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

The integral of e^{-nx} is -1/n e^{-nx}+C

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integral of e^{-nx}

\int e^{- n x} d x

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

Solution steps

\int e^{- n x} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - n x

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

Add a constant to the solution

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

(x \frac{d y}{d x} + 2 y) = 3

f (x) = 9 - x, at x = 2

y^{^{'}} = e^{8 x + y}

\frac{\partial}{\partial y} (z e^{x y})

x \to 1 lim (3 x^{3} - 4 x^{2} + x + 2)