integral of 1/3 sin(x)-1/4 cos(x)

解

\int \frac{1}{3} sin (x) - \frac{1}{4} cos (x) d x

- \frac{1}{3} cos (x) - \frac{1}{4} sin (x) + C

解答ステップ

\int \frac{1}{3} sin (x) - \frac{1}{4} 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{1}{3} sin (x) d x - \int \frac{1}{4} cos (x) d x

\int \frac{1}{3} sin (x) d x = - \frac{1}{3} cos (x)

\int \frac{1}{4} cos (x) d x = \frac{1}{4} sin (x)

= - \frac{1}{3} cos (x) - \frac{1}{4} sin (x)

定数を解答に追加する

= - \frac{1}{3} cos (x) - \frac{1}{4} sin (x) + C