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人気のある微分積分 >

integral from e to e^2 of (ln(x))^2(1/x)

解

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

解

\frac{7}{3}

+1

十進法表記

2.33333 \dots

解答ステップ

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

簡素化

(ln (x))^{2} \frac{1}{x} : \frac{ln ^{2} ( x )}{x}

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

u置換積分法を適用する

= \int_{1}^{2} u^{2} d u

べき乗則を適用する

= [\frac{u ^{3}}{3}]_{1}^{2}

限度を計算する:

\frac{7}{3}

= \frac{7}{3}

グラフ

人気の例

integral from-1 to 1 of (x+1)/(x-1)

\int_{- 1}^{1} \frac{x + 1}{x - 1} d x

integral from 0 to 8 of |4-x|

\int_{0}^{8} ∣ 4 - x ∣ d x

integral from 2 to 4 of (4x^2)

\int_{2}^{4} (4 x^{2}) d x

integral from 1 to 2 of x^2*ln(x)

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

integral from-3 to-1 of x^2-2x

\int_{- 3}^{- 1} x^{2} - 2 x d x