What is the integral of e^{-6t} ?

The integral of e^{-6t} is -1/6 e^{-6t}+C

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integral of e^{-6t}

\int e^{- 6 t} d t

- \frac{1}{6} e^{- 6 t} + C

Solution steps

\int e^{- 6 t} d t

Apply u-substitution

: \int - \frac{1}{6} e^{u} d u

= \int - \frac{1}{6} e^{u} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - 6 t

= - \frac{1}{6} e^{- 6 t}

Add a constant to the solution

= - \frac{1}{6} e^{- 6 t} + C

x + y \cdot y^{^{'}} = 0

f (x) = (3 x - 1)^{2}, at x = 1

x \to 2 lim (x^{2} - x - 6)

\frac{\partial}{\partial x} (2 x^{3} - 10 y)

(- 7.2) (9.6)