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

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

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

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

sinh (x) + C

Solution steps

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

Rewrite using trig identities

= \frac{1}{2} \cdot \int 2 cosh (x) d x

Take the constant out:

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

= \frac{1}{2} \cdot 2 \cdot \int cosh (x) d x

Use the common integral:

\int cosh (x) d x = sinh (x)

= \frac{1}{2} \cdot 2 sinh (x)

Simplify

\frac{1}{2} \cdot 2 sinh (x) : sinh (x)

= sinh (x)

Add a constant to the solution

= sinh (x) + C

\frac{ln ( x )}{2 x} + \frac{1}{x}

x \to 0 lim (\frac{2 x}{x})

x \to - 4 - lim (\frac{2}{x ^{2} - 16})

\frac{d y}{d x} = \frac{( e ^{x} - e ^{- x} )}{3 + y}

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

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