integral of (sec(x)+tan(x))/(cos(x))

解

\int \frac{sec ( x ) + tan ( x )}{cos ( x )} d x

tan (x) + sec (x) + C

解答ステップ

\int \frac{sec ( x ) + tan ( x )}{cos ( x )} d x

拡張

\frac{sec ( x ) + tan ( x )}{cos ( x )} : \frac{sec ( x )}{cos ( x )} + \frac{tan ( x )}{cos ( x )}

= \int \frac{sec ( x )}{cos ( x )} + \frac{tan ( x )}{cos ( 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 \frac{sec ( x )}{cos ( x )} d x + \int \frac{tan ( x )}{cos ( x )} d x

\int \frac{sec ( x )}{cos ( x )} d x = tan (x)

\int \frac{tan ( x )}{cos ( x )} d x = sec (x)

= tan (x) + sec (x)

定数を解答に追加する

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