1,0,0,0,1.790920," ","integrate(1/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x^{2} - 2^{\frac{2}{3}} x + 2 \cdot 2^{\frac{1}{3}}\right)}}{x^{6} + 5 \, x^{3} + 4}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x^2 - 2^(2/3)*x + 2*2^(1/3))/(x^6 + 5*x^3 + 4), x)","F",0
2,0,0,0,1.619336," ","integrate(1/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} + 1} {\left(x^{2} + 2^{\frac{2}{3}} x + 2 \cdot 2^{\frac{1}{3}}\right)}}{x^{6} - 5 \, x^{3} + 4}, x\right)"," ",0,"integral(sqrt(-x^3 + 1)*(x^2 + 2^(2/3)*x + 2*2^(1/3))/(x^6 - 5*x^3 + 4), x)","F",0
3,-2,0,0,0.000000," ","integrate(1/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
4,-2,0,0,0.000000," ","integrate(1/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
5,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,0,0,0,1.761637," ","integrate(1/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, d^{3} x^{3} + c^{3}}}{4 \, d^{4} x^{4} + 4 \, c d^{3} x^{3} + c^{3} d x + c^{4}}, x\right)"," ",0,"integral(sqrt(4*d^3*x^3 + c^3)/(4*d^4*x^4 + 4*c*d^3*x^3 + c^3*d*x + c^4), x)","F",0
10,0,0,0,2.086965," ","integrate(1/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x - \sqrt{3} + 1\right)}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x - sqrt(3) + 1)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
11,0,0,0,1.887532," ","integrate(1/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} + 1} {\left(x + \sqrt{3} - 1\right)}}{x^{5} - 2 \, x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 2}, x\right)"," ",0,"integral(sqrt(-x^3 + 1)*(x + sqrt(3) - 1)/(x^5 - 2*x^4 - 2*x^3 - x^2 + 2*x + 2), x)","F",0
12,0,0,0,1.859258," ","integrate(1/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} - 1} {\left(x + \sqrt{3} - 1\right)}}{x^{5} - 2 \, x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 2}, x\right)"," ",0,"integral(-sqrt(x^3 - 1)*(x + sqrt(3) - 1)/(x^5 - 2*x^4 - 2*x^3 - x^2 + 2*x + 2), x)","F",0
13,0,0,0,1.265248," ","integrate(1/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} {\left(x - \sqrt{3} + 1\right)}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*(x - sqrt(3) + 1)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
14,0,0,0,1.500162," ","integrate(1/(3+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1}}{x^{4} + 3 \, x^{3} + x + 3}, x\right)"," ",0,"integral(sqrt(x^3 + 1)/(x^4 + 3*x^3 + x + 3), x)","F",0
15,0,0,0,1.352080," ","integrate(1/(3+x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1}}{x^{4} + 3 \, x^{3} - x - 3}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)/(x^4 + 3*x^3 - x - 3), x)","F",0
16,0,0,0,1.155378," ","integrate(1/(3+x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1}}{x^{4} + 3 \, x^{3} - x - 3}, x\right)"," ",0,"integral(sqrt(x^3 - 1)/(x^4 + 3*x^3 - x - 3), x)","F",0
17,0,0,0,1.792892," ","integrate(1/(3+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1}}{x^{4} + 3 \, x^{3} + x + 3}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)/(x^4 + 3*x^3 + x + 3), x)","F",0
18,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(d^3*x^3-c^3)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(d^3*x^3+2*c^3)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,712,0,19.238525," ","integrate(1/(1+2^(1/3)*x)/(x^3+1)^(2/3),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(-\frac{13910019318573948542 \, \sqrt{3} {\left(44297109310930172741433829405399636654451725916403400759596345420183 \, x^{16} + 469911753877577297266687493361266274298219751726156511748796788210304 \, x^{13} - 168603219036433260440647021325346295645242325246375460547582960409424 \, x^{10} - 1978806301182376573938292954227792627373330283397876582611558332893440 \, x^{7} - 1440090891687177581422918763089301968602581036872213084389912370301872 \, x^{4} - 2^{\frac{2}{3}} {\left(52271077453125107612995923977654758349394876922885552819209999866413 \, x^{15} + 590674547854548577293285820788340778493299281255213360593997994805172 \, x^{12} + 3063142612229314316198873829666304230648222176902796253391978577817900 \, x^{9} + 7331049558697577809008352571597039403457968857066730277786114959327080 \, x^{6} + 7723244806756290443759770546780872971739444750173519635544186114816064 \, x^{3} + 2911680898783900921956348574183551415589190446015106452608070501424800\right)} + 6 \cdot 2^{\frac{1}{3}} {\left(12601355996216322093314748679149120543302140685677058235520929344665 \, x^{14} - 55586906300196651392462719491921267847820798890019850227115938089718 \, x^{11} - 450398920105320599307639536027883986131793624729303407436233610788504 \, x^{8} - 721888705880948261432517052670394106238338943844373553906510879866584 \, x^{5} - 338668158068684373436309273067849464405691360751378507442472921774544 \, x^{2}\right)} - 62367643045453979229021701235594440425380660140976292433240780519680 \, x\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}} - 13910019318573948542 \, \sqrt{3} {\left(20244151386762728582873176440916642276036913846721964342570319874272 \, x^{17} + 741146137078834990968958694956953525786968216162791369141561079231342 \, x^{14} + 2179843197271775401147438396101666875537043663345199103065290718350660 \, x^{11} + 2111024935028444803027635033172373996998638870275081528835019029426808 \, x^{8} + 690583979302212649541846671752323578671762361564987198532372077617072 \, x^{5} + 42560446719395994043503690929493089250376947849898596094387069196992 \, x^{2} + 2^{\frac{2}{3}} {\left(58175953016441250552894129028785848895343146706912452780410096144857 \, x^{16} + 603329123440225928459512442880846367498086340467210508410170807919392 \, x^{13} + 993217724421160514640802924970216148872138006799356417482692017634440 \, x^{10} - 315373668616978600368729679828820826067145203897860799345951918357208 \, x^{7} - 1535989781175898454904009764080477698123439140009523257833795294171024 \, x^{4} - 774581653994506522185065060515457999562469670838035710700279100960480 \, x\right)} - 2 \cdot 2^{\frac{1}{3}} {\left(44250337395862623641308432146105265591584981692216944246872622437586 \, x^{15} + 93730331994553087914588193029404165015738145719370012253256237142833 \, x^{12} + 1321854131659545520395638093435834861993288285254840631143087754453816 \, x^{9} + 4247705767701746889589213825725278162202431773760010908121531655858240 \, x^{6} + 4593245463688643634993735851341621838359838170188285500151733185855040 \, x^{3} + 1615883737614789297142910770786922880950970969890530541101538638738800\right)}\right)} {\left(x^{3} + 1\right)}^{\frac{1}{3}} + \sqrt{3} {\left(580845856624814138058536658925035752422341023745042657144110018434133971171392378653765 \, x^{18} + 8512850211201658596320322423507979436745037061604662252288106173984889011398391939493844 \, x^{15} + 46037674634299399876464933353333393651798714498861959697684952859181279514449172348801132 \, x^{12} + 100016348353366812357999723948540966952435611836580420294833827058766585456463611215562912 \, x^{9} + 91397758625366807679053421068886729440495107689602121025455736534255642370122935700628112 \, x^{6} + 27679206471222147818932348914707271406554121216141734785863966451139338545569046396842944 \, x^{3} - 13910019318573948542 \cdot 2^{\frac{2}{3}} {\left(3844366680114123938578119587438413410802428820066154040455085354797 \, x^{17} - 493131971154919078063173195983280278594703770406004388326552124793591 \, x^{14} - 2263656329733750526575239788393341804272268328404078377386979655411628 \, x^{11} - 3603296088959643040065882606156977332942778368970867958841266275405688 \, x^{8} - 2375143924145462474790789297643082581023352457583644433698318090272160 \, x^{5} - 538527827084536759298395164308728360347336217790784309877024260129712 \, x^{2}\right)} + 166920231822887382504 \cdot 2^{\frac{1}{3}} {\left(13595892044042828366275982006708049395032909698880004129949511339226 \, x^{16} + 135133384885158250377179048595991346450771199327236207956421113461903 \, x^{13} + 402245899028058436823068109521885840258775610614711826343657868879359 \, x^{10} + 547258710149879334691832999834525308297790387563356879645468036532966 \, x^{7} + 363674199703640963884960012124387263106254909521640663154302302116404 \, x^{4} + 97123895740704644005292055222464498011501842944639406026020532340120 \, x\right)} - 1800774080838794461192653903259802591850188394016866170707655609076236167687893936558400\right)}}{3 \, {\left(491270574577547337465577862499678580919468289682240641599400002541818630173299555553387 \, x^{18} + 10277776658535231887928963830517649364075160462302952752368573529738604577075128345830496 \, x^{15} + 38053074604041164955598613382506657588718033800015428848687354515819408113275280820067228 \, x^{12} + 104552977375786496056156515228686393360634250389206134816652347595105200990156089430013680 \, x^{9} + 193789778786217108923832562100674176189881131732280694502358058831075231461508817660387440 \, x^{6} + 176250773615214113270216364768545940531543731282577338989973916134409349945587251955701568 \, x^{3} + 58729517358150193708087322484283950706773934182867349449322904141070201590185330889048000\right)}}\right) + \frac{1}{12} \cdot 2^{\frac{1}{3}} \log\left(\frac{6048 \, x^{16} + 6048 \, x^{13} - 9072 \, x^{10} - 12204 \, x^{7} - 2808 \, x^{4} + 2^{\frac{2}{3}} {\left(352 \, x^{18} - 5136 \, x^{15} - 10632 \, x^{12} - 3224 \, x^{9} + 3390 \, x^{6} + 1434 \, x^{3} - 35\right)} + 3 \, {\left(2032 \, x^{14} + 752 \, x^{11} - 3000 \, x^{8} - 1576 \, x^{5} + 172 \, x^{2} + 2^{\frac{2}{3}} {\left(112 \, x^{16} - 1760 \, x^{13} - 2228 \, x^{10} + 356 \, x^{7} + 707 \, x^{4} - 22 \, x\right)} - 2 \cdot 2^{\frac{1}{3}} {\left(352 \, x^{15} - 728 \, x^{12} - 1736 \, x^{9} - 451 \, x^{6} + 215 \, x^{3} - 1\right)}\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}} - 18 \cdot 2^{\frac{1}{3}} {\left(112 \, x^{17} - 192 \, x^{14} - 820 \, x^{11} - 586 \, x^{8} - 21 \, x^{5} + 49 \, x^{2}\right)} + 3 \, {\left(2096 \, x^{15} + 1664 \, x^{12} - 2680 \, x^{9} - 2492 \, x^{6} - 224 \, x^{3} + 2^{\frac{2}{3}} {\left(112 \, x^{17} - 1760 \, x^{14} - 2996 \, x^{11} - 472 \, x^{8} + 779 \, x^{5} + 125 \, x^{2}\right)} - 2 \cdot 2^{\frac{1}{3}} {\left(336 \, x^{16} - 664 \, x^{13} - 2132 \, x^{10} - 1107 \, x^{7} + 55 \, x^{4} + 29 \, x\right)} + 16\right)} {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 324 \, x}{64 \, x^{18} + 192 \, x^{15} + 240 \, x^{12} + 160 \, x^{9} + 60 \, x^{6} + 12 \, x^{3} + 1}\right)"," ",0,"1/6*sqrt(3)*2^(1/3)*arctan(-1/3*(13910019318573948542*sqrt(3)*(44297109310930172741433829405399636654451725916403400759596345420183*x^16 + 469911753877577297266687493361266274298219751726156511748796788210304*x^13 - 168603219036433260440647021325346295645242325246375460547582960409424*x^10 - 1978806301182376573938292954227792627373330283397876582611558332893440*x^7 - 1440090891687177581422918763089301968602581036872213084389912370301872*x^4 - 2^(2/3)*(52271077453125107612995923977654758349394876922885552819209999866413*x^15 + 590674547854548577293285820788340778493299281255213360593997994805172*x^12 + 3063142612229314316198873829666304230648222176902796253391978577817900*x^9 + 7331049558697577809008352571597039403457968857066730277786114959327080*x^6 + 7723244806756290443759770546780872971739444750173519635544186114816064*x^3 + 2911680898783900921956348574183551415589190446015106452608070501424800) + 6*2^(1/3)*(12601355996216322093314748679149120543302140685677058235520929344665*x^14 - 55586906300196651392462719491921267847820798890019850227115938089718*x^11 - 450398920105320599307639536027883986131793624729303407436233610788504*x^8 - 721888705880948261432517052670394106238338943844373553906510879866584*x^5 - 338668158068684373436309273067849464405691360751378507442472921774544*x^2) - 62367643045453979229021701235594440425380660140976292433240780519680*x)*(x^3 + 1)^(2/3) - 13910019318573948542*sqrt(3)*(20244151386762728582873176440916642276036913846721964342570319874272*x^17 + 741146137078834990968958694956953525786968216162791369141561079231342*x^14 + 2179843197271775401147438396101666875537043663345199103065290718350660*x^11 + 2111024935028444803027635033172373996998638870275081528835019029426808*x^8 + 690583979302212649541846671752323578671762361564987198532372077617072*x^5 + 42560446719395994043503690929493089250376947849898596094387069196992*x^2 + 2^(2/3)*(58175953016441250552894129028785848895343146706912452780410096144857*x^16 + 603329123440225928459512442880846367498086340467210508410170807919392*x^13 + 993217724421160514640802924970216148872138006799356417482692017634440*x^10 - 315373668616978600368729679828820826067145203897860799345951918357208*x^7 - 1535989781175898454904009764080477698123439140009523257833795294171024*x^4 - 774581653994506522185065060515457999562469670838035710700279100960480*x) - 2*2^(1/3)*(44250337395862623641308432146105265591584981692216944246872622437586*x^15 + 93730331994553087914588193029404165015738145719370012253256237142833*x^12 + 1321854131659545520395638093435834861993288285254840631143087754453816*x^9 + 4247705767701746889589213825725278162202431773760010908121531655858240*x^6 + 4593245463688643634993735851341621838359838170188285500151733185855040*x^3 + 1615883737614789297142910770786922880950970969890530541101538638738800))*(x^3 + 1)^(1/3) + sqrt(3)*(580845856624814138058536658925035752422341023745042657144110018434133971171392378653765*x^18 + 8512850211201658596320322423507979436745037061604662252288106173984889011398391939493844*x^15 + 46037674634299399876464933353333393651798714498861959697684952859181279514449172348801132*x^12 + 100016348353366812357999723948540966952435611836580420294833827058766585456463611215562912*x^9 + 91397758625366807679053421068886729440495107689602121025455736534255642370122935700628112*x^6 + 27679206471222147818932348914707271406554121216141734785863966451139338545569046396842944*x^3 - 13910019318573948542*2^(2/3)*(3844366680114123938578119587438413410802428820066154040455085354797*x^17 - 493131971154919078063173195983280278594703770406004388326552124793591*x^14 - 2263656329733750526575239788393341804272268328404078377386979655411628*x^11 - 3603296088959643040065882606156977332942778368970867958841266275405688*x^8 - 2375143924145462474790789297643082581023352457583644433698318090272160*x^5 - 538527827084536759298395164308728360347336217790784309877024260129712*x^2) + 166920231822887382504*2^(1/3)*(13595892044042828366275982006708049395032909698880004129949511339226*x^16 + 135133384885158250377179048595991346450771199327236207956421113461903*x^13 + 402245899028058436823068109521885840258775610614711826343657868879359*x^10 + 547258710149879334691832999834525308297790387563356879645468036532966*x^7 + 363674199703640963884960012124387263106254909521640663154302302116404*x^4 + 97123895740704644005292055222464498011501842944639406026020532340120*x) - 1800774080838794461192653903259802591850188394016866170707655609076236167687893936558400))/(491270574577547337465577862499678580919468289682240641599400002541818630173299555553387*x^18 + 10277776658535231887928963830517649364075160462302952752368573529738604577075128345830496*x^15 + 38053074604041164955598613382506657588718033800015428848687354515819408113275280820067228*x^12 + 104552977375786496056156515228686393360634250389206134816652347595105200990156089430013680*x^9 + 193789778786217108923832562100674176189881131732280694502358058831075231461508817660387440*x^6 + 176250773615214113270216364768545940531543731282577338989973916134409349945587251955701568*x^3 + 58729517358150193708087322484283950706773934182867349449322904141070201590185330889048000)) + 1/12*2^(1/3)*log((6048*x^16 + 6048*x^13 - 9072*x^10 - 12204*x^7 - 2808*x^4 + 2^(2/3)*(352*x^18 - 5136*x^15 - 10632*x^12 - 3224*x^9 + 3390*x^6 + 1434*x^3 - 35) + 3*(2032*x^14 + 752*x^11 - 3000*x^8 - 1576*x^5 + 172*x^2 + 2^(2/3)*(112*x^16 - 1760*x^13 - 2228*x^10 + 356*x^7 + 707*x^4 - 22*x) - 2*2^(1/3)*(352*x^15 - 728*x^12 - 1736*x^9 - 451*x^6 + 215*x^3 - 1))*(x^3 + 1)^(2/3) - 18*2^(1/3)*(112*x^17 - 192*x^14 - 820*x^11 - 586*x^8 - 21*x^5 + 49*x^2) + 3*(2096*x^15 + 1664*x^12 - 2680*x^9 - 2492*x^6 - 224*x^3 + 2^(2/3)*(112*x^17 - 1760*x^14 - 2996*x^11 - 472*x^8 + 779*x^5 + 125*x^2) - 2*2^(1/3)*(336*x^16 - 664*x^13 - 2132*x^10 - 1107*x^7 + 55*x^4 + 29*x) + 16)*(x^3 + 1)^(1/3) + 324*x)/(64*x^18 + 192*x^15 + 240*x^12 + 160*x^9 + 60*x^6 + 12*x^3 + 1))","B",0
22,1,720,0,14.366366," ","integrate(1/(1-2^(1/3)*x)/(-x^3+1)^(2/3),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{13910019318573948542 \, \sqrt{3} {\left(44297109310930172741433829405399636654451725916403400759596345420183 \, x^{16} - 469911753877577297266687493361266274298219751726156511748796788210304 \, x^{13} - 168603219036433260440647021325346295645242325246375460547582960409424 \, x^{10} + 1978806301182376573938292954227792627373330283397876582611558332893440 \, x^{7} - 1440090891687177581422918763089301968602581036872213084389912370301872 \, x^{4} + 2^{\frac{2}{3}} {\left(52271077453125107612995923977654758349394876922885552819209999866413 \, x^{15} - 590674547854548577293285820788340778493299281255213360593997994805172 \, x^{12} + 3063142612229314316198873829666304230648222176902796253391978577817900 \, x^{9} - 7331049558697577809008352571597039403457968857066730277786114959327080 \, x^{6} + 7723244806756290443759770546780872971739444750173519635544186114816064 \, x^{3} - 2911680898783900921956348574183551415589190446015106452608070501424800\right)} + 6 \cdot 2^{\frac{1}{3}} {\left(12601355996216322093314748679149120543302140685677058235520929344665 \, x^{14} + 55586906300196651392462719491921267847820798890019850227115938089718 \, x^{11} - 450398920105320599307639536027883986131793624729303407436233610788504 \, x^{8} + 721888705880948261432517052670394106238338943844373553906510879866584 \, x^{5} - 338668158068684373436309273067849464405691360751378507442472921774544 \, x^{2}\right)} + 62367643045453979229021701235594440425380660140976292433240780519680 \, x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 13910019318573948542 \, \sqrt{3} {\left(20244151386762728582873176440916642276036913846721964342570319874272 \, x^{17} - 741146137078834990968958694956953525786968216162791369141561079231342 \, x^{14} + 2179843197271775401147438396101666875537043663345199103065290718350660 \, x^{11} - 2111024935028444803027635033172373996998638870275081528835019029426808 \, x^{8} + 690583979302212649541846671752323578671762361564987198532372077617072 \, x^{5} - 42560446719395994043503690929493089250376947849898596094387069196992 \, x^{2} - 2^{\frac{2}{3}} {\left(58175953016441250552894129028785848895343146706912452780410096144857 \, x^{16} - 603329123440225928459512442880846367498086340467210508410170807919392 \, x^{13} + 993217724421160514640802924970216148872138006799356417482692017634440 \, x^{10} + 315373668616978600368729679828820826067145203897860799345951918357208 \, x^{7} - 1535989781175898454904009764080477698123439140009523257833795294171024 \, x^{4} + 774581653994506522185065060515457999562469670838035710700279100960480 \, x\right)} - 2 \cdot 2^{\frac{1}{3}} {\left(44250337395862623641308432146105265591584981692216944246872622437586 \, x^{15} - 93730331994553087914588193029404165015738145719370012253256237142833 \, x^{12} + 1321854131659545520395638093435834861993288285254840631143087754453816 \, x^{9} - 4247705767701746889589213825725278162202431773760010908121531655858240 \, x^{6} + 4593245463688643634993735851341621838359838170188285500151733185855040 \, x^{3} - 1615883737614789297142910770786922880950970969890530541101538638738800\right)}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \sqrt{3} {\left(580845856624814138058536658925035752422341023745042657144110018434133971171392378653765 \, x^{18} - 8512850211201658596320322423507979436745037061604662252288106173984889011398391939493844 \, x^{15} + 46037674634299399876464933353333393651798714498861959697684952859181279514449172348801132 \, x^{12} - 100016348353366812357999723948540966952435611836580420294833827058766585456463611215562912 \, x^{9} + 91397758625366807679053421068886729440495107689602121025455736534255642370122935700628112 \, x^{6} - 27679206471222147818932348914707271406554121216141734785863966451139338545569046396842944 \, x^{3} + 13910019318573948542 \cdot 2^{\frac{2}{3}} {\left(3844366680114123938578119587438413410802428820066154040455085354797 \, x^{17} + 493131971154919078063173195983280278594703770406004388326552124793591 \, x^{14} - 2263656329733750526575239788393341804272268328404078377386979655411628 \, x^{11} + 3603296088959643040065882606156977332942778368970867958841266275405688 \, x^{8} - 2375143924145462474790789297643082581023352457583644433698318090272160 \, x^{5} + 538527827084536759298395164308728360347336217790784309877024260129712 \, x^{2}\right)} + 166920231822887382504 \cdot 2^{\frac{1}{3}} {\left(13595892044042828366275982006708049395032909698880004129949511339226 \, x^{16} - 135133384885158250377179048595991346450771199327236207956421113461903 \, x^{13} + 402245899028058436823068109521885840258775610614711826343657868879359 \, x^{10} - 