integral from 0 to ln(3) of e^{2x}-e^x

解答

\int_{0}^{l n (3)} e^{2 x} - e^{x} d x

2

求解步骤

\int_{0}^{l n (3)} e^{2 x} - e^{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_{0}^{l n (3)} e^{2 x} d x - \int_{0}^{l n (3)} e^{x} d x

\int_{0}^{l n (3)} e^{2 x} d x = 4

\int_{0}^{l n (3)} e^{x} d x = 2

= 4 - 2

化简

= 2

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