integral from 1 to 3 of (ln(x))/(x^5)

解

\int_{1}^{3} \frac{ln ( x )}{x ^{5}} d x

\frac{5}{81} - \frac{1}{324} ln (3)

十進法表記

0.05833 \dots

解答ステップ

\int_{1}^{3} \frac{ln ( x )}{x ^{5}} d x

部分積分を適用する

= [- \frac{ln ( x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x]_{1}^{3}

\int - \frac{1}{4 x ^{5}} d x = \frac{1}{16 x ^{4}}

= [- \frac{ln ( x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}]_{1}^{3}

限度を計算する:

\frac{5}{81} - \frac{1}{324} ln (3)

= \frac{5}{81} - \frac{1}{324} ln (3)