integral from 1 to 2 of (ln(x))/(x^3)

解

\int_{1}^{2} \frac{ln ( x )}{x ^{3}} d x

\frac{3}{16} - \frac{1}{8} ln (2)

十進法表記

0.10085 \dots

解答ステップ

\int_{1}^{2} \frac{ln ( x )}{x ^{3}} d x

部分積分を適用する

= [- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x]_{1}^{2}

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= [- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}]_{1}^{2}

限度を計算する:

\frac{3}{16} - \frac{1}{8} ln (2)

= \frac{3}{16} - \frac{1}{8} ln (2)