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integral from-2 to 3 of (3x+2)(x+3)

解答

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

解答

\frac{185}{2}

+1

十进制

92.5

求解步骤

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

乘以

3 x + 2

的共轭根式

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

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

找到无定义的点（奇点）:

x = \frac{2}{3}

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_{- 2}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x + \int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x

\int_{- 2}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x = \frac{128}{27}

\int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x = \frac{4739}{54}

= \frac{128}{27} + \frac{4739}{54}

化简

\frac{128}{27} + \frac{4739}{54} : \frac{185}{2}

= \frac{185}{2}

作图

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