integral of 3e^x-2sin(x)+1

解答

\int 3 e^{x} - 2 sin (x) + 1 d x

3 e^{x} + 2 cos (x) + x + C

求解步骤

\int 3 e^{x} - 2 sin (x) + 1 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 e^{x} d x - \int 2 sin (x) d x + \int 1 d x

\int 3 e^{x} d x = 3 e^{x}

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

\int 1 d x = x

= 3 e^{x} - (- 2 cos (x)) + x

化简

= 3 e^{x} + 2 cos (x) + x

解答补常数

= 3 e^{x} + 2 cos (x) + x + C

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