547258710149879334691832999834525308297790387563356879645468036532966 \, x^{7} + 363674199703640963884960012124387263106254909521640663154302302116404 \, x^{4} - 97123895740704644005292055222464498011501842944639406026020532340120 \, x\right)} - 1800774080838794461192653903259802591850188394016866170707655609076236167687893936558400\right)}}{3 \, {\left(491270574577547337465577862499678580919468289682240641599400002541818630173299555553387 \, x^{18} - 10277776658535231887928963830517649364075160462302952752368573529738604577075128345830496 \, x^{15} + 38053074604041164955598613382506657588718033800015428848687354515819408113275280820067228 \, x^{12} - 104552977375786496056156515228686393360634250389206134816652347595105200990156089430013680 \, x^{9} + 193789778786217108923832562100674176189881131732280694502358058831075231461508817660387440 \, x^{6} - 176250773615214113270216364768545940531543731282577338989973916134409349945587251955701568 \, x^{3} + 58729517358150193708087322484283950706773934182867349449322904141070201590185330889048000\right)}}\right) - \frac{1}{12} \cdot 2^{\frac{1}{3}} \log\left(\frac{6048 \, x^{16} - 6048 \, x^{13} - 9072 \, x^{10} + 12204 \, x^{7} - 2808 \, x^{4} + 2^{\frac{2}{3}} {\left(352 \, x^{18} + 5136 \, x^{15} - 10632 \, x^{12} + 3224 \, x^{9} + 3390 \, x^{6} - 1434 \, x^{3} - 35\right)} + 3 \, {\left(2032 \, x^{14} - 752 \, x^{11} - 3000 \, x^{8} + 1576 \, x^{5} + 172 \, x^{2} + 2^{\frac{2}{3}} {\left(112 \, x^{16} + 1760 \, x^{13} - 2228 \, x^{10} - 356 \, x^{7} + 707 \, x^{4} + 22 \, x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(352 \, x^{15} + 728 \, x^{12} - 1736 \, x^{9} + 451 \, x^{6} + 215 \, x^{3} + 1\right)}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 18 \cdot 2^{\frac{1}{3}} {\left(112 \, x^{17} + 192 \, x^{14} - 820 \, x^{11} + 586 \, x^{8} - 21 \, x^{5} - 49 \, x^{2}\right)} - 3 \, {\left(2096 \, x^{15} - 1664 \, x^{12} - 2680 \, x^{9} + 2492 \, x^{6} - 224 \, x^{3} + 2^{\frac{2}{3}} {\left(112 \, x^{17} + 1760 \, x^{14} - 2996 \, x^{11} + 472 \, x^{8} + 779 \, x^{5} - 125 \, x^{2}\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(336 \, x^{16} + 664 \, x^{13} - 2132 \, x^{10} + 1107 \, x^{7} + 55 \, x^{4} - 29 \, x\right)} - 16\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 324 \, x}{64 \, x^{18} - 192 \, x^{15} + 240 \, x^{12} - 160 \, x^{9} + 60 \, x^{6} - 12 \, x^{3} + 1}\right)"," ",0,"1/6*sqrt(3)*2^(1/3)*arctan(1/3*(13910019318573948542*sqrt(3)*(44297109310930172741433829405399636654451725916403400759596345420183*x^16 - 469911753877577297266687493361266274298219751726156511748796788210304*x^13 - 168603219036433260440647021325346295645242325246375460547582960409424*x^10 + 1978806301182376573938292954227792627373330283397876582611558332893440*x^7 - 1440090891687177581422918763089301968602581036872213084389912370301872*x^4 + 2^(2/3)*(52271077453125107612995923977654758349394876922885552819209999866413*x^15 - 590674547854548577293285820788340778493299281255213360593997994805172*x^12 + 3063142612229314316198873829666304230648222176902796253391978577817900*x^9 - 7331049558697577809008352571597039403457968857066730277786114959327080*x^6 + 7723244806756290443759770546780872971739444750173519635544186114816064*x^3 - 2911680898783900921956348574183551415589190446015106452608070501424800) + 6*2^(1/3)*(12601355996216322093314748679149120543302140685677058235520929344665*x^14 + 55586906300196651392462719491921267847820798890019850227115938089718*x^11 - 450398920105320599307639536027883986131793624729303407436233610788504*x^8 + 721888705880948261432517052670394106238338943844373553906510879866584*x^5 - 338668158068684373436309273067849464405691360751378507442472921774544*x^2) + 62367643045453979229021701235594440425380660140976292433240780519680*x)*(-x^3 + 1)^(2/3) + 13910019318573948542*sqrt(3)*(20244151386762728582873176440916642276036913846721964342570319874272*x^17 - 741146137078834990968958694956953525786968216162791369141561079231342*x^14 + 2179843197271775401147438396101666875537043663345199103065290718350660*x^11 - 2111024935028444803027635033172373996998638870275081528835019029426808*x^8 + 690583979302212649541846671752323578671762361564987198532372077617072*x^5 - 42560446719395994043503690929493089250376947849898596094387069196992*x^2 - 2^(2/3)*(58175953016441250552894129028785848895343146706912452780410096144857*x^16 - 603329123440225928459512442880846367498086340467210508410170807919392*x^13 + 993217724421160514640802924970216148872138006799356417482692017634440*x^10 + 315373668616978600368729679828820826067145203897860799345951918357208*x^7 - 1535989781175898454904009764080477698123439140009523257833795294171024*x^4 + 774581653994506522185065060515457999562469670838035710700279100960480*x) - 2*2^(1/3)*(44250337395862623641308432146105265591584981692216944246872622437586*x^15 - 93730331994553087914588193029404165015738145719370012253256237142833*x^12 + 1321854131659545520395638093435834861993288285254840631143087754453816*x^9 - 4247705767701746889589213825725278162202431773760010908121531655858240*x^6 + 4593245463688643634993735851341621838359838170188285500151733185855040*x^3 - 1615883737614789297142910770786922880950970969890530541101538638738800))*(-x^3 + 1)^(1/3) + sqrt(3)*(580845856624814138058536658925035752422341023745042657144110018434133971171392378653765*x^18 - 8512850211201658596320322423507979436745037061604662252288106173984889011398391939493844*x^15 + 46037674634299399876464933353333393651798714498861959697684952859181279514449172348801132*x^12 - 100016348353366812357999723948540966952435611836580420294833827058766585456463611215562912*x^9 + 91397758625366807679053421068886729440495107689602121025455736534255642370122935700628112*x^6 - 27679206471222147818932348914707271406554121216141734785863966451139338545569046396842944*x^3 + 13910019318573948542*2^(2/3)*(3844366680114123938578119587438413410802428820066154040455085354797*x^17 + 493131971154919078063173195983280278594703770406004388326552124793591*x^14 - 2263656329733750526575239788393341804272268328404078377386979655411628*x^11 + 3603296088959643040065882606156977332942778368970867958841266275405688*x^8 - 2375143924145462474790789297643082581023352457583644433698318090272160*x^5 + 538527827084536759298395164308728360347336217790784309877024260129712*x^2) + 166920231822887382504*2^(1/3)*(13595892044042828366275982006708049395032909698880004129949511339226*x^16 - 135133384885158250377179048595991346450771199327236207956421113461903*x^13 + 402245899028058436823068109521885840258775610614711826343657868879359*x^10 - 547258710149879334691832999834525308297790387563356879645468036532966*x^7 + 363674199703640963884960012124387263106254909521640663154302302116404*x^4 - 97123895740704644005292055222464498011501842944639406026020532340120*x) - 1800774080838794461192653903259802591850188394016866170707655609076236167687893936558400))/(491270574577547337465577862499678580919468289682240641599400002541818630173299555553387*x^18 - 10277776658535231887928963830517649364075160462302952752368573529738604577075128345830496*x^15 + 38053074604041164955598613382506657588718033800015428848687354515819408113275280820067228*x^12 - 104552977375786496056156515228686393360634250389206134816652347595105200990156089430013680*x^9 + 193789778786217108923832562100674176189881131732280694502358058831075231461508817660387440*x^6 - 176250773615214113270216364768545940531543731282577338989973916134409349945587251955701568*x^3 + 58729517358150193708087322484283950706773934182867349449322904141070201590185330889048000)) - 1/12*2^(1/3)*log((6048*x^16 - 6048*x^13 - 9072*x^10 + 12204*x^7 - 2808*x^4 + 2^(2/3)*(352*x^18 + 5136*x^15 - 10632*x^12 + 3224*x^9 + 3390*x^6 - 1434*x^3 - 35) + 3*(2032*x^14 - 752*x^11 - 3000*x^8 + 1576*x^5 + 172*x^2 + 2^(2/3)*(112*x^16 + 1760*x^13 - 2228*x^10 - 356*x^7 + 707*x^4 + 22*x) + 2*2^(1/3)*(352*x^15 + 728*x^12 - 1736*x^9 + 451*x^6 + 215*x^3 + 1))*(-x^3 + 1)^(2/3) + 18*2^(1/3)*(112*x^17 + 192*x^14 - 820*x^11 + 586*x^8 - 21*x^5 - 49*x^2) - 3*(2096*x^15 - 1664*x^12 - 2680*x^9 + 2492*x^6 - 224*x^3 + 2^(2/3)*(112*x^17 + 1760*x^14 - 2996*x^11 + 472*x^8 + 779*x^5 - 125*x^2) + 2*2^(1/3)*(336*x^16 + 664*x^13 - 2132*x^10 + 1107*x^7 + 55*x^4 - 29*x) - 16)*(-x^3 + 1)^(1/3) - 324*x)/(64*x^18 - 192*x^15 + 240*x^12 - 160*x^9 + 60*x^6 - 12*x^3 + 1))","B",0
23,-1,0,0,0.000000," ","integrate((d*x+c)^4*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate((d*x+c)^3*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate((d*x+c)^2*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,0,0,0,47.793888," ","integrate((d*x+c)*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)*(d*x + c), x)","F",0
27,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate((d*x+c)^4/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate((d*x+c)^3/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((d*x+c)^2/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,0,0,0,107.978955," ","integrate((d*x+c)/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d x + c}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((d*x + c)/(b*x^3 + a)^(1/3), x)","F",0
33,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate(1/(d*x+c)^3/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate((d*x+c)^4/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate((d*x+c)^3/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,0,0,0,141.908630," ","integrate((d*x+c)^2/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d^{2} x^{2} + 2 \, c d x + c^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)/(b*x^3 + a)^(2/3), x)","F",0
39,0,0,0,26.326074," ","integrate((d*x+c)/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d x + c}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((d*x + c)/(b*x^3 + a)^(2/3), x)","F",0
40,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(1/(d*x+c)^3/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,1,75,0,2.046468," ","integrate((2^(2/3)-2*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(-\frac{\sqrt{6} 2^{\frac{1}{6}} {\left(2 \, x^{5} + 2 \, x^{2} - 2^{\frac{2}{3}} {\left(7 \, x^{4} + 4 \, x\right)} - 2^{\frac{1}{3}} {\left(5 \, x^{3} + 2\right)}\right)} \sqrt{x^{3} + 1}}{12 \, {\left(2 \, x^{6} + 3 \, x^{3} + 1\right)}}\right)"," ",0,"1/3*sqrt(6)*2^(1/6)*arctan(-1/12*sqrt(6)*2^(1/6)*(2*x^5 + 2*x^2 - 2^(2/3)*(7*x^4 + 4*x) - 2^(1/3)*(5*x^3 + 2))*sqrt(x^3 + 1)/(2*x^6 + 3*x^3 + 1))","B",0
