integral of rivative of cos(x)

解

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

x \frac{d}{d x} (cos (x)) + x sin (x) + cos (x) + C

解答ステップ

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

部分積分を適用する

= x \frac{d}{d x} (cos (x)) - \int - x cos (x) d x

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

= x \frac{d}{d x} (cos (x)) - (- x sin (x) - cos (x))

簡素化

= x \frac{d}{d x} (cos (x)) + x sin (x) + cos (x)

定数を解答に追加する

= x \frac{d}{d x} (cos (x)) + x sin (x) + cos (x) + C