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人気のある微分積分 >

integral from 1 to 4 of (12(ln(x))^3)/x

解

\int_{1}^{4} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

解

48 ln^{4} (2)

+1

十進法表記

11.08008 \dots

解答ステップ

\int_{1}^{4} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

定数を除く:

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

= 12 \cdot \int_{1}^{4} \frac{( ln ( x ) ) ^{3}}{x} d x

u置換積分法を適用する

= 12 \cdot \int_{0}^{2 l n (2)} u^{3} d u

べき乗則を適用する

= 12 [\frac{u ^{4}}{4}]_{0}^{2 l n (2)}

限度を計算する:

4 ln^{4} (2)

= 12 \cdot 4 ln^{4} (2)

簡素化

= 48 ln^{4} (2)

グラフ

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