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

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

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

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

= \frac{1}{2} (\int e^{- 2 x} d x + \int e^{2 x} d x)

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

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

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

Add a constant to the solution

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

f (x) = \frac{18}{( 2 x + 4 ) ^{2}}, at x = 9

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\frac{\partial}{\partial x} (5^{x y})

x \to 0 lim (x^{2} sin (\frac{3}{x}))

\int_{0}^{π} sin^{3} (x) d x

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