What is the integral of (e^{2x}-4)/(e^{2x)} ?

The integral of (e^{2x}-4)/(e^{2x)} is -1/2 e^{-2x}(e^{2x}-4)+x+C

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integral of (e^{2x}-4)/(e^{2x)}

\int \frac{e ^{2 x} - 4}{e ^{2 x}} d x

- \frac{1}{2} e^{- 2 x} (e^{2 x} - 4) + x + C

Solution steps

\int \frac{e ^{2 x} - 4}{e ^{2 x}} d x

Apply Integration By Parts

: - \frac{1}{2} e^{- 2 x} (e^{2 x} - 4) - \int - 1 d x

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 4) - \int - 1 d x

\int - 1 d x = - x

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 4) - (- x)

Simplify

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 4) + x

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 4) + x + C

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What is the integral of (e^{2x}-4)/(e^{2x)} ?
The integral of (e^{2x}-4)/(e^{2x)} is -1/2 e^{-2x}(e^{2x}-4)+x+C