What is the integral of 2xy^{-2} ?

The integral of 2xy^{-2} is (x^2)/(y^2)+C

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integral of 2xy^{-2}

\int 2 x y^{- 2} d x

\frac{x ^{2}}{y ^{2}} + C

Solution steps

\int 2 x y^{- 2} d x

Take the constant out:

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

= 2 y^{- 2} \cdot \int x d x

Simplify

2 y^{- 2} : \frac{2}{y ^{2}}

= \frac{2}{y ^{2}} \cdot \int x d x

Apply the Power Rule

= \frac{2}{y ^{2}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{2}{y ^{2}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{y ^{2}}

= \frac{x ^{2}}{y ^{2}}

Add a constant to the solution

= \frac{x ^{2}}{y ^{2}} + C