Интеграл asin(e^-x) d{x}

                                      /                             
  /                                  |                              
 |                                   |              -x              
 |     / -x\                / -x\    |           x*e                
 | asin\e  / dx = C + x*asin\e  / +  | -------------------------- dx
 |                                   |    _______________________   
/                                    |   /  /     -x\ /      -x\    
                                     | \/  -\1 + e  /*\-1 + e  /    
                                     |                              
                                    /                               

$${{2\,\int {{{x\,e^{{{\log \left(e^{x}+1\right)}\over{2}}+{{\log \left(e^{x}-1\right)}\over{2}}+2\,x}}\over{\left(e^{2\,x}-1\right)\, e^{\log \left(e^{x}+1\right)+\log \left(e^{x}-1\right)}+e^{2\,x}-1}} }{\;dx}-2\,i\,\int {{{x\,e^{2\,x}}\over{\left(e^{2\,x}-1\right)\,e^{ \log \left(e^{x}+1\right)+\log \left(e^{x}-1\right)}+e^{2\,x}-1}} }{\;dx}+i\,x\,\log \left(e^{x}+1\right)+i\,{\it li}_{2}(e^{x})+i\, {\it li}_{2}(-e^{x})+i\,x\,\log \left(1-e^{x}\right)-i\,x^2+2\, {\rm atan2}\left(1 , \sqrt{e^{x}-1}\,\sqrt{e^{x}+1}\right)\,x}\over{ 2}}$$

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