integral of (sqrt(x)+1/(\sqrt[6]{x)})

解

\int (x + \frac{1}{6 x}) d x

\frac{2}{3} x^{\frac{3}{2}} + \frac{6}{5} x^{\frac{5}{6}} + C

解答ステップ

\int x + \frac{1}{6 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 x d x + \int \frac{1}{6 x} d x

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

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

= \frac{2}{3} x^{\frac{3}{2}} + \frac{6}{5} x^{\frac{5}{6}}

定数を解答に追加する

= \frac{2}{3} x^{\frac{3}{2}} + \frac{6}{5} x^{\frac{5}{6}} + C