integral of (\sqrt[11]{x}+\sqrt[12]{x})

解

\int (11 x + 12 x) d x

\frac{11}{12} x^{\frac{12}{11}} + \frac{12}{13} x^{\frac{13}{12}} + C

解答ステップ

\int 11 x + 12 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

= \int 11 x d x + \int 12 x d x

\int 11 x d x = \frac{11}{12} x^{\frac{12}{11}}

\int 12 x d x = \frac{12}{13} x^{\frac{13}{12}}

= \frac{11}{12} x^{\frac{12}{11}} + \frac{12}{13} x^{\frac{13}{12}}

定数を解答に追加する

= \frac{11}{12} x^{\frac{12}{11}} + \frac{12}{13} x^{\frac{13}{12}} + C