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人気のある微分積分 >

integral from 1 to 5 of xln(x)

解

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

解

- 6 + \frac{25}{2} ln (5)

+1

十進法表記

14.11797 \dots

解答ステップ

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

部分積分を適用する

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

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{5}

限度を計算する:

- 6 + \frac{25}{2} ln (5)

= - 6 + \frac{25}{2} ln (5)

グラフ

人気の例

integral from 2 to 3 of sqrt(9-r^2)r

\int_{2}^{3} 9 - r^{2} r d r

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\int_{0}^{9} \frac{8}{( 3 + x ) ^{2}} d x

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\int_{0}^{1} e^{\frac{x}{2}} d x

integral from 0 to 1 of k(1-x)

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

integral from 1 to 4 of x^2-x-6

\int_{1}^{4} x^{2} - x - 6 d x