What is the integral of 0.5e^{-0.5x} ?

The integral of 0.5e^{-0.5x} is -e^{-0.5x}+C

Popular >

integral of 0.5e^{-0.5x}

\int 0.5 e^{- 0.5 x} d x

- e^{- 0.5 x} + C

Solution steps

\int 0.5 e^{- 0.5 x} d x

Take the constant out:

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

= 0.5 \cdot \int e^{- 0.5 x} d x

Apply u-substitution

: \int - \frac{1}{0.5} e^{u} d u

= 0.5 \cdot \int - \frac{1}{0.5} e^{u} d u

Take the constant out:

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

= 0.5 (- \frac{1}{0.5} \cdot \int e^{u} d u)

Simplify

= 0.5 (- 2 \cdot \int e^{u} d u)

Use the common integral:

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

= 0.5 (- 2 e^{u})

Substitute back

u = - 0.5 x

= 0.5 (- 2 e^{- 0.5 x})

Simplify

= - e^{- 0.5 x}

Add a constant to the solution

= - e^{- 0.5 x} + C

\frac{d}{d x} (4 π)

5 s

\frac{c e ^{t}}{1 + c e ^{t}}

\frac{\partial}{\partial x} ((\frac{( x + 4 )}{y + 5})^{\frac{1}{2}})

\int (x^{2} + 7 x - 5) cos (2 x) d x

What is the integral of 0.5e^{-0.5x} ?
The integral of 0.5e^{-0.5x} is -e^{-0.5x}+C