integral of (7-2x)/(x^{1/2)}

解

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x

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

解答ステップ

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x

拡張

\frac{7 - 2 x}{x ^{\frac{1}{2}}} : \frac{7}{x ^{\frac{1}{2}}} - 2 x^{\frac{1}{2}}

= \int \frac{7}{x ^{\frac{1}{2}}} - 2 x^{\frac{1}{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 \frac{7}{x ^{\frac{1}{2}}} d x - \int 2 x^{\frac{1}{2}} d x

\int \frac{7}{x ^{\frac{1}{2}}} d x = 14 x^{\frac{1}{2}}

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

= 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}}

定数を解答に追加する

= 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}} + C