44,1,76,0,1.951260," ","integrate((2^(2/3)+2*x)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(\frac{\sqrt{6} 2^{\frac{1}{6}} {\left(2 \, x^{5} - 2 \, x^{2} + 2^{\frac{2}{3}} {\left(7 \, x^{4} - 4 \, x\right)} - 2^{\frac{1}{3}} {\left(5 \, x^{3} - 2\right)}\right)} \sqrt{-x^{3} + 1}}{12 \, {\left(2 \, x^{6} - 3 \, x^{3} + 1\right)}}\right)"," ",0,"-1/3*sqrt(6)*2^(1/6)*arctan(1/12*sqrt(6)*2^(1/6)*(2*x^5 - 2*x^2 + 2^(2/3)*(7*x^4 - 4*x) - 2^(1/3)*(5*x^3 - 2))*sqrt(-x^3 + 1)/(2*x^6 - 3*x^3 + 1))","B",0
45,1,238,0,1.994179," ","integrate((2^(2/3)+2*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \log\left(\frac{x^{18} + 1440 \, x^{15} + 17400 \, x^{12} - 21056 \, x^{9} - 10368 \, x^{6} + 15360 \, x^{3} + 2 \, \sqrt{6} 2^{\frac{1}{6}} {\left(126 \, x^{14} + 2664 \, x^{11} - 4608 \, x^{5} + 2304 \, x^{2} + 2^{\frac{2}{3}} {\left(x^{16} + 310 \, x^{13} + 2332 \, x^{10} - 2656 \, x^{7} - 256 \, x^{4} + 512 \, x\right)} + 2^{\frac{1}{3}} {\left(17 \, x^{15} + 1058 \, x^{12} + 2528 \, x^{9} - 5408 \, x^{6} + 2560 \, x^{3} - 512\right)}\right)} \sqrt{x^{3} - 1} + 24 \cdot 2^{\frac{2}{3}} {\left(x^{17} + 121 \, x^{14} + 478 \, x^{11} - 1144 \, x^{8} + 608 \, x^{5} - 64 \, x^{2}\right)} + 48 \cdot 2^{\frac{1}{3}} {\left(5 \, x^{16} + 176 \, x^{13} + 83 \, x^{10} - 680 \, x^{7} + 544 \, x^{4} - 128 \, x\right)} - 2048}{x^{18} - 24 \, x^{15} + 240 \, x^{12} - 1280 \, x^{9} + 3840 \, x^{6} - 6144 \, x^{3} + 4096}\right)"," ",0,"1/6*sqrt(6)*2^(1/6)*log((x^18 + 1440*x^15 + 17400*x^12 - 21056*x^9 - 10368*x^6 + 15360*x^3 + 2*sqrt(6)*2^(1/6)*(126*x^14 + 2664*x^11 - 4608*x^5 + 2304*x^2 + 2^(2/3)*(x^16 + 310*x^13 + 2332*x^10 - 2656*x^7 - 256*x^4 + 512*x) + 2^(1/3)*(17*x^15 + 1058*x^12 + 2528*x^9 - 5408*x^6 + 2560*x^3 - 512))*sqrt(x^3 - 1) + 24*2^(2/3)*(x^17 + 121*x^14 + 478*x^11 - 1144*x^8 + 608*x^5 - 64*x^2) + 48*2^(1/3)*(5*x^16 + 176*x^13 + 83*x^10 - 680*x^7 + 544*x^4 - 128*x) - 2048)/(x^18 - 24*x^15 + 240*x^12 - 1280*x^9 + 3840*x^6 - 6144*x^3 + 4096))","B",0
46,1,241,0,1.820021," ","integrate((2^(2/3)-2*x)/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \log\left(\frac{x^{18} - 1440 \, x^{15} + 17400 \, x^{12} + 21056 \, x^{9} - 10368 \, x^{6} - 15360 \, x^{3} - 2 \, \sqrt{6} 2^{\frac{1}{6}} {\left(126 \, x^{14} - 2664 \, x^{11} + 4608 \, x^{5} + 2304 \, x^{2} + 2^{\frac{2}{3}} {\left(x^{16} - 310 \, x^{13} + 2332 \, x^{10} + 2656 \, x^{7} - 256 \, x^{4} - 512 \, x\right)} - 2^{\frac{1}{3}} {\left(17 \, x^{15} - 1058 \, x^{12} + 2528 \, x^{9} + 5408 \, x^{6} + 2560 \, x^{3} + 512\right)}\right)} \sqrt{-x^{3} - 1} - 24 \cdot 2^{\frac{2}{3}} {\left(x^{17} - 121 \, x^{14} + 478 \, x^{11} + 1144 \, x^{8} + 608 \, x^{5} + 64 \, x^{2}\right)} + 48 \cdot 2^{\frac{1}{3}} {\left(5 \, x^{16} - 176 \, x^{13} + 83 \, x^{10} + 680 \, x^{7} + 544 \, x^{4} + 128 \, x\right)} - 2048}{x^{18} + 24 \, x^{15} + 240 \, x^{12} + 1280 \, x^{9} + 3840 \, x^{6} + 6144 \, x^{3} + 4096}\right)"," ",0,"1/6*sqrt(6)*2^(1/6)*log((x^18 - 1440*x^15 + 17400*x^12 + 21056*x^9 - 10368*x^6 - 15360*x^3 - 2*sqrt(6)*2^(1/6)*(126*x^14 - 2664*x^11 + 4608*x^5 + 2304*x^2 + 2^(2/3)*(x^16 - 310*x^13 + 2332*x^10 + 2656*x^7 - 256*x^4 - 512*x) - 2^(1/3)*(17*x^15 - 1058*x^12 + 2528*x^9 + 5408*x^6 + 2560*x^3 + 512))*sqrt(-x^3 - 1) - 24*2^(2/3)*(x^17 - 121*x^14 + 478*x^11 + 1144*x^8 + 608*x^5 + 64*x^2) + 48*2^(1/3)*(5*x^16 - 176*x^13 + 83*x^10 + 680*x^7 + 544*x^4 + 128*x) - 2048)/(x^18 + 24*x^15 + 240*x^12 + 1280*x^9 + 3840*x^6 + 6144*x^3 + 4096))","B",0
47,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)-2*b^(1/3)*x)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)+2*b^(1/3)*x)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)+2*b^(1/3)*x)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)-2*b^(1/3)*x)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,1,300,0,2.121199," ","integrate((-2*d*x+c)/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} \sqrt{-\frac{1}{c}} \log\left(\frac{2 \, d^{6} x^{6} - 36 \, c d^{5} x^{5} - 18 \, c^{2} d^{4} x^{4} + 28 \, c^{3} d^{3} x^{3} + 18 \, c^{4} d^{2} x^{2} - c^{6} - \sqrt{3} {\left(4 \, c d^{4} x^{4} - 10 \, c^{2} d^{3} x^{3} - 18 \, c^{3} d^{2} x^{2} - 8 \, c^{4} d x - c^{5}\right)} \sqrt{4 \, d^{3} x^{3} + c^{3}} \sqrt{-\frac{1}{c}}}{d^{6} x^{6} + 6 \, c d^{5} x^{5} + 15 \, c^{2} d^{4} x^{4} + 20 \, c^{3} d^{3} x^{3} + 15 \, c^{4} d^{2} x^{2} + 6 \, c^{5} d x + c^{6}}\right)}{6 \, d}, -\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{4 \, d^{3} x^{3} + c^{3}} {\left(2 \, d^{3} x^{3} - 6 \, c d^{2} x^{2} - 6 \, c^{2} d x - c^{3}\right)}}{3 \, {\left(8 \, d^{4} x^{4} + 4 \, c d^{3} x^{3} + 2 \, c^{3} d x + c^{4}\right)} \sqrt{c}}\right)}{3 \, \sqrt{c} d}\right]"," ",0,"[1/6*sqrt(3)*sqrt(-1/c)*log((2*d^6*x^6 - 36*c*d^5*x^5 - 18*c^2*d^4*x^4 + 28*c^3*d^3*x^3 + 18*c^4*d^2*x^2 - c^6 - sqrt(3)*(4*c*d^4*x^4 - 10*c^2*d^3*x^3 - 18*c^3*d^2*x^2 - 8*c^4*d*x - c^5)*sqrt(4*d^3*x^3 + c^3)*sqrt(-1/c))/(d^6*x^6 + 6*c*d^5*x^5 + 15*c^2*d^4*x^4 + 20*c^3*d^3*x^3 + 15*c^4*d^2*x^2 + 6*c^5*d*x + c^6))/d, -1/3*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(4*d^3*x^3 + c^3)*(2*d^3*x^3 - 6*c*d^2*x^2 - 6*c^2*d*x - c^3)/((8*d^4*x^4 + 4*c*d^3*x^3 + 2*c^3*d*x + c^4)*sqrt(c)))/(sqrt(c)*d)]","B",0
52,0,0,0,1.531083," ","integrate((2+3*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{3} + 2 \, x^{2} - 2^{\frac{2}{3}} {\left(3 \, x^{2} + 2 \, x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(3 \, x + 2\right)}\right)} \sqrt{x^{3} + 1}}{x^{6} + 5 \, x^{3} + 4}, x\right)"," ",0,"integral((3*x^3 + 2*x^2 - 2^(2/3)*(3*x^2 + 2*x) + 2*2^(1/3)*(3*x + 2))*sqrt(x^3 + 1)/(x^6 + 5*x^3 + 4), x)","F",0
53,0,0,0,2.561017," ","integrate((2+3*x)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{3} + 2 \, x^{2} + 2^{\frac{2}{3}} {\left(3 \, x^{2} + 2 \, x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(3 \, x + 2\right)}\right)} \sqrt{-x^{3} + 1}}{x^{6} - 5 \, x^{3} + 4}, x\right)"," ",0,"integral((3*x^3 + 2*x^2 + 2^(2/3)*(3*x^2 + 2*x) + 2*2^(1/3)*(3*x + 2))*sqrt(-x^3 + 1)/(x^6 - 5*x^3 + 4), x)","F",0
54,-2,0,0,0.000000," ","integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
55,0,0,0,1.657752," ","integrate((2+3*x)/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x^{3} + 2 \, x^{2} - 2^{\frac{2}{3}} {\left(3 \, x^{2} + 2 \, x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(3 \, x + 2\right)}\right)} \sqrt{-x^{3} - 1}}{x^{6} + 5 \, x^{3} + 4}, x\right)"," ",0,"integral(-(3*x^3 + 2*x^2 - 2^(2/3)*(3*x^2 + 2*x) + 2*2^(1/3)*(3*x + 2))*sqrt(-x^3 - 1)/(x^6 + 5*x^3 + 4), x)","F",0
56,-2,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
57,0,0,0,1.410533," ","integrate((f*x+e)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x^{3} + e x^{2} + 2^{\frac{2}{3}} {\left(f x^{2} + e x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(f x + e\right)}\right)} \sqrt{-x^{3} + 1}}{x^{6} - 5 \, x^{3} + 4}, x\right)"," ",0,"integral((f*x^3 + e*x^2 + 2^(2/3)*(f*x^2 + e*x) + 2*2^(1/3)*(f*x + e))*sqrt(-x^3 + 1)/(x^6 - 5*x^3 + 4), x)","F",0
58,0,0,0,2.148657," ","integrate((f*x+e)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(f x^{3} + e x^{2} + 2^{\frac{2}{3}} {\left(f x^{2} + e x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(f x + e\right)}\right)} \sqrt{x^{3} - 1}}{x^{6} - 5 \, x^{3} + 4}, x\right)"," ",0,"integral(-(f*x^3 + e*x^2 + 2^(2/3)*(f*x^2 + e*x) + 2*2^(1/3)*(f*x + e))*sqrt(x^3 - 1)/(x^6 - 5*x^3 + 4), x)","F",0
59,0,0,0,2.089605," ","integrate((f*x+e)/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(f x^{3} + e x^{2} - 2^{\frac{2}{3}} {\left(f x^{2} + e x\right)} + 2 \cdot 2^{\frac{1}{3}} {\left(f x + e\right)}\right)} \sqrt{-x^{3} - 1}}{x^{6} + 5 \, x^{3} + 4}, x\right)"," ",0,"integral(-(f*x^3 + e*x^2 - 2^(2/3)*(f*x^2 + e*x) + 2*2^(1/3)*(f*x + e))*sqrt(-x^3 - 1)/(x^6 + 5*x^3 + 4), x)","F",0
60,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,0,0,0,3.134151," ","integrate((f*x+e)/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, d^{3} x^{3} + c^{3}} {\left(f x + e\right)}}{4 \, d^{4} x^{4} + 4 \, c d^{3} x^{3} + c^{3} d x + c^{4}}, x\right)"," ",0,"integral(sqrt(4*d^3*x^3 + c^3)*(f*x + e)/(4*d^4*x^4 + 4*c*d^3*x^3 + c^3*d*x + c^4), x)","F",0
65,0,0,0,2.189911," ","integrate(x/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{3} - 2^{\frac{2}{3}} x^{2} + 2 \cdot 2^{\frac{1}{3}} x\right)} \sqrt{x^{3} + 1}}{x^{6} + 5 \, x^{3} + 4}, x\right)"," ",0,"integral((x^3 - 2^(2/3)*x^2 + 2*2^(1/3)*x)*sqrt(x^3 + 1)/(x^6 + 5*x^3 + 4), x)","F",0
66,0,0,0,1.566261," ","integrate(x/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{3} + 2^{\frac{2}{3}} x^{2} + 2 \cdot 2^{\frac{1}{3}} x\right)} \sqrt{-x^{3} + 1}}{x^{6} - 5 \, x^{3} + 4}, x\right)"," ",0,"integral((x^3 + 2^(2/3)*x^2 + 2*2^(1/3)*x)*sqrt(-x^3 + 1)/(x^6 - 5*x^3 + 4), x)","F",0
67,0,0,0,2.034883," ","integrate(x/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(x^{3} + 2^{\frac{2}{3}} x^{2} + 2 \cdot 2^{\frac{1}{3}} x\right)} \sqrt{x^{3} - 1}}{x^{6} - 5 \, x^{3} + 4}, x\right)"," ",0,"integral(-(x^3 + 2^(2/3)*x^2 + 2*2^(1/3)*x)*sqrt(x^3 - 1)/(x^6 - 5*x^3 + 4), x)","F",0
68,0,0,0,1.715371," ","integrate(x/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(x^{3} - 2^{\frac{2}{3}} x^{2} + 2 \cdot 2^{\frac{1}{3}} x\right)} \sqrt{-x^{3} - 1}}{x^{6} + 5 \, x^{3} + 4}, x\right)"," ",0,"integral(-(x^3 - 2^(2/3)*x^2 + 2*2^(1/3)*x)*sqrt(-x^3 - 1)/(x^6 + 5*x^3 + 4), x)","F",0
69,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,0,0,0,2.009026," ","integrate(x/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, d^{3} x^{3} + c^{3}} x}{4 \, d^{4} x^{4} + 4 \, c d^{3} x^{3} + c^{3} d x + c^{4}}, x\right)"," ",0,"integral(sqrt(4*d^3*x^3 + c^3)*x/(4*d^4*x^4 + 4*c*d^3*x^3 + c^3*d*x + c^4), x)","F",0
74,1,44,0,2.022058," ","integrate((1+x)/(2-x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(\frac{x^{3} + 12 \, x^{2} + 6 \, \sqrt{x^{3} + 1} {\left(x + 1\right)} - 6 \, x + 10}{x^{3} - 6 \, x^{2} + 12 \, x - 8}\right)"," ",0,"1/3*log((x^3 + 12*x^2 + 6*sqrt(x^3 + 1)*(x + 1) - 6*x + 10)/(x^3 - 6*x^2 + 12*x - 8))","B",0
75,1,47,0,1.445751," ","integrate((1-x)/(2+x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(-\frac{x^{3} - 12 \, x^{2} - 6 \, \sqrt{-x^{3} + 1} {\left(x - 1\right)} - 6 \, x - 10}{x^{3} + 6 \, x^{2} + 12 \, x + 8}\right)"," ",0,"1/3*log(-(x^3 - 12*x^2 - 6*sqrt(-x^3 + 1)*(x - 1) - 6*x - 10)/(x^3 + 6*x^2 + 12*x + 8))","B",0
76,1,40,0,1.662925," ","integrate((1-x)/(2+x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \arctan\left(\frac{{\left(x^{3} - 12 \, x^{2} - 6 \, x - 10\right)} \sqrt{x^{3} - 1}}{6 \, {\left(x^{4} - x^{3} - x + 1\right)}}\right)"," ",0,"-1/3*arctan(1/6*(x^3 - 12*x^2 - 6*x - 10)*sqrt(x^3 - 1)/(x^4 - x^3 - x + 1))","B",0
