What is the integral of 5/(3y^{-2)} ?

The integral of 5/(3y^{-2)} is (5y^3)/9+C

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integral of 5/(3y^{-2)}

\int \frac{5}{3 y ^{- 2}} d y

\frac{5 y ^{3}}{9} + C

Solution steps

\int \frac{5}{3 y ^{- 2}} d y

Take the constant out:

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

= \frac{5}{3} \cdot \int \frac{1}{y ^{- 2}} d y

Apply the Power Rule

= \frac{5}{3} \cdot \frac{y ^{3}}{3}

Simplify

\frac{5}{3} \cdot \frac{y ^{3}}{3} : \frac{5 y ^{3}}{9}

= \frac{5 y ^{3}}{9}

Add a constant to the solution

= \frac{5 y ^{3}}{9} + C

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