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人気のある微分積分 >

integral from 1 to 3 of e^xln(x)

解

\int_{1}^{3} e^{x} ln (x) d x

解

e^{3} ln (3) - Ei (3) + Ei (1)

解答ステップ

\int_{1}^{3} e^{x} ln (x) d x

部分積分を適用する

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

\int \frac{e ^{x}}{x} d x = Ei (x)

= [e^{x} ln (x) - Ei (x)]_{1}^{3}

限度を計算する:

e^{3} ln (3) - Ei (3) + Ei (1)

= e^{3} ln (3) - Ei (3) + Ei (1)

人気の例

integral from 1 to 3 of 2/x+1

\int_{1}^{3} \frac{2}{x} + 1 d x

integral from 0 to r of (br^2+cr)2pir

\int_{0}^{r} (b r^{2} + cr) 2 π r d r

integral from 0 to pi/3 of (cos(x)+sec(x))^2

\int_{0}^{\frac{π}{3}} (cos (x) + sec (x))^{2} d x

integral from 0 to 4 of sqrt(2-\sqrt{x)}

\int_{0}^{4} 2 - x d x

integral from 0 to 1 of x(x^2-1)^3

\int_{0}^{1} x (x^{2} - 1)^{3} d x