{-0.3x} is 9x+33.33333…e^{-0.3x}+C