integral from 0 to 8 of 6xln(x)

解

\int_{0}^{8} 6 x ln (x) d x

6 (96 ln (2) - 16)

十進法表記

303.25277 \dots

解答ステップ

\int_{0}^{8} 6 x ln (x) d x

定数を除く:

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

= 6 \cdot \int_{0}^{8} x ln (x) d x

部分積分を適用する

= 6 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{8}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 6 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{8}

限度を計算する:

96 ln (2) - 16

= 6 (96 ln (2) - 16)