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人気のある微分積分 >

integral from 1 to e of (x+1)ln(x)

解

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

解

\frac{e ^{2} + 5}{4}

+1

十進法表記

3.09726 \dots

解答ステップ

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

部分積分を適用する

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

\int \frac{1}{2} (x + 2) d x = \frac{x ^{2}}{4} + x

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

簡素化

[ln (x) (\frac{x ^{2}}{2} + x) - (\frac{x ^{2}}{4} + x)]_{1}^{e} : [\frac{1}{4} (2 x^{2} ln (x) + 4 x ln (x) - x^{2} - 4 x)]_{1}^{e}

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

限度を計算する:

\frac{e ^{2}}{4} + \frac{5}{4}

= \frac{e ^{2}}{4} + \frac{5}{4}

簡素化

= \frac{e ^{2} + 5}{4}

グラフ

人気の例

integral from 1 to 4 of xsqrt(9+x^2)

\int_{1}^{4} x 9 + x^{2} d x

integral from 0 to 2 of x^3e^{x^4}

\int_{0}^{2} x^{3} e^{x^{4}} d x

integral from 0 to 3 of x+2

\int_{0}^{3} x + 2 d x

integral from-2 to 0 of 3-x^2

\int_{- 2}^{0} 3 - x^{2} d x

integral from 0 to pi/2 of cos(y)

\int_{0}^{\frac{π}{2}} cos (y) d y