What is the integral of (e^{-1})/(x^3) ?

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

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integral of (e^{-1})/(x^3)

integral

\frac{e ^{- 1}}{x ^{3}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule

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

Simplify

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

= - \frac{1}{2 e x ^{2}}

Add a constant to the solution

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

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