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integral from-1 to 2 of (3x^2-5x)^3

解答

\int_{- 1}^{2} (3 x^{2} - 5 x)^{3} d x

解答

\frac{2697}{28}

+1

十进制

96.32142 \dots

求解步骤

\int_{- 1}^{2} (3 x^{2} - 5 x)^{3} d x

乘以

3 x^{2} - 5 x

的共轭根式

: \frac{9 x ^{4} - 25 x ^{2}}{3 x ^{2} + 5 x}

= \int_{- 1}^{2} (\frac{9 x ^{4} - 25 x ^{2}}{3 x ^{2} + 5 x})^{3} d x

找到无定义的点（奇点）:

x = 0

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{0} (\frac{9 x ^{4} - 25 x ^{2}}{3 x ^{2} + 5 x})^{3} d x + \int_{0}^{2} (\frac{9 x ^{4} - 25 x ^{2}}{3 x ^{2} + 5 x})^{3} d x

\int_{- 1}^{0} (\frac{9 x ^{4} - 25 x ^{2}}{3 x ^{2} + 5 x})^{3} d x = \frac{2873}{28}

\int_{0}^{2} (\frac{9 x ^{4} - 25 x ^{2}}{3 x ^{2} + 5 x})^{3} d x = - \frac{44}{7}

= \frac{2873}{28} - \frac{44}{7}

化简

\frac{2873}{28} - \frac{44}{7} : \frac{2697}{28}

= \frac{2697}{28}

作图

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