integral from 1 to 3 of (2x^2-7x+2)/x

解答

\int_{1}^{3} \frac{2 x ^{2} - 7 x + 2}{x} d x

2 ln (3) - 6

十进制

- 3.80277 \dots

求解步骤

\int_{1}^{3} \frac{2 x ^{2} - 7 x + 2}{x} d x

乘开

\frac{2 x ^{2} - 7 x + 2}{x} : 2 x - 7 + \frac{2}{x}

= \int_{1}^{3} 2 x - 7 + \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} 7 d x + \int_{1}^{3} \frac{2}{x} d x

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

\int_{1}^{3} 7 d x = 14

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

= 8 - 14 + 2 ln (3)

化简

= 2 ln (3) - 6

\int_{0}^{x} \frac{1}{2} d x

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