integral of 21x^2-12x-5

解答

\int 21 x^{2} - 12 x - 5 d x

7 x^{3} - 6 x^{2} - 5 x + C

求解步骤

\int 21 x^{2} - 12 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 21 x^{2} d x - \int 12 x d x - \int 5 d x

\int 21 x^{2} d x = 7 x^{3}

\int 12 x d x = 6 x^{2}

\int 5 d x = 5 x

= 7 x^{3} - 6 x^{2} - 5 x

解答补常数

= 7 x^{3} - 6 x^{2} - 5 x + C

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