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 x} (\frac{h ( x ) c}{x})

\int \frac{1}{4 x ( 3 + x )} d x

\int \frac{7 x}{x - 1} d x

d er i v a t i v e 2 x - x^{2}

x \to \infty lim (\frac{2 x ^{3} + 3 x - 4}{5 - 4 x ^{3}})