What is the integral of e^{-22x} ?

The integral of e^{-22x} is -1/22 e^{-22x}+C

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integral of e^{-22x}

\int e^{- 22 x} d x

- \frac{1}{22} e^{- 22 x} + C

Solution steps

\int e^{- 22 x} d x

Apply u-substitution

: \int - \frac{1}{22} e^{u} d u

= \int - \frac{1}{22} e^{u} d u

Take the constant out:

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

= - \frac{1}{22} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{22} e^{u}

Substitute back

u = - 22 x

= - \frac{1}{22} e^{- 22 x}

Add a constant to the solution

= - \frac{1}{22} e^{- 22 x} + C

y = 108 - 90 e^{- 0.4 t}

f (x) = x^{2} e^{x} - 2 x e^{x} + 8 e^{x}

h \to 0 lim (\frac{( 1 + h ) - ( 1 )}{h})

\frac{d y}{d x} = - y - 8

g (x) = 7 e^{x} x