What is the integral of (e^{-x})/(x^3) ?

The integral of (e^{-x})/(x^3) is -(e^{-x}}{2x^2}-1/2 (-\frac{e^{-x})/x-\Ei(-x))+C

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integral of (e^{-x})/(x^3)

\int \frac{e ^{- x}}{x ^{3}} d x

- \frac{e ^{- x}}{2 x ^{2}} - \frac{1}{2} (- \frac{e ^{- x}}{x} - Ei (- x)) + C

Solution steps

\int \frac{e ^{- x}}{x ^{3}} d x

Apply Integration By Parts

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

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

\int \frac{e ^{- x}}{2 x ^{2}} d x = \frac{1}{2} (- \frac{e ^{- x}}{x} - Ei (- x))

= - \frac{e ^{- x}}{2 x ^{2}} - \frac{1}{2} (- \frac{e ^{- x}}{x} - Ei (- x))

Add a constant to the solution

= - \frac{e ^{- x}}{2 x ^{2}} - \frac{1}{2} (- \frac{e ^{- x}}{x} - Ei (- x)) + C

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What is the integral of (e^{-x})/(x^3) ?
The integral of (e^{-x})/(x^3) is -(e^{-x}}{2x^2}-1/2 (-\frac{e^{-x})/x-\Ei(-x))+C