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

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

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

integral

\frac{( e ^{- x} ) ^{2}}{x}

Ei (- 2 x) + C

Solution steps

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

(e^{- x})^{2} = e^{- 2 x}

= \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{1}{( y ^{2} + 1 )}

\frac{x}{( e ^{x} ) ^{2}}

(e^{x} + 2)^{2}

\frac{2 - x}{1 - x}

\frac{tan ( x )}{( 1 + cos ^{4} ( x ) )}

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