What is the integral of 11-e^{3x-6}-10 ?

The integral of 11-e^{3x-6}-10 is x-1/3 e^{3x-6}+C

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integral of 11-e^{3x-6}-10

\int 11 - e^{3 x - 6} - 10 d x

x - \frac{1}{3} e^{3 x - 6} + C

Solution steps

\int 11 - e^{3 x - 6} - 10 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 e^{3 x - 6} d x - \int 10 d x

\int 11 d x = 11 x

\int e^{3 x - 6} d x = \frac{1}{3} e^{3 x - 6}

\int 10 d x = 10 x

= 11 x - \frac{1}{3} e^{3 x - 6} - 10 x

Simplify

= x - \frac{1}{3} e^{3 x - 6}

Add a constant to the solution

= x - \frac{1}{3} e^{3 x - 6} + C

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\frac{d}{d x} (\frac{1 + 6 x}{9 - 4 x})

What is the integral of 11-e^{3x-6}-10 ?
The integral of 11-e^{3x-6}-10 is x-1/3 e^{3x-6}+C