integral of 20x^4+12x^3+6x+9

解答

\int 20 x^{4} + 12 x^{3} + 6 x + 9 d x

4 x^{5} + 3 x^{4} + 3 x^{2} + 9 x + C

求解步骤

\int 20 x^{4} + 12 x^{3} + 6 x + 9 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 20 x^{4} d x + \int 12 x^{3} d x + \int 6 x d x + \int 9 d x

\int 20 x^{4} d x = 4 x^{5}

\int 12 x^{3} d x = 3 x^{4}

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

\int 9 d x = 9 x

= 4 x^{5} + 3 x^{4} + 3 x^{2} + 9 x

解答补常数

= 4 x^{5} + 3 x^{4} + 3 x^{2} + 9 x + C

\int y e^{2 x y} d x

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