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人気のある微分積分 >

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

解

\int_{e}^{l n (x)} ln (x) d x

解

ln (x) ln (ln (x)) - ln (x)

解答ステップ

\int_{e}^{l n (x)} ln (x) d x

部分積分を適用する

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

\int 1 d x = x

= [x ln (x) - x]_{e}^{l n (x)}

限度を計算する:

ln (x) ln (ln (x)) - ln (x)

= ln (x) ln (ln (x)) - ln (x)

人気の例

integral from 0 to 3 of 6x^2

\int_{0}^{3} 6 x^{2} d x

integral from-pi/3 to pi/3 of 2sin(x)

\int_{- \frac{π}{3}}^{\frac{π}{3}} 2 sin (x) d x

integral from-1 to 2 of (x+2)^2-(x^2)^2

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

integral from 0 to 1 of pi(xe^x)^2

\int_{0}^{1} π (x e^{x})^{2} d x

integral from 0 to 1 of sin^4(x)*cos(x)

\int_{0}^{1} sin^{4} (x) \cdot cos (x) d x