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

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

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integral of e^{2x}-e^{-2x}

\int e^{2 x} - e^{- 2 x} d x

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

Solution steps

\int e^{2 x} - e^{- 2 x} d x

e^{2 x} - e^{- 2 x} = (e^{x} + e^{- x}) (e^{x} - e^{- x})

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = e^{x} + e^{- x}

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

Add a constant to the solution

= \frac{( e ^{x} + e ^{- x} ) ^{2}}{2} + C

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