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

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

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

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

2 Ei (- 2 x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= 2 Ei (u)

Substitute back

u = - 2 x

= 2 Ei (- 2 x)

Add a constant to the solution

= 2 Ei (- 2 x) + C

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