What is the integral of e^{-12x} ?

The integral of e^{-12x} is -1/12 e^{-12x}+C

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integral of e^{-12x}

\int e^{- 12 x} d x

- \frac{1}{12} e^{- 12 x} + C

Solution steps

\int e^{- 12 x} d x

Apply u-substitution

: \int - \frac{1}{12} e^{u} d u

= \int - \frac{1}{12} e^{u} d u

Take the constant out:

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

= - \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{12} e^{u}

Substitute back

u = - 12 x

= - \frac{1}{12} e^{- 12 x}

Add a constant to the solution

= - \frac{1}{12} e^{- 12 x} + C

x \to 5 lim (\frac{7 x}{x - 5})

y^{^{'}} + y = e^{2 x}

x + \frac{5}{x}

\int (x^{2} - 1)^{2} (3 x^{2}) d x

\frac{d x}{d y} = e^{3 x + 2 y}