integral of ln(x)+sin(x)+8

解

\int ln (x) + sin (x) + 8 d x

x ln (x) + 7 x - cos (x) + C

解答ステップ

\int ln (x) + sin (x) + 8 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 ln (x) d x + \int sin (x) d x + \int 8 d x

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

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

\int 8 d x = 8 x

= x ln (x) - x - cos (x) + 8 x

簡素化

= x ln (x) + 7 x - cos (x)

定数を解答に追加する

= x ln (x) + 7 x - cos (x) + C