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

\frac{d}{d x} (\frac{6}{( 1 - x ) ^{3}})

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 3 z^{2})

y = 10 x, y = x^{2} - 11

\int x (2 x + 1) d x

\frac{\partial}{\partial y} (m sin (2 (m x + n y)))

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