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

解

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

- \frac{2}{e} + 1

十進法表記

0.26424 \dots

解答ステップ

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

部分積分を適用する

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

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

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

x \frac{1}{x} = 1

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

限度を計算する:

- \frac{2}{e} + 1

= - \frac{2}{e} + 1