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

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

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

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

\frac{1}{e} Ei (x) + C

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

a^{- 1} = \frac{1}{a}

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

Use the nonelementary integral:

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

= \frac{1}{e} Ei (x)

Add a constant to the solution

= \frac{1}{e} Ei (x) + C

35 x - x x

x \to 0 lim (sin (4 x))

\int \frac{x - 1}{x ^{2} - 4 x - 5} d x

\int_{0}^{1} 4 t^{2} + 9 t^{4} d t

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

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