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人気のある微分積分 >

integral from 1 to e of (4ln(x))/x

解

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

解

2

解答ステップ

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

定数を除く:

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

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

u置換積分法を適用する

= 4 \cdot \int_{0}^{1} u d u

べき乗則を適用する

= 4 [\frac{u ^{2}}{2}]_{0}^{1}

限度を計算する:

\frac{1}{2}

= 4 \cdot \frac{1}{2}

簡素化

= 2

グラフ

人気の例

integral from 0 to infinity of t

\int_{0}^{\infty} t d t

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\int_{0}^{1} (5 x^{3} - \frac{1}{2}) d x

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\int_{1}^{6} t^{2} - 4 t - 12 d t

integral from-7 to 8 of | 1/2 x|

\int_{- 7}^{8} \frac{1}{2} x d x

integral from 0 to 6 of-5/12 x^2-5x

\int_{0}^{6} - \frac{5}{12} x^{2} - 5 x d x