What is the integral of e^x*x^{-2} ?

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

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integral of e^x*x^{-2}

integral

e^{x} \cdot x^{- 2}

- \frac{e ^{x}}{x} + Ei (x) + C

Solution steps

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

Simplify

e^{x} x^{- 2} : \frac{e ^{x}}{x ^{2}}

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

x (ln (x))^{2}

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

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

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

\frac{x ^{3}}{( x + 1 ) ^{3}}

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