What is the integral of sqrt(y)-y ?

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

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integral of sqrt(y)-y

\int y - y d y

\frac{2}{3} y^{\frac{3}{2}} - \frac{y ^{2}}{2} + C

Solution steps

\int y - y d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y d y - \int y d y

\int y d y = \frac{2}{3} y^{\frac{3}{2}}

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

= \frac{2}{3} y^{\frac{3}{2}} - \frac{y ^{2}}{2}

Add a constant to the solution

= \frac{2}{3} y^{\frac{3}{2}} - \frac{y ^{2}}{2} + C

What is the integral of sqrt(y)-y ?
The integral of sqrt(y)-y is 2/3 y^{3/2}-(y^2)/2+C