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

The integral of 4e^{-1/2 x} is -8e^{-1/2 x}+C

integral of 4e^{-1/2 x}

\int 4 e^{- \frac{1}{2} x} d x

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

Solution steps

\int 4 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

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

Apply u-substitution

= 4 \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

= 4 (- 2 \cdot \int e^{u} d u)

Use the common integral:

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

= 4 (- 2 e^{u})

Substitute back

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

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

Simplify

= - 8 e^{- \frac{1}{2} x}

Add a constant to the solution

= - 8 e^{- \frac{1}{2} x} + C

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What is the integral of 4e^{-1/2 x} ?
The integral of 4e^{-1/2 x} is -8e^{-1/2 x}+C