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Popular Calculus >

integral of 1-e^{3x}

Solution

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

Solution

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

Solution steps

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

\int 1 d x = x

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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