What is the integral of-2e^{-1/2 x} ?

The integral of-2e^{-1/2 x} is 4e^{-1/2 x}+C

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integral of-2e^{-1/2 x}

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= - 2 (- 2 e^{u})

Substitute back

u = - \frac{1}{2} x

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

Simplify

= 4 e^{- \frac{1}{2} x}

Add a constant to the solution

= 4 e^{- \frac{1}{2} x} + C

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What is the integral of-2e^{-1/2 x} ?
The integral of-2e^{-1/2 x} is 4e^{-1/2 x}+C