第三周第一节课。

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unlockable
2023-03-09 17:35:53 +08:00
parent 45e60b1ac1
commit 81c1f824fc
4 changed files with 167 additions and 5 deletions

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@@ -586,7 +586,7 @@ C^n [a,b] = \{f \in C[a,b] \mid f^{(n)} \in C[a,b]\}\]
$p \neq 1$时,
\begin{align*}
\int_e^{+\infty} \frac{1}{x(\ln x)^p \dif x} & = \int_e^{+\infty} \frac{1}{(\ln x)^p} \dif \ln x\\
\int_e^{+\infty} \frac{1}{x(\ln x)^p} \dif x & = \int_e^{+\infty} \frac{1}{(\ln x)^p} \dif \ln x\\
& = \eval{\frac{1}{1 - p}(\ln x)^{1 - p}}_e^{+\infty}\\
& = \begin{cases}
\frac{1}{p - 1}, p > 1\\