What is the integral of (-2)/(e^x) ?

The integral of (-2)/(e^x) is 2/(e^x)+C

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integral of (-2)/(e^x)

\int \frac{- 2}{e ^{x}} d x

\frac{2}{e ^{x}} + C

Solution steps

\int \frac{- 2}{e ^{x}} d x

Take the constant out:

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

= - 2 \cdot \int \frac{1}{e ^{x}} d x

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - 2 (- \frac{1}{u})

Substitute back

u = e^{x}

= - 2 (- \frac{1}{e ^{x}})

Simplify

- 2 (- \frac{1}{e ^{x}}) : \frac{2}{e ^{x}}

= \frac{2}{e ^{x}}

Add a constant to the solution

= \frac{2}{e ^{x}} + C

\frac{d}{d x} (2 + 4 x^{\frac{3}{2}})

\frac{d}{d x} (ln (1 - 5 x^{2} + x^{3}))

x^{4} + 9 e^{x}

f (x) = x^{2} - 3

x \to \infty lim ((1 + \frac{1}{x ^{3}})^{2 x^{2}})