integral of (5x^2+9)^2

解

\int (5 x^{2} + 9)^{2} d x

5 x^{5} + 30 x^{3} + 81 x + C

解答ステップ

\int (5 x^{2} + 9)^{2} d x

拡張

(5 x^{2} + 9)^{2} : 25 x^{4} + 90 x^{2} + 81

= \int 25 x^{4} + 90 x^{2} + 81 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 25 x^{4} d x + \int 90 x^{2} d x + \int 81 d x

\int 25 x^{4} d x = 5 x^{5}

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

\int 81 d x = 81 x

= 5 x^{5} + 30 x^{3} + 81 x

定数を解答に追加する

= 5 x^{5} + 30 x^{3} + 81 x + C