integral of 5/6 x^{6/5}

解

\int \frac{5}{6} x^{\frac{6}{5}} d x

\frac{25}{66} x^{\frac{11}{5}} + C

解答ステップ

\int \frac{5}{6} x^{\frac{6}{5}} d x

定数を除く:

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

= \frac{5}{6} \cdot \int x^{\frac{6}{5}} d x

べき乗則を適用する

= \frac{5}{6} \cdot \frac{5}{11} x^{\frac{11}{5}}

簡素化

\frac{5}{6} \cdot \frac{5}{11} x^{\frac{11}{5}} : \frac{25}{66} x^{\frac{11}{5}}

= \frac{25}{66} x^{\frac{11}{5}}

定数を解答に追加する

= \frac{25}{66} x^{\frac{11}{5}} + C