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 4 of ((ln(x)+4)^4)/x

解

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

解

\frac{32}{5} ln^{5} (2) + 64 ln^{4} (2) + 256 ln^{3} (2) + 512 ln^{2} (2) + 512 ln (2)

+1

十進法表記

701.93507 \dots

解答ステップ

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

部分積分を適用する

= [(ln (x) + 4)^{4} - \int \frac{4 ( ln ( x ) + 4 ) ^{3} - ( ln ( x ) + 4 ) ^{4}}{x} d x]_{1}^{4}

\int \frac{4 ( ln ( x ) + 4 ) ^{3} - ( ln ( x ) + 4 ) ^{4}}{x} d x = (ln (x) + 4)^{4} - \frac{( ln ( x ) + 4 ) ^{5}}{5}

= [(ln (x) + 4)^{4} - ((ln (x) + 4)^{4} - \frac{( ln ( x ) + 4 ) ^{5}}{5})]_{1}^{4}

簡素化

[(ln (x) + 4)^{4} - ((ln (x) + 4)^{4} - \frac{( ln ( x ) + 4 ) ^{5}}{5})]_{1}^{4} : [\frac{1}{5} (ln (x) + 4)^{5}]_{1}^{4}

= [\frac{1}{5} (ln (x) + 4)^{5}]_{1}^{4}

限度を計算する:

\frac{1}{5} (2 ln (2) + 4)^{5} - \frac{1024}{5}

= \frac{1}{5} (2 ln (2) + 4)^{5} - \frac{1024}{5}

簡素化

= \frac{32}{5} ln^{5} (2) + 64 ln^{4} (2) + 256 ln^{3} (2) + 512 ln^{2} (2) + 512 ln (2)

グラフ

人気の例

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

\int_{1}^{2} \frac{x ^{2} + 3}{x ^{3} + 2 x} d x

integral from 2 to k of sqrt(x-2)

\int_{2}^{k} x - 2 d x

integral from 0 to 2 of (x^4+5)^3x^3

\int_{0}^{2} (x^{4} + 5)^{3} x^{3} d x

integral from 0 to infinity of x/(x^2+4)

\int_{0}^{\infty} \frac{x}{x ^{2} + 4} d x

integral from 0 to 1 of (1-x^2)^6

\int_{0}^{1} (1 - x^{2})^{6} d x