integral of (4x^3-4x+6)

解答

\int (4 x^{3} - 4 x + 6) d x

x^{4} - 2 x^{2} + 6 x + C

求解步骤

\int 4 x^{3} - 4 x + 6 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 4 x^{3} d x - \int 4 x d x + \int 6 d x

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

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

\int 6 d x = 6 x

= x^{4} - 2 x^{2} + 6 x

解答补常数

= x^{4} - 2 x^{2} + 6 x + C

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