What is the integral of-e^{3x-6}+1 ?

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

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integral of-e^{3x-6}+1

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

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

Solution steps

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

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

\int 1 d x = x

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

Add a constant to the solution

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

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