77,1,38,0,1.454464," ","integrate((1+x)/(2-x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \arctan\left(\frac{{\left(x^{3} + 12 \, x^{2} - 6 \, x + 10\right)} \sqrt{-x^{3} - 1}}{6 \, {\left(x^{4} + x^{3} + x + 1\right)}}\right)"," ",0,"-1/3*arctan(1/6*(x^3 + 12*x^2 - 6*x + 10)*sqrt(-x^3 - 1)/(x^4 + x^3 + x + 1))","A",0
78,-1,0,0,0.000000," ","integrate((a^(1/3)+b^(1/3)*x)/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((a^(1/3)-b^(1/3)*x)/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((a^(1/3)-b^(1/3)*x)/(2*a^(1/3)+b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((a^(1/3)+b^(1/3)*x)/(2*a^(1/3)-b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,1,294,0,1.762760," ","integrate((-2*d*x+c)/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{8 \, d^{6} x^{6} - 240 \, c d^{5} x^{5} + 408 \, c^{2} d^{4} x^{4} + 88 \, c^{3} d^{3} x^{3} + 156 \, c^{4} d^{2} x^{2} + 12 \, c^{5} d x + 17 \, c^{6} - 3 \, {\left(8 \, d^{4} x^{4} - 52 \, c d^{3} x^{3} + 12 \, c^{2} d^{2} x^{2} - 4 \, c^{3} d x + 5 \, c^{4}\right)} \sqrt{-8 \, d^{3} x^{3} + c^{3}} \sqrt{c}}{d^{6} x^{6} + 6 \, c d^{5} x^{5} + 15 \, c^{2} d^{4} x^{4} + 20 \, c^{3} d^{3} x^{3} + 15 \, c^{4} d^{2} x^{2} + 6 \, c^{5} d x + c^{6}}\right)}{6 \, \sqrt{c} d}, -\frac{\sqrt{-c} \arctan\left(\frac{{\left(4 \, d^{3} x^{3} - 24 \, c d^{2} x^{2} - 6 \, c^{2} d x - 5 \, c^{3}\right)} \sqrt{-8 \, d^{3} x^{3} + c^{3}} \sqrt{-c}}{3 \, {\left(16 \, c d^{4} x^{4} - 8 \, c^{2} d^{3} x^{3} - 2 \, c^{4} d x + c^{5}\right)}}\right)}{3 \, c d}\right]"," ",0,"[1/6*log((8*d^6*x^6 - 240*c*d^5*x^5 + 408*c^2*d^4*x^4 + 88*c^3*d^3*x^3 + 156*c^4*d^2*x^2 + 12*c^5*d*x + 17*c^6 - 3*(8*d^4*x^4 - 52*c*d^3*x^3 + 12*c^2*d^2*x^2 - 4*c^3*d*x + 5*c^4)*sqrt(-8*d^3*x^3 + c^3)*sqrt(c))/(d^6*x^6 + 6*c*d^5*x^5 + 15*c^2*d^4*x^4 + 20*c^3*d^3*x^3 + 15*c^4*d^2*x^2 + 6*c^5*d*x + c^6))/(sqrt(c)*d), -1/3*sqrt(-c)*arctan(1/3*(4*d^3*x^3 - 24*c*d^2*x^2 - 6*c^2*d*x - 5*c^3)*sqrt(-8*d^3*x^3 + c^3)*sqrt(-c)/(16*c*d^4*x^4 - 8*c^2*d^3*x^3 - 2*c^4*d*x + c^5))/(c*d)]","B",0
83,0,0,0,1.469117," ","integrate((f*x+e)/(2-x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} + 1} {\left(f x + e\right)}}{x^{4} - 2 \, x^{3} + x - 2}, x\right)"," ",0,"integral(-sqrt(x^3 + 1)*(f*x + e)/(x^4 - 2*x^3 + x - 2), x)","F",0
84,0,0,0,1.276648," ","integrate((f*x+e)/(2+x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} {\left(f x + e\right)}}{x^{4} + 2 \, x^{3} - x - 2}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*(f*x + e)/(x^4 + 2*x^3 - x - 2), x)","F",0
85,0,0,0,1.545873," ","integrate((f*x+e)/(2+x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1} {\left(f x + e\right)}}{x^{4} + 2 \, x^{3} - x - 2}, x\right)"," ",0,"integral(sqrt(x^3 - 1)*(f*x + e)/(x^4 + 2*x^3 - x - 2), x)","F",0
86,0,0,0,1.608816," ","integrate((f*x+e)/(2-x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} - 1} {\left(f x + e\right)}}{x^{4} - 2 \, x^{3} + x - 2}, x\right)"," ",0,"integral(sqrt(-x^3 - 1)*(f*x + e)/(x^4 - 2*x^3 + x - 2), x)","F",0
87,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)+b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)-b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,0,0,0,1.219434," ","integrate((f*x+e)/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-8 \, d^{3} x^{3} + c^{3}} {\left(f x + e\right)}}{8 \, d^{4} x^{4} + 8 \, c d^{3} x^{3} - c^{3} d x - c^{4}}, x\right)"," ",0,"integral(-sqrt(-8*d^3*x^3 + c^3)*(f*x + e)/(8*d^4*x^4 + 8*c*d^3*x^3 - c^3*d*x - c^4), x)","F",0
92,0,0,0,0.960464," ","integrate(x/(2-x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} + 1} x}{x^{4} - 2 \, x^{3} + x - 2}, x\right)"," ",0,"integral(-sqrt(x^3 + 1)*x/(x^4 - 2*x^3 + x - 2), x)","F",0
93,0,0,0,0.929576," ","integrate(x/(2+x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x}{x^{4} + 2 \, x^{3} - x - 2}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x/(x^4 + 2*x^3 - x - 2), x)","F",0
94,0,0,0,0.866319," ","integrate(x/(2+x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1} x}{x^{4} + 2 \, x^{3} - x - 2}, x\right)"," ",0,"integral(sqrt(x^3 - 1)*x/(x^4 + 2*x^3 - x - 2), x)","F",0
95,0,0,0,0.892802," ","integrate(x/(2-x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} - 1} x}{x^{4} - 2 \, x^{3} + x - 2}, x\right)"," ",0,"integral(sqrt(-x^3 - 1)*x/(x^4 - 2*x^3 + x - 2), x)","F",0
96,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)+b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)-b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,1.597425," ","integrate(x/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-8 \, d^{3} x^{3} + c^{3}} x}{8 \, d^{4} x^{4} + 8 \, c d^{3} x^{3} - c^{3} d x - c^{4}}, x\right)"," ",0,"integral(-sqrt(-8*d^3*x^3 + c^3)*x/(8*d^4*x^4 + 8*c*d^3*x^3 - c^3*d*x - c^4), x)","F",0
101,1,205,0,1.726581," ","integrate((1+x+3^(1/2))/(1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \sqrt{2 \, \sqrt{3} + 3} \log\left(\frac{x^{8} - 16 \, x^{7} + 112 \, x^{6} - 16 \, x^{5} + 112 \, x^{4} + 224 \, x^{3} + 64 \, x^{2} - 4 \, {\left(2 \, x^{6} - 18 \, x^{5} + 42 \, x^{4} - 8 \, x^{3} - \sqrt{3} {\left(x^{6} - 12 \, x^{5} + 18 \, x^{4} - 16 \, x^{3} - 12 \, x^{2} - 8\right)} + 24 \, x + 8\right)} \sqrt{x^{3} + 1} \sqrt{2 \, \sqrt{3} + 3} + 16 \, \sqrt{3} {\left(x^{7} - 2 \, x^{6} + 6 \, x^{5} + 5 \, x^{4} + 2 \, x^{3} + 6 \, x^{2} + 4 \, x + 4\right)} + 128 \, x + 112}{x^{8} + 8 \, x^{7} + 16 \, x^{6} - 16 \, x^{5} - 56 \, x^{4} + 32 \, x^{3} + 64 \, x^{2} - 64 \, x + 16}\right)"," ",0,"1/6*sqrt(3)*sqrt(2*sqrt(3) + 3)*log((x^8 - 16*x^7 + 112*x^6 - 16*x^5 + 112*x^4 + 224*x^3 + 64*x^2 - 4*(2*x^6 - 18*x^5 + 42*x^4 - 8*x^3 - sqrt(3)*(x^6 - 12*x^5 + 18*x^4 - 16*x^3 - 12*x^2 - 8) + 24*x + 8)*sqrt(x^3 + 1)*sqrt(2*sqrt(3) + 3) + 16*sqrt(3)*(x^7 - 2*x^6 + 6*x^5 + 5*x^4 + 2*x^3 + 6*x^2 + 4*x + 4) + 128*x + 112)/(x^8 + 8*x^7 + 16*x^6 - 16*x^5 - 56*x^4 + 32*x^3 + 64*x^2 - 64*x + 16))","B",0
102,1,207,0,1.570652," ","integrate((1-x+3^(1/2))/(1-x-3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \sqrt{2 \, \sqrt{3} + 3} \log\left(\frac{x^{8} + 16 \, x^{7} + 112 \, x^{6} + 16 \, x^{5} + 112 \, x^{4} - 224 \, x^{3} + 64 \, x^{2} + 4 \, {\left(2 \, x^{6} + 18 \, x^{5} + 42 \, x^{4} + 8 \, x^{3} - \sqrt{3} {\left(x^{6} + 12 \, x^{5} + 18 \, x^{4} + 16 \, x^{3} - 12 \, x^{2} - 8\right)} - 24 \, x + 8\right)} \sqrt{-x^{3} + 1} \sqrt{2 \, \sqrt{3} + 3} - 16 \, \sqrt{3} {\left(x^{7} + 2 \, x^{6} + 6 \, x^{5} - 5 \, x^{4} + 2 \, x^{3} - 6 \, x^{2} + 4 \, x - 4\right)} - 128 \, x + 112}{x^{8} - 8 \, x^{7} + 16 \, x^{6} + 16 \, x^{5} - 56 \, x^{4} - 32 \, x^{3} + 64 \, x^{2} + 64 \, x + 16}\right)"," ",0,"1/6*sqrt(3)*sqrt(2*sqrt(3) + 3)*log((x^8 + 16*x^7 + 112*x^6 + 16*x^5 + 112*x^4 - 224*x^3 + 64*x^2 + 4*(2*x^6 + 18*x^5 + 42*x^4 + 8*x^3 - sqrt(3)*(x^6 + 12*x^5 + 18*x^4 + 16*x^3 - 12*x^2 - 8) - 24*x + 8)*sqrt(-x^3 + 1)*sqrt(2*sqrt(3) + 3) - 16*sqrt(3)*(x^7 + 2*x^6 + 6*x^5 - 5*x^4 + 2*x^3 - 6*x^2 + 4*x - 4) - 128*x + 112)/(x^8 - 8*x^7 + 16*x^6 + 16*x^5 - 56*x^4 - 32*x^3 + 64*x^2 + 64*x + 16))","B",0
103,1,50,0,1.411595," ","integrate((1-x+3^(1/2))/(1-x-3^(1/2))/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \sqrt{2 \, \sqrt{3} + 3} \arctan\left(\frac{{\left(\sqrt{3} {\left(x^{2} + 4 \, x - 2\right)} - 6 \, x + 6\right)} \sqrt{2 \, \sqrt{3} + 3}}{6 \, \sqrt{x^{3} - 1}}\right)"," ",0,"1/3*sqrt(3)*sqrt(2*sqrt(3) + 3)*arctan(1/6*(sqrt(3)*(x^2 + 4*x - 2) - 6*x + 6)*sqrt(2*sqrt(3) + 3)/sqrt(x^3 - 1))","A",0
104,1,59,0,0.933176," ","integrate((1+x+3^(1/2))/(1+x-3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \sqrt{2 \, \sqrt{3} + 3} \arctan\left(\frac{\sqrt{-x^{3} - 1} {\left(\sqrt{3} {\left(x^{2} - 4 \, x - 2\right)} + 6 \, x + 6\right)} \sqrt{2 \, \sqrt{3} + 3}}{6 \, {\left(x^{3} + 1\right)}}\right)"," ",0,"1/3*sqrt(3)*sqrt(2*sqrt(3) + 3)*arctan(1/6*sqrt(-x^3 - 1)*(sqrt(3)*(x^2 - 4*x - 2) + 6*x + 6)*sqrt(2*sqrt(3) + 3)/(x^3 + 1))","A",0
105,1,1240,0,4.522574," ","integrate((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 4 \, \sqrt{\frac{1}{3}} \sqrt{b x^{3} + a} {\left({\left(3 \, b^{7} x^{22} - 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} - 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} - 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} - 24576 \, a^{7} x - 2 \, \sqrt{3} {\left(b^{7} x^{22} - 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} - 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} + 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} + 7168 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} - 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} - 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} - 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} - \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} a^{\frac{1}{3}} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} + 32 \, {\left(9 \, b^{7} x^{22} - 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} + 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} + 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} + 4608 \, a^{7} x - \sqrt{3} {\left(5 \, b^{7} x^{22} - 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} - 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} - 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} - 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} - 8 \, {\left(3 \, b^{7} x^{23} - 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} - 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} - 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} - 61440 \, a^{7} x^{2} - 2 \, \sqrt{3} {\left(b^{7} x^{23} - 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} + 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} + 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} + 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(a^{\frac{1}{3}} b x^{2} + 2 \, {\left(\sqrt{3} x - 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 2 \, {\left(\sqrt{3} a - a\right)} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}}}{2 \, \sqrt{b x^{3} + a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) + 3)/(a*b^(2/3)))*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 4*sqrt(1/3)*sqrt(b*x^3 + a)*((3*b^7*x^22 - 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 - 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 - 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 - 24576*a^7*x - 2*sqrt(3)*(b^7*x^22 - 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 - 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 + 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 + 7168*a^7*x))*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 - 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 - 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 - 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 - sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*a^(1/3) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*b^(1/3))*sqrt((2*sqrt(3) + 3)/(a*b^(2/3))) + 32*(9*b^7*x^22 - 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 + 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 + 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 + 4608*a^7*x - sqrt(3)*(5*b^7*x^22 - 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 - 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 - 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 - 2560*a^7*x))*a^(2/3)*b^(1/3) - 8*(3*b^7*x^23 - 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 - 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 - 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 - 61440*a^7*x^2 - 2*sqrt(3)*(b^7*x^23 - 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 + 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 + 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 + 17920*a^7*x^2))*a^(1/3)*b^(2/3) + 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3)))*arctan(1/2*sqrt(1/3)*(a^(1/3)*b*x^2 + 2*(sqrt(3)*x - 2*x)*a^(2/3)*b^(2/3) + 2*(sqrt(3)*a - a)*b^(1/3))*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3)))/sqrt(b*x^3 + a))]","A",0
