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

\int \frac{1}{cosh ( x )} d x

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 14

\int \frac{a}{x} d x

(a (t) sin^{3} (t))^{^{'}}

y = sin (7 x)

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