integral from 1 to 10 of xln(x)

解答

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

50 ln (10) - \frac{99}{4}

十进制

90.37925 \dots

求解步骤

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

使用分布积分法

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{10}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{10}

带入上下限计算后得:

50 ln (10) - \frac{99}{4}

= 50 ln (10) - \frac{99}{4}

x \to \infty lim (3 x - 9 x^{2} + x)

\int \frac{3 x - 1}{x ^{2} + 10 x + 28} d x

d er i v a t i v e x^{2} sin^{6} (x) + x cos^{- 3} (x)

\frac{d}{d x} (\frac{e ^{2 x}}{e ^{2 x} + 1})

\frac{d}{d y} (\frac{y}{y + \frac{c}{y}})