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Popular >

integral of 1/x e^x

Solution

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

Solution

Ei (x) + C

Solution steps

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

Simplify

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

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

Use the nonelementary integral:

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

= Ei (x)

Add a constant to the solution

= Ei (x) + C

Popular Examples

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f (x) = \frac{4 x ^{2} + 6 x + 6}{x}

integral of e^{-2x}cos(4x)

\int e^{- 2 x} cos (4 x) d x

integral of 1/(sqrt(48x+6x^2))

\int \frac{1}{48 x + 6 x ^{2}} d x

limit as x approaches 6 of 8x^2-7x+1

x \to 6 lim (8 x^{2} - 7 x + 1)

derivative of 3cos(-x^3+3x+1)

\frac{d}{d x} (3 cos (- x^{3} + 3 x + 1))

Frequently Asked Questions (FAQ)

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