integral of (10+2x^2+2y^2)

解

\int (10 + 2 x^{2} + 2 y^{2}) d x

10 x + 2 y^{2} x + \frac{2 x ^{3}}{3} + C

解答ステップ

\int 10 + 2 x^{2} + 2 y^{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 10 d x + \int 2 y^{2} d x + \int 2 x^{2} d x

\int 10 d x = 10 x

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

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

= 10 x + 2 y^{2} x + \frac{2 x ^{3}}{3}

定数を解答に追加する

= 10 x + 2 y^{2} x + \frac{2 x ^{3}}{3} + C