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人気のある微分積分 >

integral from 1 to 5 of (2ln(x))/x

解

\int_{1}^{5} \frac{2 ln ( x )}{x} d x

解

ln^{2} (5)

+1

十進法表記

2.59029 \dots

解答ステップ

\int_{1}^{5} \frac{2 ln ( x )}{x} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{5} \frac{ln ( x )}{x} d x

u置換積分法を適用する

= 2 \cdot \int_{0}^{l n (5)} u d u

べき乗則を適用する

= 2 [\frac{u ^{2}}{2}]_{0}^{l n (5)}

限度を計算する:

\frac{ln ^{2} ( 5 )}{2}

= 2 \cdot \frac{ln ^{2} ( 5 )}{2}

簡素化

= ln^{2} (5)

グラフ

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