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 10 of ((ln(x))/(ln(10)))

解

\int_{1}^{10} (\frac{ln ( x )}{ln ( 10 )}) d x

解

\frac{10 ln ( 10 ) - 9}{ln ( 10 )}

+1

十進法表記

6.09134 \dots

解答ステップ

\int_{1}^{10} \frac{ln ( x )}{ln ( 10 )} d x

定数を除く:

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

= \frac{1}{ln ( 10 )} \cdot \int_{1}^{10} ln (x) d x

部分積分を適用する

= \frac{1}{ln ( 10 )} [x ln (x) - \int 1 d x]_{1}^{10}

\int 1 d x = x

= \frac{1}{ln ( 10 )} [x ln (x) - x]_{1}^{10}

限度を計算する:

10 ln (10) - 9

= \frac{1}{ln ( 10 )} (10 ln (10) - 9)

簡素化

= \frac{10 ln ( 10 ) - 9}{ln ( 10 )}

グラフ

人気の例

integral from 0 to 3 of (x^2-4x+3)

\int_{0}^{3} (x^{2} - 4 x + 3) d x

integral from 1/2 to 2 of 1-1/(x^2)

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

integral from 0 to 1 of (x^4+3x^3+1)

\int_{0}^{1} (x^{4} + 3 x^{3} + 1) d x

integral from-5 to 4 of 20-x-x^2

\int_{- 5}^{4} 20 - x - x^{2} d x

integral from 2 to 3 of cx

\int_{2}^{3} c x d x