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

The integral of e^{-kNx} is -1/(kN)e^{-kNx}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-kNx}

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

- \frac{1}{k N} e^{- k N x} + C

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{k N} e^{u}

Substitute back

u = - k N x

= - \frac{1}{k N} e^{- k N x}

Add a constant to the solution

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

2 (x - 6)^{3}

z \to 0 lim (z^{3} cos (\frac{1}{z}))

cos^{3} (e^{4 x})

\frac{\partial}{\partial x} (x y + \frac{4}{x} + \frac{2}{y})

x, 16

What is the integral of e^{-kNx} ?
The integral of e^{-kNx} is -1/(kN)e^{-kNx}+C