integral of cos(x)+1/6 x

解

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

sin (x) + \frac{x ^{2}}{12} + C

解答ステップ

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

\int cos (x) d x = sin (x)

\int \frac{1}{6} x d x = \frac{x ^{2}}{12}

= sin (x) + \frac{x ^{2}}{12}

定数を解答に追加する

= sin (x) + \frac{x ^{2}}{12} + C