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

解答

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

27 + 112

十进制

117.29150 \dots

求解步骤

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

乘开

\frac{x + x ^{3}}{x} : \frac{1}{x} + x^{2}

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

\int_{1}^{7} \frac{1}{x} d x = 27 - 2

\int_{1}^{7} x^{2} d x = 114

= 27 - 2 + 114

化简

= 27 + 112

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