What is the integral of (e^{-x})/(3x^2) ?

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

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integral of (e^{-x})/(3x^2)

\int \frac{e ^{- x}}{3 x ^{2}} d x

\frac{1}{3} (- \frac{e ^{- x}}{x} - Ei (- x)) + C

Solution steps

\int \frac{e ^{- x}}{3 x ^{2}} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{e ^{- x}}{x ^{2}} d x

Apply Integration By Parts

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

= \frac{1}{3} (- \frac{e ^{- x}}{x} - \int \frac{e ^{- x}}{x} d x)

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

= \frac{1}{3} (- \frac{e ^{- x}}{x} - Ei (- x))

Add a constant to the solution

= \frac{1}{3} (- \frac{e ^{- x}}{x} - Ei (- x)) + C

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