What is the integral of 11+5e^{6-3x}-16 ?

The integral of 11+5e^{6-3x}-16 is -5x-5/3 e^{-3x+6}+C

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integral of 11+5e^{6-3x}-16

\int 11 + 5 e^{6 - 3 x} - 16 d x

- 5 x - \frac{5}{3} e^{- 3 x + 6} + C

Solution steps

\int 11 + 5 e^{6 - 3 x} - 16 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 11 d x + \int 5 e^{6 - 3 x} d x - \int 16 d x

\int 11 d x = 11 x

\int 5 e^{6 - 3 x} d x = - \frac{5}{3} e^{6 - 3 x}

\int 16 d x = 16 x

= 11 x - \frac{5}{3} e^{6 - 3 x} - 16 x

Simplify

= - 5 x - \frac{5}{3} e^{- 3 x + 6}

Add a constant to the solution

= - 5 x - \frac{5}{3} e^{- 3 x + 6} + C

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What is the integral of 11+5e^{6-3x}-16 ?
The integral of 11+5e^{6-3x}-16 is -5x-5/3 e^{-3x+6}+C