integral from 1 to 3 of 2x+2/x

解答

\int_{1}^{3} 2 x + \frac{2}{x} d x

8 + 2 ln (3)

十进制

10.19722 \dots

求解步骤

\int_{1}^{3} 2 x + \frac{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_{1}^{3} 2 x d x + \int_{1}^{3} \frac{2}{x} d x

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} \frac{2}{x} d x = 2 ln (3)

= 8 + 2 ln (3)

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