What is the integral of (e^{2x}-3e^x)/(e^x) ?

The integral of (e^{2x}-3e^x)/(e^x) is e^x-3x+C

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integral of (e^{2x}-3e^x)/(e^x)

\int \frac{e ^{2 x} - 3 e ^{x}}{e ^{x}} d x

e^{x} - 3 x + C

Solution steps

\int \frac{e ^{2 x} - 3 e ^{x}}{e ^{x}} d x

Expand

\frac{e ^{2 x} - 3 e ^{x}}{e ^{x}} : \frac{e ^{2 x}}{e ^{x}} - \frac{3 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{3 e ^{x}}{e ^{x}} d x

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

\int \frac{3 e ^{x}}{e ^{x}} d x = 3 x

= e^{x} - 3 x

Add a constant to the solution

= e^{x} - 3 x + C

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What is the integral of (e^{2x}-3e^x)/(e^x) ?
The integral of (e^{2x}-3e^x)/(e^x) is e^x-3x+C