integral of (v^{3/2}+1/(v^{3/2)})

解

\int (v^{\frac{3}{2}} + \frac{1}{v ^{\frac{3}{2}}}) d v

\frac{2}{5} v^{\frac{5}{2}} - \frac{2}{v ^{\frac{1}{2}}} + C

解答ステップ

\int v^{\frac{3}{2}} + \frac{1}{v ^{\frac{3}{2}}} d v

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 v^{\frac{3}{2}} d v + \int \frac{1}{v ^{\frac{3}{2}}} d v

\int v^{\frac{3}{2}} d v = \frac{2}{5} v^{\frac{5}{2}}

\int \frac{1}{v ^{\frac{3}{2}}} d v = - \frac{2}{v ^{\frac{1}{2}}}

= \frac{2}{5} v^{\frac{5}{2}} - \frac{2}{v ^{\frac{1}{2}}}

定数を解答に追加する

= \frac{2}{5} v^{\frac{5}{2}} - \frac{2}{v ^{\frac{1}{2}}} + C