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

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

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integral of e^{-t/2}

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

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

Solution steps

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

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{t}{2}

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

Add a constant to the solution

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

y^{^{''}} = 8 t^{2}

\frac{d}{d x} (\frac{x}{x ^{3} + 2})

n = 0 \sum \infty n e^{- \frac{n}{2}}

\int_{4}^{\infty} \frac{1}{x ^{2} - 1} d x

\frac{d}{d x} (e^{x} cosh (x))