What is the integral of (x^{-2}(1/x))/(1/(x^5)) ?

The integral of (x^{-2}(1/x))/(1/(x^5)) is (x^3)/3+C

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integral of (x^{-2}(1/x))/(1/(x^5))

\int \frac{x ^{- 2} ( \frac{1}{x} )}{\frac{1}{x ^{5}}} d x

\frac{x ^{3}}{3} + C

Solution steps

\int \frac{x ^{- 2} \frac{1}{x}}{\frac{1}{x ^{5}}} d x

Simplify

\frac{x ^{- 2} \frac{1}{x}}{\frac{1}{x ^{5}}} : x^{2}

= \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{3}}{3} + C

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What is the integral of (x^{-2}(1/x))/(1/(x^5)) ?
The integral of (x^{-2}(1/x))/(1/(x^5)) is (x^3)/3+C