What is the integral of sqrt(z)(z^2-1/(4z)) ?

The integral of sqrt(z)(z^2-1/(4z)) is 2/7 z^3sqrt(z)-1/2 sqrt(z)+C

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integral of sqrt(z)(z^2-1/(4z))

\int z (z^{2} - \frac{1}{4 z}) d z

\frac{2}{7} z^{3} z - \frac{1}{2} z + C

Solution steps

\int z (z^{2} - \frac{1}{4 z}) d z

Apply Integration By Parts

: z^{3} z - \frac{1}{4} z - \int \frac{20 z ^{3} + 1}{8 z} d z

= z^{3} z - \frac{1}{4} z - \int \frac{20 z ^{3} + 1}{8 z} d z

\int \frac{20 z ^{3} + 1}{8 z} d z = \frac{1}{28} z (20 z^{3} + 7)

= z^{3} z - \frac{1}{4} z - \frac{1}{28} z (20 z^{3} + 7)

Simplify

z^{3} z - \frac{1}{4} z - \frac{1}{28} z (20 z^{3} + 7) : \frac{2}{7} z^{3} z - \frac{1}{2} z

= \frac{2}{7} z^{3} z - \frac{1}{2} z

Add a constant to the solution

= \frac{2}{7} z^{3} z - \frac{1}{2} z + C

\int_{0}^{1} x e^{x^{2}} d x

\int \frac{ln ^{5} ( x )}{x} d x

y^{^{'}} = \frac{( 2 y + 3 ) ^{2}}{( 4 x + 5 ) ^{2}}

\frac{\partial}{\partial y} ((x + 2 y)^{2})

\frac{d}{d x} (\frac{e ^{x} - 2}{( 1 - e ^{- x} ) ^{2}})

What is the integral of sqrt(z)(z^2-1/(4z)) ?
The integral of sqrt(z)(z^2-1/(4z)) is 2/7 z^3sqrt(z)-1/2 sqrt(z)+C