integral from 1 to 2 of (ln(x))/(x^{10)}

解

\int_{1}^{2} \frac{ln ( x )}{x ^{10}} d x

\frac{511}{41472} - \frac{1}{4608} ln (2)

十進法表記

0.01217 \dots

解答ステップ

\int_{1}^{2} \frac{ln ( x )}{x ^{10}} d x

部分積分を適用する

= [- \frac{ln ( x )}{9 x ^{9}} - \int - \frac{1}{9 x ^{10}} d x]_{1}^{2}

\int - \frac{1}{9 x ^{10}} d x = \frac{1}{81 x ^{9}}

= [- \frac{ln ( x )}{9 x ^{9}} - \frac{1}{81 x ^{9}}]_{1}^{2}

限度を計算する:

\frac{511}{41472} - \frac{1}{4608} ln (2)

= \frac{511}{41472} - \frac{1}{4608} ln (2)