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

The integral of-(e^{-2x})/2 2 is 1/2 e^{-2x}+C

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

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

\frac{1}{2} e^{- 2 x} + C

Solution steps

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

Take the constant out:

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

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

- \frac{1}{2} \cdot 2 = - 1

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int e^{u} d u = e^{u}

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

Substitute back

u = - 2 x

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

Simplify

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

Add a constant to the solution

= \frac{1}{2} e^{- 2 x} + C

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What is the integral of-(e^{-2x})/2 2 ?
The integral of-(e^{-2x})/2 2 is 1/2 e^{-2x}+C