oldk1331@gmail.com schrieb:   
   >   
   > FYI, the site is back on.  However the result for this integral is   
   > very long.   
      
   Thanks! And (1 + x)/((1 + x + x^2)*(2 + x^3)^(1/3)) can at least be   
   integrated by FriCAS 1.3.0; converted to Derive expressions, the   
   integral and result are:   
      
   INT((1+x)/((1+x+x^2)*(2+x^3)^(1/3)),x)   
      
   (4*(-1)^(1/6)*3^(1/2)*(243^(1/6))^5*ATAN(((((20148*x^10+(-48258)~   
   *x^9+(-44058)*x^8+222432*x^7+(-98040)*x^6+(-328872)*x^5+391308*x~   
   ^4+36024*x^3+(-315408)*x^2+218880*x+(-6528))*(-1)^(1/6)*3^(1/2)*~   
   (243^(1/6))^5+((-138186)*x^10+(-3402)*x^9+1361934*x^8+(-2311092)~   
   *x^7+(-2674944)*x^6+8787528*x^5+(-2206116)*x^4+(-13275576)*x^3+9~   
   905328*x^2+5971968*x+(-9183456))*((-1)^(1/6))^4*3^(1/2)*(243^(1/~   
   6))^2)*((x^3+2)^(1/3))^2+((83961*x^11+(-177570)*x^10+(-286110)*x~   
   ^9+1430892*x^8+(-674892)*x^7+(-3467340)*x^6+4966164*x^5+2155464*~   
   x^4+(-8587296)*x^3+3393288*x^2+4851216*x+(-4101120))*((-1)^(1/6)~   
   )^3*3^(1/2)*(243^(1/6))^3+((-1696707)*x^11+5782914*x^10+(-10854)~   
   *x^9+(-22530960)*x^8+26293572*x^7+25187436*x^6+(-63079884)*x^5+1~   
   5483960*x^4+57192480*x^3+(-42803640)*x^2+(-7787664)*x+26845344)*~   
   3^(1/2))*(x^3+2)^(1/3)+(((-43125)*x^12+153686*x^11+(-72898)*x^10~   
   +(-640678)*x^9+1265808*x^8+228000*x^7+(-3098976)*x^6+2642712*x^5~   
   +2366736*x^4+(-4644456)*x^3+1037392*x^2+2577760*x+(-1491296))*((~   
   -1)^(1/6))^2*3^(1/2)*(243^(1/6))^4+((-533889)*x^12+2296242*x^11+~   
   (-884142)*x^10+(-9565974)*x^9+17276328*x^8+6220800*x^7+(-4336200~   
   0)*x^6+31830408*x^5+32555520*x^4+(-60375384)*x^3+15129936*x^2+28~   
   640736*x+(-24234624))*((-1)^(1/6))^5*3^(1/2)*243^(1/6)))*((((144~   
   812448*x^4+285157584*x^3+(-421035408)*x^2+724062240*x+570315168)~   
   *(-1)^(1/6)*(243^(1/6))^5+(3829524480*x^4+(-40205808)*x^3+116091~   
   90864*x^2+19147622400*x+(-80411616))*((-1)^(1/6))^4*(243^(1/6))^~   
   2)*((x^3+2)^(1/3))^2+((2566418256*x^5+3789318672*x^4+(-651656016~   
   0)*x^3+(-17964927792)*x^2+(-7578637344)*x+2606624064)*((-1)^(1/6~   
   ))^3*(243^(1/6))^3+(361852272*x^5+104482717776*x^4+172328601600*~   
   x^3+(-2532965904)*x^2+(-208965435552)*x+(-68931440640)))*(x^3+2)~   
   ^(1/3)+((1000285200*x^6+1258638912*x^5+(-4295233008)*x^4+(-15169~   
   92624)*x^3+7703722080*x^2+1648403136*x+(-2009505024))*((-1)^(1/6~   
   ))^2*(243^(1/6))^4+(3708907056*x^6+(-42526827360)*x^5+(-30193931~   
