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

The integral of (e^{7x}-e^{2x})/(e^{2x)} is 1/5 e^{5x}-x+C

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

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

\frac{1}{5} e^{5 x} - x + C

Solution steps

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

Expand

\frac{e ^{7 x} - e ^{2 x}}{e ^{2 x}} : \frac{e ^{7 x}}{e ^{2 x}} - \frac{e ^{2 x}}{e ^{2 x}}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{e ^{7 x}}{e ^{2 x}} d x = \frac{1}{5} e^{5 x}

\int \frac{e ^{2 x}}{e ^{2 x}} d x = x

= \frac{1}{5} e^{5 x} - x

Add a constant to the solution

= \frac{1}{5} e^{5 x} - x + C

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What is the integral of (e^{7x}-e^{2x})/(e^{2x)} ?
The integral of (e^{7x}-e^{2x})/(e^{2x)} is 1/5 e^{5x}-x+C