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 x^5ln(x^2)

解

\int_{1}^{e} x^{5} ln (x^{2}) d x

解

\frac{5 e ^{6} + 1}{18}

+1

十進法表記

112.11910 \dots

解答ステップ

\int_{1}^{e} x^{5} ln (x^{2}) d x

部分積分を適用する

= [\frac{1}{6} (x^{6} ln (x^{2}) - 6 \cdot \int \frac{x ^{5}}{3} d x)]_{1}^{e}

\int \frac{x ^{5}}{3} d x = \frac{x ^{6}}{18}

= [\frac{1}{6} (x^{6} ln (x^{2}) - 6 \cdot \frac{x ^{6}}{18})]_{1}^{e}

簡素化

[\frac{1}{6} (x^{6} ln (x^{2}) - 6 \cdot \frac{x ^{6}}{18})]_{1}^{e} : [\frac{1}{6} (2 x^{6} ln (x) - \frac{x ^{6}}{3})]_{1}^{e}

= [\frac{1}{6} (2 x^{6} ln (x) - \frac{x ^{6}}{3})]_{1}^{e}

限度を計算する:

\frac{5 e ^{6}}{18} + \frac{1}{18}

= \frac{5 e ^{6}}{18} + \frac{1}{18}

簡素化

= \frac{5 e ^{6} + 1}{18}

グラフ

人気の例

integral from y^2 to y of sqrt(x/y)

\int_{y^{2}}^{y} \frac{x}{y} d x

integral from 0 to 2pi of |sin(2x)|

\int_{0}^{2 π} ∣ sin (2 x) ∣ d x

integral from 0 to 1 of (6x^2+15/2 x^3)

\int_{0}^{1} (6 x^{2} + \frac{15}{2} x^{3}) d x

integral from 0 to 1 of xcosh(2x)

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

integral from 3 to 6 of sqrt(x-2)

\int_{3}^{6} x - 2 d x