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

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

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

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

2 sinh (x) + C

Solution steps

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

Rewrite using trig identities

= \int 2 cosh (x) d x

Take the constant out:

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

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

Use the common integral:

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

= 2 sinh (x)

Add a constant to the solution

= 2 sinh (x) + C

\int \frac{x ^{3}}{1 - x ^{4}} d x

x = - 5, x = 1, y = 11 x, y = x^{2} - 12

2 x^{4}

\frac{s + 4}{s ^{2} + 6 s + 25}

(ln (3) + e^{x^{e}})^{e}

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