What is the integral of ke^{-kx} ?

The integral of ke^{-kx} is -e^{-kx}+C

Popular >

integral of ke^{-kx}

\int k e^{- k x} d x

- e^{- k x} + C

Solution steps

\int k e^{- k x} d x

Take the constant out:

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

= k \cdot \int e^{- k x} d x

Apply u-substitution

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

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

Take the constant out:

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

= k (- \frac{1}{k} \cdot \int e^{u} d u)

Use the common integral:

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

= k (- \frac{1}{k} e^{u})

Substitute back

u = - k x

= k (- \frac{1}{k} e^{- k x})

Simplify

k (- \frac{1}{k} e^{- k x}) : - e^{- k x}

= - e^{- k x}

Add a constant to the solution

= - e^{- k x} + C

ln (x^{100})

\int_{- 2}^{2} x^{2} d x

\frac{b}{( 1 - ( \frac{y}{x} ) )}

x^{\frac{2}{3}} - x^{\frac{1}{3}}

\int 7 sin (2) (x) cos (3) (x) d x