106,1,1294,0,4.322333," ","integrate((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 32 \, {\left(9 \, b^{7} x^{22} + 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} - 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} - 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} - 4608 \, a^{7} x - \sqrt{3} {\left(5 \, b^{7} x^{22} + 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} + 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} + 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} + 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} + 8 \, {\left(3 \, b^{7} x^{23} + 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} + 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} + 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} + 61440 \, a^{7} x^{2} - 2 \, \sqrt{3} {\left(b^{7} x^{23} + 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} - 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} - 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} - 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} - 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, b^{7} x^{22} + 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} + 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} + 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} + 24576 \, a^{7} x - 2 \, \sqrt{3} {\left(b^{7} x^{22} + 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} + 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} - 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} - 7168 \, a^{7} x\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} + 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} + 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} + 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} - \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{1}{3}} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} + a} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} + a} a^{\frac{1}{3}} b x^{2} - 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} x - 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} a - a\right)} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}}}{2 \, {\left(b x^{3} - a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) + 3)/(a*b^(2/3)))*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 + 32*(9*b^7*x^22 + 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 - 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 - 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 - 4608*a^7*x - sqrt(3)*(5*b^7*x^22 + 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 + 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 + 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 + 2560*a^7*x))*a^(2/3)*b^(1/3) + 8*(3*b^7*x^23 + 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 + 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 + 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 + 61440*a^7*x^2 - 2*sqrt(3)*(b^7*x^23 + 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 - 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 - 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 - 17920*a^7*x^2))*a^(1/3)*b^(2/3) - 4*sqrt(1/3)*((3*b^7*x^22 + 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 + 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 + 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 + 24576*a^7*x - 2*sqrt(3)*(b^7*x^22 + 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 + 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 - 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 - 7168*a^7*x))*sqrt(-b*x^3 + a)*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 + 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 + 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 + 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 - sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 + a)*a^(1/3) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*sqrt(-b*x^3 + a)*b^(1/3))*sqrt((2*sqrt(3) + 3)/(a*b^(2/3))) - 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3)))*arctan(-1/2*sqrt(1/3)*(sqrt(-b*x^3 + a)*a^(1/3)*b*x^2 - 2*sqrt(-b*x^3 + a)*(sqrt(3)*x - 2*x)*a^(2/3)*b^(2/3) + 2*sqrt(-b*x^3 + a)*(sqrt(3)*a - a)*b^(1/3))*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3)))/(b*x^3 - a))]","B",0
107,1,1245,0,4.246704," ","integrate((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} - 4 \, \sqrt{\frac{1}{3}} \sqrt{b x^{3} - a} {\left({\left(3 \, b^{7} x^{22} + 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} + 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} + 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} + 24576 \, a^{7} x - 2 \, \sqrt{3} {\left(b^{7} x^{22} + 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} + 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} - 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} - 7168 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} + 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} + 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} + 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} - \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} a^{\frac{1}{3}} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} + 32 \, {\left(9 \, b^{7} x^{22} + 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} - 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} - 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} - 4608 \, a^{7} x - \sqrt{3} {\left(5 \, b^{7} x^{22} + 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} + 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} + 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} + 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} + 8 \, {\left(3 \, b^{7} x^{23} + 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} + 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} + 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} + 61440 \, a^{7} x^{2} - 2 \, \sqrt{3} {\left(b^{7} x^{23} + 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} - 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} - 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} - 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(a^{\frac{1}{3}} b x^{2} - 2 \, {\left(\sqrt{3} x - 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 2 \, {\left(\sqrt{3} a - a\right)} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}}}{2 \, \sqrt{b x^{3} - a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3)))*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 - 4*sqrt(1/3)*sqrt(b*x^3 - a)*((3*b^7*x^22 + 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 + 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 + 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 + 24576*a^7*x - 2*sqrt(3)*(b^7*x^22 + 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 + 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 - 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 - 7168*a^7*x))*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 + 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 + 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 + 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 - sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*a^(1/3) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*b^(1/3))*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3))) + 32*(9*b^7*x^22 + 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 - 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 - 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 - 4608*a^7*x - sqrt(3)*(5*b^7*x^22 + 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 + 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 + 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 + 2560*a^7*x))*a^(2/3)*b^(1/3) + 8*(3*b^7*x^23 + 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 + 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 + 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 + 61440*a^7*x^2 - 2*sqrt(3)*(b^7*x^23 + 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 - 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 - 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 - 17920*a^7*x^2))*a^(1/3)*b^(2/3) - 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) + 3)/(a*b^(2/3)))*arctan(-1/2*sqrt(1/3)*(a^(1/3)*b*x^2 - 2*(sqrt(3)*x - 2*x)*a^(2/3)*b^(2/3) + 2*(sqrt(3)*a - a)*b^(1/3))*sqrt((2*sqrt(3) + 3)/(a*b^(2/3)))/sqrt(b*x^3 - a))]","A",0
