积分 1-cos(6x)

解答

积分

1 - cos (6 x)

x - \frac{1}{6} sin (6 x) + C

求解步骤

\int 1 - cos (6 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 1 d x - \int cos (6 x) d x

\int 1 d x = x

\int cos (6 x) d x = \frac{1}{6} sin (6 x)

= x - \frac{1}{6} sin (6 x)

解答补常数

= x - \frac{1}{6} sin (6 x) + C

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