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

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

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

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

e^{x} - x + C

Solution steps

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

Expand

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

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

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

= e^{x} - x

Add a constant to the solution

= e^{x} - x + C

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