integral of (-12xy^2+8x^3y+3)

解答

\int (- 12 x y^{2} + 8 x^{3} y + 3) d x

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

求解步骤

\int - 12 x y^{2} + 8 x^{3} y + 3 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 3 d x - \int 12 y^{2} x d x + \int 8 y x^{3} d x

\int 3 d x = 3 x

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

\int 8 y x^{3} d x = 2 y x^{4}

= 3 x - 6 y^{2} x^{2} + 2 y x^{4}

解答补常数

= 3 x - 6 y^{2} x^{2} + 2 y x^{4} + C

\int \frac{x}{x ^{2} - 4 x + 1} d x

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