108,1,1303,0,3.776003," ","integrate((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 32 \, {\left(9 \, b^{7} x^{22} - 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} + 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} + 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} + 4608 \, a^{7} x - \sqrt{3} {\left(5 \, b^{7} x^{22} - 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} - 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} - 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} - 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} - 8 \, {\left(3 \, b^{7} x^{23} - 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} - 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} - 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} - 61440 \, a^{7} x^{2} - 2 \, \sqrt{3} {\left(b^{7} x^{23} - 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} + 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} + 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} + 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} + 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, b^{7} x^{22} - 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} - 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} - 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} - 24576 \, a^{7} x - 2 \, \sqrt{3} {\left(b^{7} x^{22} - 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} - 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} + 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} + 7168 \, a^{7} x\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} - 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} - 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} - 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} - \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{1}{3}} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} - a} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} - a} a^{\frac{1}{3}} b x^{2} + 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} x - 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} a - a\right)} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} + 3}{a b^{\frac{2}{3}}}}}{2 \, {\left(b x^{3} + a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3)))*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 32*(9*b^7*x^22 - 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 + 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 + 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 + 4608*a^7*x - sqrt(3)*(5*b^7*x^22 - 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 - 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 - 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 - 2560*a^7*x))*a^(2/3)*b^(1/3) - 8*(3*b^7*x^23 - 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 - 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 - 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 - 61440*a^7*x^2 - 2*sqrt(3)*(b^7*x^23 - 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 + 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 + 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 + 17920*a^7*x^2))*a^(1/3)*b^(2/3) + 4*sqrt(1/3)*((3*b^7*x^22 - 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 - 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 - 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 - 24576*a^7*x - 2*sqrt(3)*(b^7*x^22 - 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 - 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 + 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 + 7168*a^7*x))*sqrt(-b*x^3 - a)*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 - 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 - 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 - 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 - sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 - a)*a^(1/3) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*sqrt(-b*x^3 - a)*b^(1/3))*sqrt(-(2*sqrt(3) + 3)/(a*b^(2/3))) + 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) + 3)/(a*b^(2/3)))*arctan(1/2*sqrt(1/3)*(sqrt(-b*x^3 - a)*a^(1/3)*b*x^2 + 2*sqrt(-b*x^3 - a)*(sqrt(3)*x - 2*x)*a^(2/3)*b^(2/3) + 2*sqrt(-b*x^3 - a)*(sqrt(3)*a - a)*b^(1/3))*sqrt((2*sqrt(3) + 3)/(a*b^(2/3)))/(b*x^3 + a))]","B",0
109,1,1273,0,2.657574," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(1+(b/a)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 4 \, \sqrt{\frac{1}{3}} {\left(486 \, a b^{7} x^{20} - 28512 \, a^{2} b^{6} x^{17} + 86832 \, a^{3} b^{5} x^{14} - 145152 \, a^{4} b^{4} x^{11} - 238464 \, a^{5} b^{3} x^{8} - 414720 \, a^{6} b^{2} x^{5} - 82944 \, a^{7} b x^{2} + {\left(3 \, a b^{7} x^{22} - 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} - 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} - 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} - 24576 \, a^{8} x - 2 \, \sqrt{3} {\left(a b^{7} x^{22} - 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} - 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} + 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} + 7168 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 6 \, \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{b x^{3} + a} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} - 8 \, {\left(3 \, a b^{7} x^{23} - 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} - 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} - 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} - 61440 \, a^{8} x^{2} - 2 \, \sqrt{3} {\left(a b^{7} x^{23} - 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} + 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} + 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} + 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} - 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} + 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} + 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} + 4608 \, a^{8} x - \sqrt{3} {\left(5 \, a b^{7} x^{22} - 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} - 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} - 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} - 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b x^{2} + 2 \, {\left(\sqrt{3} a x - 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, {\left(\sqrt{3} a - a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, \sqrt{b x^{3} + a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b)*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 4*sqrt(1/3)*(486*a*b^7*x^20 - 28512*a^2*b^6*x^17 + 86832*a^3*b^5*x^14 - 145152*a^4*b^4*x^11 - 238464*a^5*b^3*x^8 - 414720*a^6*b^2*x^5 - 82944*a^7*b*x^2 + (3*a*b^7*x^22 - 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 - 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 - 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 - 24576*a^8*x - 2*sqrt(3)*(a*b^7*x^22 - 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 - 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 + 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 + 7168*a^8*x))*(b/a)^(2/3) - 6*sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*(b/a)^(1/3))*sqrt(b*x^3 + a)*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b) - 8*(3*a*b^7*x^23 - 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 - 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 - 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 - 61440*a^8*x^2 - 2*sqrt(3)*(a*b^7*x^23 - 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 + 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 + 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 + 17920*a^8*x^2))*(b/a)^(2/3) + 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8) + 32*(9*a*b^7*x^22 - 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 + 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 + 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 + 4608*a^8*x - sqrt(3)*(5*a*b^7*x^22 - 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 - 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 - 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 - 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b)*arctan(1/2*sqrt(1/3)*(b*x^2 + 2*(sqrt(3)*a*x - 2*a*x)*(b/a)^(2/3) + 2*(sqrt(3)*a - a)*(b/a)^(1/3))*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b)/sqrt(b*x^3 + a))]","A",0
110,1,1330,0,2.846401," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(1-(b/a)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} - 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, a b^{7} x^{22} + 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} + 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} + 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} + 24576 \, a^{8} x - 2 \, \sqrt{3} {\left(a b^{7} x^{22} + 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} + 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} - 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} - 7168 \, a^{8} x\right)}\right)} \sqrt{-b x^{3} + a} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} + a} \left(\frac{b}{a}\right)^{\frac{1}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} + 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} + 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} + 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} - \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} + a}\right)} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} + 8 \, {\left(3 \, a b^{7} x^{23} + 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} + 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} + 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} + 61440 \, a^{8} x^{2} - 2 \, \sqrt{3} {\left(a b^{7} x^{23} + 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} - 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} - 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} - 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} + 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} - 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} - 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} - 4608 \, a^{8} x - \sqrt{3} {\left(5 \, a b^{7} x^{22} + 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} + 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} + 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} + 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} + a} b x^{2} - 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} a x - 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} a - a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, {\left(b x^{3} - a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b)*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 - 4*sqrt(1/3)*((3*a*b^7*x^22 + 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 + 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 + 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 + 24576*a^8*x - 2*sqrt(3)*(a*b^7*x^22 + 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 + 