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

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

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

integral

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

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

Solution steps

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

Simplify

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

Apply u-substitution

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

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

Use the common integral:

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

= - 2 e^{u}

Substitute back

u = - \frac{x}{2}

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

Add a constant to the solution

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

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

t^{3} + 3 t^{2} - 2 t + t^{- 1}

\frac{1}{tan ( x )}

\frac{x}{81 x ^{4} - 1}

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