What is the integral of ((1-e^{-x}))/x ?

The integral of ((1-e^{-x}))/x is ln|x|-\Ei(-x)+C

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integral of ((1-e^{-x}))/x

integral

\frac{( 1 - e ^{- x} )}{x}

ln ∣ x ∣ - Ei (- x) + C

Solution steps

\int \frac{1 - e ^{- x}}{x} d x

Expand

\frac{1 - e ^{- x}}{x} : \frac{1}{x} - \frac{e ^{- x}}{x}

= \int \frac{1}{x} - \frac{e ^{- x}}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x} d x - \int \frac{e ^{- x}}{x} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - Ei (- x)

Add a constant to the solution

= ln ∣ x ∣ - Ei (- x) + C

\frac{sin ( x )}{cos ^{3} ( x )}

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

ln (3 x - 2)

\frac{( 1 + 2 x )}{( 1 + x )}

\frac{1}{( x ^{2} - 9 ) ^{2}}

What is the integral of ((1-e^{-x}))/x ?
The integral of ((1-e^{-x}))/x is ln|x|-\Ei(-x)+C