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) with respect to x

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

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

Solution steps

\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}}

Add a constant to the solution

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

- \frac{d}{d x} y = sec (x) + tan (x)

x \to \infty lim (\frac{x}{2})

sin (θ)

- \frac{d}{d x} (csc (x))

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