integral from 0 to 1 of (ln(x))/(x^{1/3)}

解

\int_{0}^{1} \frac{ln ( x )}{x ^{\frac{1}{3}}} d x

- \frac{9}{4}

十進法表記

- 2.25

解答ステップ

\int_{0}^{1} \frac{ln ( x )}{x ^{\frac{1}{3}}} d x

部分積分を適用する

= [\frac{3}{2} x^{\frac{2}{3}} ln (x) - \int \frac{3}{2 x ^{\frac{1}{3}}} d x]_{0}^{1}

\int \frac{3}{2 x ^{\frac{1}{3}}} d x = \frac{9}{4} x^{\frac{2}{3}}

= [\frac{3}{2} x^{\frac{2}{3}} ln (x) - \frac{9}{4} x^{\frac{2}{3}}]_{0}^{1}

限度を計算する:

- \frac{9}{4}

= - \frac{9}{4}