integral of (ln(x))/(x^{3/2)}

解

\int \frac{ln ( x )}{x ^{\frac{3}{2}}} d x

- \frac{2 ln ( x )}{x ^{\frac{1}{2}}} - \frac{4}{x ^{\frac{1}{2}}} + C

解答ステップ

\int \frac{ln ( x )}{x ^{\frac{3}{2}}} d x

部分積分を適用する

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

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

= - \frac{2 ln ( x )}{x ^{\frac{1}{2}}} - \frac{4}{x ^{\frac{1}{2}}}

定数を解答に追加する

= - \frac{2 ln ( x )}{x ^{\frac{1}{2}}} - \frac{4}{x ^{\frac{1}{2}}} + C