integral of x^2(1-x^3)

解答

\int x^{2} (1 - x^{3}) d x

\frac{x ^{3}}{3} - \frac{x ^{6}}{6} + C

求解步骤

\int x^{2} (1 - x^{3}) d x

乘开

x^{2} (1 - x^{3}) : x^{2} - x^{5}

= \int x^{2} - x^{5} d x

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 x^{2} d x - \int x^{5} d x

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

\int x^{5} d x = \frac{x ^{6}}{6}

= \frac{x ^{3}}{3} - \frac{x ^{6}}{6}

解答补常数

= \frac{x ^{3}}{3} - \frac{x ^{6}}{6} + C

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