What is the integral of ((1+e^x))/(e^x) ?

The integral of ((1+e^x))/(e^x) is -1/(e^x)+x+C

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integral of ((1+e^x))/(e^x)

\int \frac{( 1 + e ^{x} )}{e ^{x}} d x

- \frac{1}{e ^{x}} + x + C

Solution steps

\int \frac{1 + e ^{x}}{e ^{x}} d x

Expand

\frac{1 + e ^{x}}{e ^{x}} : \frac{1}{e ^{x}} + 1

= \int \frac{1}{e ^{x}} + 1 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 \frac{1}{e ^{x}} d x + \int 1 d x

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

\int 1 d x = x

= - \frac{1}{e ^{x}} + x

Add a constant to the solution

= - \frac{1}{e ^{x}} + x + C

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What is the integral of ((1+e^x))/(e^x) ?
The integral of ((1+e^x))/(e^x) is -1/(e^x)+x+C