   952)*x^4+88762561776*x^3+6613697952*x^2+(-108030801600)*x+(-2281~   
   6323648))*((-1)^(1/6))^5*243^(1/6)))/(x^6+3*x^5+6*x^4+7*x^3+6*x^~   
   2+3*x+1))^(1/2)+(((2138769360*x^10+(-2566523232)*x^9+(-158268932~   
   64)*x^8+35503571376*x^7+5988554208*x^6+(-99238898304)*x^5+650185~   
   88544*x^4+65018588544*x^3+(-104371944768)*x^2+(-10266092928)*x+2~   
   3954216832)*((-1)^(1/6))^2*3^(1/2)*(243^(1/6))^4+((-82128743424)~   
   *x^10+359313252480*x^9+(-458124396912)*x^8+(-835403312016)*x^7+2~   
   748746381472*x^6+(-1509115660416)*x^5+(-3557201199552)*x^4+54820~   
   93623552*x^3+(-631364715072)*x^2+(-3736857825792)*x+284370774105~   
   6)*((-1)^(1/6))^5*3^(1/2)*243^(1/6))*((x^3+2)^(1/3))^2+(((-32319~   
   18144)*x^11+10123508304*x^10+4372595136*x^9+(-49191695280)*x^8+3~   
   9068186976*x^7+89257974624*x^6+(-151139701440)*x^5+(-30227940288~   
   )*x^4+224143028928*x^3+(-100569688128)*x^2+(-115208376192)*x+105~   
   702734592)*(-1)^(1/6)*3^(1/2)*(243^(1/6))^5+(8982831312*x^11+320~   
   81540400*x^10+(-125759638368)*x^9+11549354544*x^8+438875472672*x~   
   ^7+(-485072890848)*x^6+(-292583648448)*x^5+1000944060480*x^4+(-3~   
   84978484800)*x^3+(-559502064576)*x^2+503038553472*x+164257486848~   
   )*((-1)^(1/6))^4*3^(1/2)*(243^(1/6))^2)*(x^3+2)^(1/3)+(((-834120~   
   0504)*x^12+15399139392*x^11+7699569696*x^10+(-35931325248)*x^9+2~   
   3098709088*x^7+123193115136*x^6+(-184789672704)*x^5+(-1385922545~   
   28)*x^4+518437692864*x^3+(-246386230272)*x^2+(-307982787840)*x+3~   
   90111531264)*((-1)^(1/6))^3*3^(1/2)*(243^(1/6))^3+(56463511104*x~   
   ^12+(-296433433296)*x^11+65446342416*x^10+1321759464480*x^9+(-26~   
   10154126944)*x^8+(-785356108992)*x^7+6298248011328*x^6+(-5220308~   
   253888)*x^5+(-4758334072128)*x^4+7535312209152*x^3+(-15399139392~   
   00)*x^2+(-4188565914624)*x+379845438336)*3^(1/2))))/(70643551960~   
   8*x^12+(-2829591863280)*x^11+1374373190736*x^10+11726444647008*x~   
   ^9+(-21551095579104)*x^8+(-5474394053856)*x^7+54235768938624*x^6~   
   +(-42270637631040)*x^5+(-39637384795008)*x^4+81784829310912*x^3+~   
   (-18478967270400)*x^2+(-41392886685696)*x+31629832311168))+(4*(-~   
   1)^(1/6)*3^(1/2)*(243^(1/6))^5*ATAN(((((20148*x^10+(-48258)*x^9+~   
   (-44058)*x^8+222432*x^7+(-98040)*x^6+(-328872)*x^5+391308*x^4+36~   
   024*x^3+(-315408)*x^2+218880*x+(-6528))*(-1)^(1/6)*3^(1/2)*(243^~   
   (1/6))^5+(138186*x^10+3402*x^9+(-1361934)*x^8+2311092*x^7+267494~   
   4*x^6+(-8787528)*x^5+2206116*x^4+13275576*x^3+(-9905328)*x^2+(-5~   
