integral of (z^2-z+2)

解答

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

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

求解步骤

\int z^{2} - z + 2 d z

使用积分加法定则:

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

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

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

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

\int 2 d z = 2 z

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

解答补常数

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

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