integral of (x^2+1/4 y^2+3)

解

\int (x^{2} + \frac{1}{4} y^{2} + 3) d x

3 x + \frac{x ^{3}}{3} + \frac{1}{4} y^{2} x + C

解答ステップ

\int x^{2} + \frac{1}{4} y^{2} + 3 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 x^{2} d x + \int \frac{1}{4} y^{2} d x

\int 3 d x = 3 x

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

\int \frac{1}{4} y^{2} d x = \frac{1}{4} y^{2} x

= 3 x + \frac{x ^{3}}{3} + \frac{1}{4} y^{2} x

定数を解答に追加する

= 3 x + \frac{x ^{3}}{3} + \frac{1}{4} y^{2} x + C