   971968)*x+9183456)*((-1)^(1/6))^4*3^(1/2)*(243^(1/6))^2)*((x^3+2~   
   )^(1/3))^2+((83961*x^11+(-177570)*x^10+(-286110)*x^9+1430892*x^8~   
   +(-674892)*x^7+(-3467340)*x^6+4966164*x^5+2155464*x^4+(-8587296)~   
   *x^3+3393288*x^2+4851216*x+(-4101120))*((-1)^(1/6))^3*3^(1/2)*(2~   
   43^(1/6))^3+(1696707*x^11+(-5782914)*x^10+10854*x^9+22530960*x^8~   
   +(-26293572)*x^7+(-25187436)*x^6+63079884*x^5+(-15483960)*x^4+(-~   
   57192480)*x^3+42803640*x^2+7787664*x+(-26845344))*3^(1/2))*(x^3+~   
   2)^(1/3)+((43125*x^12+(-153686)*x^11+72898*x^10+640678*x^9+(-126~   
   5808)*x^8+(-228000)*x^7+3098976*x^6+(-2642712)*x^5+(-2366736)*x^~   
   4+4644456*x^3+(-1037392)*x^2+(-2577760)*x+1491296)*((-1)^(1/6))^~   
   2*3^(1/2)*(243^(1/6))^4+((-533889)*x^12+2296242*x^11+(-884142)*x~   
   ^10+(-9565974)*x^9+17276328*x^8+6220800*x^7+(-43362000)*x^6+3183~   
   0408*x^5+32555520*x^4+(-60375384)*x^3+15129936*x^2+28640736*x+(-~   
   24234624))*((-1)^(1/6))^5*3^(1/2)*243^(1/6)))*(((((-144812448)*x~   
   ^4+(-285157584)*x^3+421035408*x^2+(-724062240)*x+(-570315168))*(~   
   -1)^(1/6)*(243^(1/6))^5+(3829524480*x^4+(-40205808)*x^3+11609190~   
   864*x^2+19147622400*x+(-80411616))*((-1)^(1/6))^4*(243^(1/6))^2)~   
   *((x^3+2)^(1/3))^2+(((-2566418256)*x^5+(-3789318672)*x^4+6516560~   
   160*x^3+17964927792*x^2+7578637344*x+(-2606624064))*((-1)^(1/6))~   
   ^3*(243^(1/6))^3+(361852272*x^5+104482717776*x^4+172328601600*x^~   
   3+(-2532965904)*x^2+(-208965435552)*x+(-68931440640)))*(x^3+2)^(~   
   1/3)+((1000285200*x^6+1258638912*x^5+(-4295233008)*x^4+(-1516992~   
   624)*x^3+7703722080*x^2+1648403136*x+(-2009505024))*((-1)^(1/6))~   
   ^2*(243^(1/6))^4+((-3708907056)*x^6+42526827360*x^5+30193931952*~   
   x^4+(-88762561776)*x^3+(-6613697952)*x^2+108030801600*x+22816323~   
   648)*((-1)^(1/6))^5*243^(1/6)))/(x^6+3*x^5+6*x^4+7*x^3+6*x^2+3*x~   
   +1))^(1/2)+((((-2138769360)*x^10+2566523232*x^9+15826893264*x^8+~   
   (-35503571376)*x^7+(-5988554208)*x^6+99238898304*x^5+(-650185885~   
   44)*x^4+(-65018588544)*x^3+104371944768*x^2+10266092928*x+(-2395~   
   4216832))*((-1)^(1/6))^2*3^(1/2)*(243^(1/6))^4+((-82128743424)*x~   
   ^10+359313252480*x^9+(-458124396912)*x^8+(-835403312016)*x^7+274~   
   8746381472*x^6+(-1509115660416)*x^5+(-3557201199552)*x^4+5482093~   
   623552*x^3+(-631364715072)*x^2+(-3736857825792)*x+2843707741056)~   
      
   [continued in next message]   
      
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