integral of (sqrt(1+ln(x)))/x

解答

\int \frac{1 + ln ( x )}{x} d x

\frac{2}{3} (1 + ln (x))^{\frac{3}{2}} + C

求解步骤

\int \frac{1 + ln ( x )}{x} d x

使用换元积分法

= \int u d u

使用幂法则

= \frac{2}{3} u^{\frac{3}{2}}

u = 1 + ln (x)

代回

= \frac{2}{3} (1 + ln (x))^{\frac{3}{2}}

解答补常数

= \frac{2}{3} (1 + ln (x))^{\frac{3}{2}} + C