integral of 6x^2-4x+7

解答

\int 6 x^{2} - 4 x + 7 d x

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

求解步骤

\int 6 x^{2} - 4 x + 7 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 6 x^{2} d x - \int 4 x d x + \int 7 d x

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

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

\int 7 d x = 7 x

= 2 x^{3} - 2 x^{2} + 7 x

解答补常数

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

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