积分 1+e^v

解答

积分

1 + e^{v}

v + e^{v} + C

求解步骤

\int 1 + e^{v} d v

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 v + \int e^{v} d v

\int 1 d v = v

\int e^{v} d v = e^{v}

= v + e^{v}

解答补常数

= v + e^{v} + C

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