What is the integral of 4e^{-2x}+5e^{3x} ?

The integral of 4e^{-2x}+5e^{3x} is -2e^{-2x}+5/3 e^{3x}+C

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integral of 4e^{-2x}+5e^{3x}

\int 4 e^{- 2 x} + 5 e^{3 x} d x

- 2 e^{- 2 x} + \frac{5}{3} e^{3 x} + C

Solution steps

\int 4 e^{- 2 x} + 5 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 4 e^{- 2 x} d x + \int 5 e^{3 x} d x

\int 4 e^{- 2 x} d x = - 2 e^{- 2 x}

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

= - 2 e^{- 2 x} + \frac{5}{3} e^{3 x}

Add a constant to the solution

= - 2 e^{- 2 x} + \frac{5}{3} e^{3 x} + C

What is the integral of 4e^{-2x}+5e^{3x} ?
The integral of 4e^{-2x}+5e^{3x} is -2e^{-2x}+5/3 e^{3x}+C