integral of x^3-6x

解答

\int x^{3} - 6 x d x

\frac{x ^{4}}{4} - 3 x^{2} + C

求解步骤

\int x^{3} - 6 x 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^{3} d x - \int 6 x d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 6 x d x = 3 x^{2}

= \frac{x ^{4}}{4} - 3 x^{2}

解答补常数

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

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