ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

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

解

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

解

\frac{1}{4}

+1

十進法表記

0.25

解答ステップ

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

定数を除く:

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

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

u置換積分法を適用する

= \frac{1}{2} \cdot \int_{0}^{1} u d u

べき乗則を適用する

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

限度を計算する:

\frac{1}{2}

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

簡素化

= \frac{1}{4}

グラフ

人気の例

integral from 2 to 4 of (3x-1+2x^2)

\int_{2}^{4} (3 x - 1 + 2 x^{2}) d x

integral from 0 to 1 of 4xe^{-2x}

\int_{0}^{1} 4 x e^{- 2 x} d x

integral from 0 to pi of (sin^2(x))/2

\int_{0}^{π} \frac{sin ^{2} ( x )}{2} d x

integral from 1 to e^3 of (1-ln(x))/x

\int_{1}^{e^{3}} \frac{1 - ln ( x )}{x} d x

integral from 0 to 1 of e^{2t}

\int_{0}^{1} e^{2 t} d t