What is the integral of (sqrt(z)-z)^2 ?

The integral of (sqrt(z)-z)^2 is (z^2)/2-4/5 z^{5/2}+(z^3)/3+C

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integral of (sqrt(z)-z)^2

\int (z - z)^{2} d z

\frac{z ^{2}}{2} - \frac{4}{5} z^{\frac{5}{2}} + \frac{z ^{3}}{3} + C

Solution steps

\int (z - z)^{2} d z

Expand

(z - z)^{2} : z - 2 z^{\frac{3}{2}} + z^{2}

= \int z - 2 z^{\frac{3}{2}} + z^{2} d z

Apply the Sum Rule:

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

= \int z d z - \int 2 z^{\frac{3}{2}} d z + \int z^{2} d z

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

\int 2 z^{\frac{3}{2}} d z = \frac{4}{5} z^{\frac{5}{2}}

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

= \frac{z ^{2}}{2} - \frac{4}{5} z^{\frac{5}{2}} + \frac{z ^{3}}{3}

Add a constant to the solution

= \frac{z ^{2}}{2} - \frac{4}{5} z^{\frac{5}{2}} + \frac{z ^{3}}{3} + C

\int \frac{x}{16 - x ^{2}} d x

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x \to 2 - lim (x)

\frac{d}{d x} (sin (20 x))

\frac{d}{d x} ((x^{2} - 5)^{2})

What is the integral of (sqrt(z)-z)^2 ?
The integral of (sqrt(z)-z)^2 is (z^2)/2-4/5 z^{5/2}+(z^3)/3+C