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

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

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

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

2 x + e^{x} + C

Solution steps

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

Simplify

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

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

\int 2 d x = 2 x

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

= 2 x + e^{x}

Add a constant to the solution

= 2 x + e^{x} + C

x \to + 2 lim (\frac{5 x}{x - 2})

\int - \frac{12}{y} d y

\frac{\partial}{\partial x} (- 3 x y sin (z))

\frac{d}{d x} (\frac{1}{9} ln (- ln (x)) + 5)

x \frac{d y}{d x} + 3 y = 2 x^{5}

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