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

解答

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

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

求解步骤

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

使用分布积分法

= 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)

化简

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

解答补常数

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

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