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

e^{- 2 t} sin (t)

x \to a lim (\frac{3}{0})

\frac{20}{s ( s + 10 )}

\frac{- x ^{2} - 4}{( x ^{2} - 4 ) ^{2}}

n = 0 \sum \infty \frac{1}{( 1 + n ^{2} )}

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