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

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

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

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

x - 3 e^{x} + C

Solution steps

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

Simplify

\frac{e ^{x} - 3 e ^{2 x}}{e ^{x}} : 1 - 3 e^{x}

= \int 1 - 3 e^{x} d 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 1 d x - \int 3 e^{x} d x

\int 1 d x = x

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

= x - 3 e^{x}

Add a constant to the solution

= x - 3 e^{x} + C

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