integral of 12x^{5/7}+5x^{-6/7}

解

\int 12 x^{\frac{5}{7}} + 5 x^{- \frac{6}{7}} d x

7 x^{\frac{12}{7}} + 35 x^{\frac{1}{7}} + C

解答ステップ

\int 12 x^{\frac{5}{7}} + 5 x^{- \frac{6}{7}} 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 12 x^{\frac{5}{7}} d x + \int 5 x^{- \frac{6}{7}} d x

\int 12 x^{\frac{5}{7}} d x = 7 x^{\frac{12}{7}}

\int 5 x^{- \frac{6}{7}} d x = 35 x^{\frac{1}{7}}

= 7 x^{\frac{12}{7}} + 35 x^{\frac{1}{7}}

定数を解答に追加する

= 7 x^{\frac{12}{7}} + 35 x^{\frac{1}{7}} + C