integral of (-2sin(2x)+2cos(2x))

解答

\int (- 2 sin (2 x) + 2 cos (2 x)) d x

cos (2 x) + sin (2 x) + C

求解步骤

\int - 2 sin (2 x) + 2 cos (2 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 2 sin (2 x) d x + \int 2 cos (2 x) d x

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

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

= - (- cos (2 x)) + sin (2 x)

化简

= cos (2 x) + sin (2 x)

解答补常数

= cos (2 x) + sin (2 x) + C

h \to 0 lim (\frac{cos ( \frac{π}{6} + h ) - \frac{3}{2}}{h})

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