What is the integral of 8+5e^{9-3x}-13 ?

The integral of 8+5e^{9-3x}-13 is -5x-5/3 e^{-3x+9}+C

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integral of 8+5e^{9-3x}-13

\int 8 + 5 e^{9 - 3 x} - 13 d x

- 5 x - \frac{5}{3} e^{- 3 x + 9} + C

Solution steps

\int 8 + 5 e^{9 - 3 x} - 13 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 8 d x + \int 5 e^{9 - 3 x} d x - \int 13 d x

\int 8 d x = 8 x

\int 5 e^{9 - 3 x} d x = - \frac{5}{3} e^{9 - 3 x}

\int 13 d x = 13 x

= 8 x - \frac{5}{3} e^{9 - 3 x} - 13 x

Simplify

= - 5 x - \frac{5}{3} e^{- 3 x + 9}

Add a constant to the solution

= - 5 x - \frac{5}{3} e^{- 3 x + 9} + C

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f (x) = ln (cos (x))

What is the integral of 8+5e^{9-3x}-13 ?
The integral of 8+5e^{9-3x}-13 is -5x-5/3 e^{-3x+9}+C