integral of sec(x)tan(x)-9e^x

解

\int sec (x) tan (x) - 9 e^{x} d x

sec (x) - 9 e^{x} + C

解答ステップ

\int sec (x) tan (x) - 9 e^{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 sec (x) tan (x) d x - \int 9 e^{x} d x

\int sec (x) tan (x) d x = sec (x)

\int 9 e^{x} d x = 9 e^{x}

= sec (x) - 9 e^{x}

定数を解答に追加する

= sec (x) - 9 e^{x} + C