integral from 0 to 2 of ln(x^3)

解答

\int_{0}^{2} ln (x^{3}) d x

6 ln (2) - 6

十进制

- 1.84111 \dots

求解步骤

\int_{0}^{2} ln (x^{3}) d x

使用分布积分法

= [x ln (x^{3}) - \int 3 d x]_{0}^{2}

\int 3 d x = 3 x

= [x ln (x^{3}) - 3 x]_{0}^{2}

使用对数运算法则:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

假定

x \geq 0

= [3 x ln (x) - 3 x]_{0}^{2}

带入上下限计算后得:

6 ln (2) - 6

= 6 ln (2) - 6

\int_{3 x}^{8} \frac{x + y}{60} d y

\int_{1}^{k} \frac{k}{2 w ^{2}} d w

\int_{1}^{5} x^{4} ln (x) d x

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\int_{1}^{2} ∣ 2 x - 3 ∣ d x