integral of 2(sin(x)-cos(x)+1)

解

\int 2 (sin (x) - cos (x) + 1) d x

2 (- cos (x) - sin (x) + x) + C

解答ステップ

\int 2 (sin (x) - cos (x) + 1) d x

定数を除く:

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

= 2 \cdot \int sin (x) - cos (x) + 1 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

= 2 (\int sin (x) d x - \int cos (x) d x + \int 1 d x)

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

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

\int 1 d x = x

= 2 (- cos (x) - sin (x) + x)

定数を解答に追加する

= 2 (- cos (x) - sin (x) + x) + C