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

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

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

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

x + e^{x} + C

Solution steps

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

Expand

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

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

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

= x + e^{x}

Add a constant to the solution

= x + e^{x} + C

\frac{7 x ^{2} - 9 x + 1}{x}

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\int \frac{- 3}{x + 1} d x

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