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

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

Popular >

Find the Antiderivative -1/(e^x)

integral

\frac{- 1}{( e ^{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

- \frac{d}{d x} y = 4 x

- \frac{d}{d x} y = 2 x^{2}

- \frac{d}{d x} (cot (2 x))

- \frac{d}{d x} (1) - cos (x)

\frac{1}{( sin ( 2 x ) ) , x}

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