integral of (x-1)(x+5)

解答

\int (x - 1) (x + 5) d x

\frac{x ^{3}}{3} + 2 x^{2} - 5 x + C

求解步骤

\int (x - 1) (x + 5) d x

乘开

(x - 1) (x + 5) : x^{2} + 4 x - 5

= \int x^{2} + 4 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 4 x d x - \int 5 d x

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

\int 4 x d x = 2 x^{2}

\int 5 d x = 5 x

= \frac{x ^{3}}{3} + 2 x^{2} - 5 x

解答补常数

= \frac{x ^{3}}{3} + 2 x^{2} - 5 x + C

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