integral of sin(x)+sec^2(x)+sec(x)tan(x)

解

\int sin (x) + sec^{2} (x) + sec (x) tan (x) d x

- cos (x) + tan (x) + sec (x) + C

解答ステップ

\int sin (x) + sec^{2} (x) + sec (x) tan (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 sin (x) d x + \int sec^{2} (x) d x + \int sec (x) tan (x) d x

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

\int sec^{2} (x) d x = tan (x)

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

= - cos (x) + tan (x) + sec (x)

定数を解答に追加する

= - cos (x) + tan (x) + sec (x) + C