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

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

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

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

cosh (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 sinh (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 sinh (x) d x

Use the common integral:

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

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

Simplify

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

= cosh (x)

Add a constant to the solution

= cosh (x) + C

x^{2} - 25 ln (x^{2})

2 e^{- t}

f (x) = - 9 x^{- \frac{1}{9}}

x \to - \infty lim (1 - e^{x})

(x^{3} - 8)^{\frac{2}{3}}

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