integral of cos(1/5)x

解

\int cos (\frac{1}{5}) x d x

\frac{1}{2} cos (\frac{1}{5}) x^{2} + C

解答ステップ

\int cos (\frac{1}{5}) x d x

定数を除く:

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

= cos (\frac{1}{5}) \cdot \int x d x

べき乗則を適用する

= cos (\frac{1}{5}) \frac{x ^{2}}{2}

簡素化

cos (\frac{1}{5}) \frac{x ^{2}}{2} : \frac{1}{2} cos (\frac{1}{5}) x^{2}

= \frac{1}{2} cos (\frac{1}{5}) x^{2}

定数を解答に追加する

= \frac{1}{2} cos (\frac{1}{5}) x^{2} + C