What is the integral of (e^{-3x})/x ?

The integral of (e^{-3x})/x is \Ei(-3x)+C

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integral of (e^{-3x})/x

\int \frac{e ^{- 3 x}}{x} d x

Ei (- 3 x) + C

Solution steps

\int \frac{e ^{- 3 x}}{x} d x

Apply u-substitution

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

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (u)

Substitute back

u = - 3 x

= Ei (- 3 x)

Add a constant to the solution

= Ei (- 3 x) + C

\frac{d}{d x} (x^{2} \frac{1}{2})

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

\int \frac{x ^{2} + 1}{x - 1} d x

x e^{- 8 x}

\frac{d}{d x} ((6 x^{0.5} - x^{2})^{2})