integral of 45(1+sqrt(x))

解

\int 45 (1 + x) d x

45 (x + \frac{2}{3} x^{\frac{3}{2}}) + C

解答ステップ

\int 45 (1 + x) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 45 \cdot \int 1 + x 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

= 45 (\int 1 d x + \int x d x)

\int 1 d x = x

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

= 45 (x + \frac{2}{3} x^{\frac{3}{2}})

定数を解答に追加する

= 45 (x + \frac{2}{3} x^{\frac{3}{2}}) + C