integral from 0 to 5 of (6e^{0.2x}+2x)

解答

\int_{0}^{5} (6 e^{0.2 x} + 2 x) d x

30 e - 5

十进制

76.54845 \dots

求解步骤

\int_{0}^{5} 6 e^{0.2 x} + 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_{0}^{5} 6 e^{0.2 x} d x + \int_{0}^{5} 2 x d x

\int_{0}^{5} 6 e^{0.2 x} d x = 30 (e - 1)

\int_{0}^{5} 2 x d x = 25

= 30 (e - 1) + 25

化简

30 (e - 1) + 25 : 30 e - 5

= 30 e - 5

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