What is the integral of e^{-cx} ?

The integral of e^{-cx} is -1/c e^{-cx}+C

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integral of e^{-cx}

\int e^{- c x} d x

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

Solution steps

\int e^{- c x} d x

Apply u-substitution

: \int - \frac{e ^{u}}{c} d u

= \int - \frac{e ^{u}}{c} d u

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - c x

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (y + \frac{1}{x + y})

\frac{d}{d x} (lo g_{3} (sec (2 x)))

x \to 0 lim (tan (x) - sec (x))

(t e)^{3} e^{- 2 t} e^{- 2}

\frac{d P}{d t} = P (950 - P)