integral from 1 to e of ln(16x)

解答

\int_{1}^{e} ln (16 x) d x

e ln (16 e) - e - 4 ln (2) + 1

十进制

5.76408 \dots

求解步骤

\int_{1}^{e} ln (16 x) d x

使用分布积分法

= [x ln (16 x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (16 x) - x]_{1}^{e}

带入上下限计算后得:

e ln (16 e) - e - 4 ln (2) + 1

= e ln (16 e) - e - 4 ln (2) + 1

x \to 1 lim (\frac{4 - 3 x}{1 - x})

\int_{1}^{1000} \frac{17}{x ^{3}} d x

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