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人気のある微分積分 >

integral from 1 to 3 of (18(ln(x))^5)/x

解

\int_{1}^{3} \frac{18 ( ln ( x ) ) ^{5}}{x} d x

解

3 ln^{6} (3)

+1

十進法表記

5.27458 \dots

解答ステップ

\int_{1}^{3} \frac{18 ( ln ( x ) ) ^{5}}{x} d x

定数を除く:

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

= 18 \cdot \int_{1}^{3} \frac{( ln ( x ) ) ^{5}}{x} d x

u置換積分法を適用する

= 18 \cdot \int_{0}^{l n (3)} u^{5} d u

べき乗則を適用する

= 18 [\frac{u ^{6}}{6}]_{0}^{l n (3)}

限度を計算する:

\frac{ln ^{6} ( 3 )}{6}

= 18 \cdot \frac{ln ^{6} ( 3 )}{6}

簡素化

= 3 ln^{6} (3)

グラフ

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