悠闲数学娱乐论坛(第2版)'s Archiver

青青子衿 发表于 2019-1-4 10:30

含有对数与根式的二重瑕积分

[i=s] 本帖最后由 青青子衿 于 2019-1-4 10:31 编辑 [/i]

\[ \color{black}{\int_0^1\int_0^1 \dfrac{\ln\left(x+y\right)}{\sqrt{1+x+y\,}}{\rm\,d}x\!{\rm\,d}y} \]
\begin{array}{c}
\color{black}
-\dfrac{20}{9}+\dfrac{104}{9}\sqrt{2\,}-\dfrac{28}{3}\sqrt{3}-\dfrac{8}{3}\ln2+4\sqrt{3}\ln2\\
-\dfrac{40}{3}\ln\Big(1+\sqrt{2\,}\,\Big)+\dfrac{32}{3}\ln\Big(1+\sqrt{3\,}\,\Big)
\end{array}

页: [1]

Powered by Discuz! Archiver 7.2  © 2001-2009 Comsenz Inc.