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

解答

\int (3 sin (x) - 4 cos (x)) d x

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

求解步骤

\int 3 sin (x) - 4 cos (x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 sin (x) d x - \int 4 cos (x) d x

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

\int 4 cos (x) d x = 4 sin (x)

= - 3 cos (x) - 4 sin (x)

解答补常数

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