integral from 1 to 5 of (ln(x))/(x^7)

解

\int_{1}^{5} \frac{ln ( x )}{x ^{7}} d x

\frac{434}{15625} - \frac{1}{93750} ln (5)

十進法表記

0.02775 \dots

解答ステップ

\int_{1}^{5} \frac{ln ( x )}{x ^{7}} d x

部分積分を適用する

= [- \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x]_{1}^{5}

\int - \frac{1}{6 x ^{7}} d x = \frac{1}{36 x ^{6}}

= [- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}]_{1}^{5}

限度を計算する:

\frac{434}{15625} - \frac{1}{93750} ln (5)

= \frac{434}{15625} - \frac{1}{93750} ln (5)