What is the integral of (e^{2x}-7)/(e^{2x)} ?

The integral of (e^{2x}-7)/(e^{2x)} is -1/2 e^{-2x}(e^{2x}-7)+x+C

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integral of (e^{2x}-7)/(e^{2x)}

\int \frac{e ^{2 x} - 7}{e ^{2 x}} d x

- \frac{1}{2} e^{- 2 x} (e^{2 x} - 7) + x + C

Solution steps

\int \frac{e ^{2 x} - 7}{e ^{2 x}} d x

Apply Integration By Parts

: - \frac{1}{2} e^{- 2 x} (e^{2 x} - 7) - \int - 1 d x

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 7) - \int - 1 d x

\int - 1 d x = - x

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 7) - (- x)

Simplify

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 7) + x

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} (e^{2 x} - 7) + x + C

\frac{7}{8 t ^{4}}

\frac{d}{d x} (x^{2} + c)

x \to 2 lim (\frac{2 + x}{2 - 4})

n = 0 \sum \infty 2 (\frac{1}{3 ^{n}})

\frac{d}{d z} (e^{z})

What is the integral of (e^{2x}-7)/(e^{2x)} ?
The integral of (e^{2x}-7)/(e^{2x)} is -1/2 e^{-2x}(e^{2x}-7)+x+C