What is the integral of e^{-8x} ?

The integral of e^{-8x} is -1/8 e^{-8x}+C

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integral of e^{-8x}

\int e^{- 8 x} d x

- \frac{1}{8} e^{- 8 x} + C

Solution steps

\int e^{- 8 x} d x

Apply u-substitution

: \int - \frac{1}{8} e^{u} d u

= \int - \frac{1}{8} e^{u} d u

Take the constant out:

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

= - \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{8} e^{u}

Substitute back

u = - 8 x

= - \frac{1}{8} e^{- 8 x}

Add a constant to the solution

= - \frac{1}{8} e^{- 8 x} + C

y^{^{''}} + 36 y = 36 sin (6 t)

f (x) = x^{4} - 10 x^{2} + 9

\frac{d}{d x} (\frac{6}{x ^{2} + 36})

\int sin^{3} (x) cos^{3} (x) d x

(- 6, - 20), (1, 8)