What is the integral of ce^{2x}-e^{3x} ?

The integral of ce^{2x}-e^{3x} is c 1/2 e^{2x}-1/3 e^{3x}+C

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integral of ce^{2x}-e^{3x}

\int c e^{2 x} - e^{3 x} d x

c \frac{1}{2} e^{2 x} - \frac{1}{3} e^{3 x} + C

Solution steps

\int c e^{2 x} - 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 c e^{2 x} d x - \int e^{3 x} d x

\int c e^{2 x} d x = c \frac{1}{2} e^{2 x}

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

= c \frac{1}{2} e^{2 x} - \frac{1}{3} e^{3 x}

Add a constant to the solution

= c \frac{1}{2} e^{2 x} - \frac{1}{3} e^{3 x} + C

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What is the integral of ce^{2x}-e^{3x} ?
The integral of ce^{2x}-e^{3x} is c 1/2 e^{2x}-1/3 e^{3x}+C