integral of (12x+5)^2

解答

\int (12 x + 5)^{2} d x

48 x^{3} + 60 x^{2} + 25 x + C

求解步骤

\int (12 x + 5)^{2} d x

乘开

(12 x + 5)^{2} : 144 x^{2} + 120 x + 25

= \int 144 x^{2} + 120 x + 25 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 144 x^{2} d x + \int 120 x d x + \int 25 d x

\int 144 x^{2} d x = 48 x^{3}

\int 120 x d x = 60 x^{2}

\int 25 d x = 25 x

= 48 x^{3} + 60 x^{2} + 25 x

解答补常数

= 48 x^{3} + 60 x^{2} + 25 x + C

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