What is the integral of x/y x/y) ?

The integral of x/y x/y) is d/(y^2)*(x^3)/3+C

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integral of x/y x/y)

\int \frac{x}{y} d (\frac{x}{y})

\frac{d}{y ^{2}} \cdot \frac{x ^{3}}{3} + C

Solution steps

\int \frac{x}{y} d \frac{x}{y} d x

Take the constant out:

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

= \frac{1}{y} \cdot \frac{1}{y} d \cdot \int xx d x

Simplify

\frac{1}{y} \cdot \frac{1}{y} d : \frac{d}{y ^{2}}

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

Simplify

xx : x^{2}

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

Apply the Power Rule

= \frac{d}{y ^{2}} \cdot \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{d}{y ^{2}} \cdot \frac{x ^{3}}{3} + C

What is the integral of x/y x/y) ?
The integral of x/y x/y) is d/(y^2)*(x^3)/3+C