What is the integral of (e^{-5x}+2e^x) ?

The integral of (e^{-5x}+2e^x) is -1/5 e^{-5x}+2e^x+C

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integral of (e^{-5x}+2e^x)

\int (e^{- 5 x} + 2 e^{x}) d x

- \frac{1}{5} e^{- 5 x} + 2 e^{x} + C

Solution steps

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

\int e^{- 5 x} d x = - \frac{1}{5} e^{- 5 x}

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

= - \frac{1}{5} e^{- 5 x} + 2 e^{x}

Add a constant to the solution

= - \frac{1}{5} e^{- 5 x} + 2 e^{x} + C

\int \frac{8}{7 x} d x

f (x) = \frac{34 x - 2 π \cdot x ^{3}}{2}

\frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}})

\int (8 x^{7} - \frac{7}{x ^{7}}) d x

y = x^{10}

What is the integral of (e^{-5x}+2e^x) ?
The integral of (e^{-5x}+2e^x) is -1/5 e^{-5x}+2e^x+C