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

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

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

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

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

Solution steps

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

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

Simplify

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

Add a constant to the solution

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

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

x^{- 2}, 3

\frac{d}{d s} (\frac{k}{s ^{2} + k ^{2}})

\int (x - 1) d x

t^{2} y^{^{''}} + 5 t y^{^{'}} - 12 y = 0