求解，这个不定积分？

无法初等变换，希望闹拆有所帮穗弯贺助……猜派

不定积分结果不唯一求导验证应该能够氏袜穗提高凑微分的计算能力先写歼卜别问唉。类似。数字帝国，非初等函数好纤不可积@海离薇

令1-e^2t=x，则t=½ln(1-x)
dt=-1/[2(1-x)]dx
原式=-¼∫码裂坦ln(1-x)/源晌x(1-x)dx
=-¼∫ln(1-x)[1/x+1/(1-x)]dx
=-¼∫迟桐ln(1-x)/xdx+⅛ln²(1-x)

题目对吗？请附原题印刷版图片。

Expand the following:
(x (x - 2 log(1 - e^x)))/2 - Li_2(e^x)
x (x - 2 log(1 - e^x)) = x x + x (-2 log(1 - e^x)):
(x x - 2 x log(1 - e^x))/蠢蠢衫带腔2 - Li_2(e^x)
x x = x^2:
(x^2 - 2 x log(1 - e^x))/2 - Li_2(e^x)
(x^2 - 2 x log(1 - e^x))/2 = x^2/2 - (2 x log(1 - e^x))/2:
(x^2)/2 - (2 x log(1 - e^x))/2 - Li_2(e^x)
(-2)/2 = (2 (-1))/档空2 = -1:
Answer: |
| x^2/2 + -1 x log(1 - e^x) - Li_2(e^x)