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

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

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

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

2 cosh (x) + C

Solution steps

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

Rewrite using trig identities

= \int 2 sinh (x) d x

Take the constant out:

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

= 2 \cdot \int sinh (x) d x

Use the common integral:

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

= 2 cosh (x)

Add a constant to the solution

= 2 cosh (x) + C

\frac{\partial}{\partial u} (u cos (v))

\int (\frac{1 + cos ( 3 t )}{2}) d t

\frac{d}{d x} (\frac{x}{sin ( 2 x )})

\int 3 x^{2} - 18 x + 27 d x

\frac{d}{d x} (\frac{1}{x ^{7}})

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