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人気のある微分積分 >

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

解

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

解

2 ln (2) - 1

+1

十進法表記

0.38629 \dots

解答ステップ

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

u置換積分法を適用する

= \int_{1}^{2} ln (u) d u

部分積分を適用する

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

\int 1 d u = u

= [u ln (u) - u]_{1}^{2}

限度を計算する:

2 ln (2) - 1

= 2 ln (2) - 1

グラフ

人気の例

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