What is the integral of (e^{-2x})/x ?

The integral of (e^{-2x})/x is \Ei(-2x)+C

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integral of (e^{-2x})/x

\int \frac{e ^{- 2 x}}{x} d x

Ei (- 2 x) + C

Solution steps

\int \frac{e ^{- 2 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 = - 2 x

= Ei (- 2 x)

Add a constant to the solution

= Ei (- 2 x) + C

\frac{\partial}{\partial x} ((x - 1)^{2} + (y - 1)^{2})

\int_{- 1}^{1} \frac{tan ( x )}{1 + x ^{4}} d x

\int_{- \infty}^{0} \frac{1}{2 - 8 x} d x

x = y^{4}, 2 - x, y = 0

\frac{4 x - 6}{2 x ^{2} + x - 2}