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

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

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

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = e^{x}

= - (- \frac{1}{e ^{x}})

Simplify

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

Add a constant to the solution

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

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