integral of (-3cos(x)+4sec^2(x))

解

\int (- 3 \cdot cos (x) + 4 \cdot sec^{2} (x)) d x

- 3 sin (x) + 4 tan (x) + C

解答ステップ

\int - 3 cos (x) + 4 sec^{2} (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 3 cos (x) d x + \int 4 sec^{2} (x) d x

\int 3 cos (x) d x = 3 sin (x)

\int 4 sec^{2} (x) d x = 4 tan (x)

= - 3 sin (x) + 4 tan (x)

定数を解答に追加する

= - 3 sin (x) + 4 tan (x) + C