integral of (5tan(x)-2cos^2(x))/(cos(x))

解

\int \frac{5 tan ( x ) - 2 cos ^{2} ( x )}{cos ( x )} d x

5 sec (x) - 2 sin (x) + C

解答ステップ

\int \frac{5 tan ( x ) - 2 cos ^{2} ( x )}{cos ( x )} d x

拡張

\frac{5 tan ( x ) - 2 cos ^{2} ( x )}{cos ( x )} : \frac{5 tan ( x )}{cos ( x )} - 2 cos (x)

= \int \frac{5 tan ( x )}{cos ( x )} - 2 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{5 tan ( x )}{cos ( x )} d x - \int 2 cos (x) d x

\int \frac{5 tan ( x )}{cos ( x )} d x = 5 sec (x)

\int 2 cos (x) d x = 2 sin (x)

= 5 sec (x) - 2 sin (x)

定数を解答に追加する

= 5 sec (x) - 2 sin (x) + C