integral of (3+e^x(y^2+3y+2))

解

\int (3 + e^{x} (y^{2} + 3 y + 2)) d x

3 x + (2 + y^{2} + 3 y) e^{x} + C

解答ステップ

\int 3 + e^{x} (y^{2} + 3 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 3 d x + \int (2 + y^{2} + 3 y) e^{x} d x

\int 3 d x = 3 x

\int (2 + y^{2} + 3 y) e^{x} d x = (2 + y^{2} + 3 y) e^{x}

= 3 x + (2 + y^{2} + 3 y) e^{x}

定数を解答に追加する

= 3 x + (2 + y^{2} + 3 y) e^{x} + C