integral of x(60x^2+90x)

解

\int x (60 x^{2} + 90 x) d x

15 x^{4} + 30 x^{3} + C

解答ステップ

\int x (60 x^{2} + 90 x) d x

拡張

x (60 x^{2} + 90 x) : 60 x^{3} + 90 x^{2}

= \int 60 x^{3} + 90 x^{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 60 x^{3} d x + \int 90 x^{2} d x

\int 60 x^{3} d x = 15 x^{4}

\int 90 x^{2} d x = 30 x^{3}

= 15 x^{4} + 30 x^{3}

定数を解答に追加する

= 15 x^{4} + 30 x^{3} + C