integral of (arccos(x)-ln(x))

解

\int (arccos (x) - ln (x)) d x

x arccos (x) - 1 - x^{2} - x ln (x) + x + C

解答ステップ

\int arccos (x) - ln (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 arccos (x) d x - \int ln (x) d x

\int arccos (x) d x = x arccos (x) - 1 - x^{2}

\int ln (x) d x = x ln (x) - x

= x arccos (x) - 1 - x^{2} - (x ln (x) - x)

簡素化

= x arccos (x) - 1 - x^{2} - x ln (x) + x

定数を解答に追加する

= x arccos (x) - 1 - x^{2} - x ln (x) + x + C