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 - 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 - 7168*a^8*x))*sqrt(-b*x^3 + a)*(b/a)^(2/3) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*sqrt(-b*x^3 + a)*(b/a)^(1/3) + 6*(81*a*b^7*x^20 + 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 + 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 + 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 - sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 + a))*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b) + 8*(3*a*b^7*x^23 + 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 + 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 + 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 + 61440*a^8*x^2 - 2*sqrt(3)*(a*b^7*x^23 + 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 - 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 - 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 - 17920*a^8*x^2))*(b/a)^(2/3) - 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8) + 32*(9*a*b^7*x^22 + 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 - 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 - 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 - 4608*a^8*x - sqrt(3)*(5*a*b^7*x^22 + 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 + 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 + 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 + 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b)*arctan(-1/2*sqrt(1/3)*(sqrt(-b*x^3 + a)*b*x^2 - 2*sqrt(-b*x^3 + a)*(sqrt(3)*a*x - 2*a*x)*(b/a)^(2/3) + 2*sqrt(-b*x^3 + a)*(sqrt(3)*a - a)*(b/a)^(1/3))*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b)/(b*x^3 - a))]","B",0
111,1,1278,0,2.919574," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(1-(b/a)^(1/3)*x-3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} - 4 \, \sqrt{\frac{1}{3}} {\left(486 \, a b^{7} x^{20} + 28512 \, a^{2} b^{6} x^{17} + 86832 \, a^{3} b^{5} x^{14} + 145152 \, a^{4} b^{4} x^{11} - 238464 \, a^{5} b^{3} x^{8} + 414720 \, a^{6} b^{2} x^{5} - 82944 \, a^{7} b x^{2} + {\left(3 \, a b^{7} x^{22} + 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} + 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} + 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} + 24576 \, a^{8} x - 2 \, \sqrt{3} {\left(a b^{7} x^{22} + 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} + 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} - 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} - 7168 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 6 \, \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{b x^{3} - a} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} + 8 \, {\left(3 \, a b^{7} x^{23} + 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} + 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} + 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} + 61440 \, a^{8} x^{2} - 2 \, \sqrt{3} {\left(a b^{7} x^{23} + 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} - 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} - 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} - 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} + 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} - 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} - 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} - 4608 \, a^{8} x - \sqrt{3} {\left(5 \, a b^{7} x^{22} + 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} + 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} + 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} + 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(b x^{2} - 2 \, {\left(\sqrt{3} a x - 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, {\left(\sqrt{3} a - a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, \sqrt{b x^{3} - a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b)*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 - 4*sqrt(1/3)*(486*a*b^7*x^20 + 28512*a^2*b^6*x^17 + 86832*a^3*b^5*x^14 + 145152*a^4*b^4*x^11 - 238464*a^5*b^3*x^8 + 414720*a^6*b^2*x^5 - 82944*a^7*b*x^2 + (3*a*b^7*x^22 + 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 + 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 + 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 + 24576*a^8*x - 2*sqrt(3)*(a*b^7*x^22 + 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 + 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 - 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 - 7168*a^8*x))*(b/a)^(2/3) - 6*sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*(b/a)^(1/3))*sqrt(b*x^3 - a)*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b) + 8*(3*a*b^7*x^23 + 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 + 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 + 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 + 61440*a^8*x^2 - 2*sqrt(3)*(a*b^7*x^23 + 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 - 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 - 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 - 17920*a^8*x^2))*(b/a)^(2/3) - 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8) + 32*(9*a*b^7*x^22 + 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 - 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 - 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 - 4608*a^8*x - sqrt(3)*(5*a*b^7*x^22 + 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 + 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 + 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 + 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b)*arctan(-1/2*sqrt(1/3)*(b*x^2 - 2*(sqrt(3)*a*x - 2*a*x)*(b/a)^(2/3) + 2*(sqrt(3)*a - a)*(b/a)^(1/3))*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b)/sqrt(b*x^3 - a))]","A",0
112,1,1339,0,3.170094," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(1+(b/a)^(1/3)*x-3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, a b^{7} x^{22} - 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} - 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} - 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} - 24576 \, a^{8} x - 2 \, \sqrt{3} {\left(a b^{7} x^{22} - 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} - 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} + 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} + 7168 \, a^{8} x\right)}\right)} \sqrt{-b x^{3} - a} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} - \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} - a} \left(\frac{b}{a}\right)^{\frac{1}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} - 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} - 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} - 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} - \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} - a}\right)} \sqrt{-\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} - 8 \, {\left(3 \, a b^{7} x^{23} - 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} - 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} - 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} - 61440 \, a^{8} x^{2} - 2 \, \sqrt{3} {\left(a b^{7} x^{23} - 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} + 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} + 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} + 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} - 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} + 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} + 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} + 4608 \, a^{8} x - \sqrt{3} {\left(5 \, a b^{7} x^{22} - 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} - 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} - 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} - 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} - a} b x^{2} + 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} a x - 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} a - a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(2 \, \sqrt{3} + 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, {\left(b x^{3} + a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b)*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 4*sqrt(1/3)*((3*a*b^7*x^22 - 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 - 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 - 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 - 24576*a^8*x - 2*sqrt(3)*(a*b^7*x^22 - 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 - 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 + 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 + 7168*a^8*x))*sqrt(-b*x^3 - a)*(b/a)^(2/3) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 - sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*sqrt(-b*x^3 - a)*(b/a)^(1/3) + 6*(81*a*b^7*x^20 - 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 - 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 - 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 - sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 - a))*sqrt(-(2*sqrt(3) + 3)*(b/a)^(1/3)/b) - 8*(3*a*b^7*x^23 - 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 - 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 - 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 - 61440*a^8*x^2 - 2*sqrt(3)*(a*b^7*x^23 - 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 + 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 + 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 + 17920*a^8*x^2))*(b/a)^(2/3) + 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8) + 32*(9*a*b^7*x^22 - 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 + 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 + 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 + 4608*a^8*x - sqrt(3)*(5*a*b^7*x^22 - 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 - 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 - 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 - 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b)*arctan(1/2*sqrt(1/3)*(sqrt(-b*x^3 - a)*b*x^2 + 2*sqrt(-b*x^3 - a)*(sqrt(3)*a*x - 2*a*x)*(b/a)^(2/3) + 2*sqrt(-b*x^3 - a)*(sqrt(3)*a - a)*(b/a)^(1/3))*sqrt((2*sqrt(3) + 3)*(b/a)^(1/3)/b)/(b*x^3 + a))]","B",0
113,1,50,0,0.911553," ","integrate((1+x-3^(1/2))/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \sqrt{2 \, \sqrt{3} - 3} \arctan\left(\frac{{\left(\sqrt{3} {\left(x^{2} - 4 \, x - 2\right)} - 6 \, x - 6\right)} \sqrt{2 \, \sqrt{3} - 3}}{6 \, \sqrt{x^{3} + 1}}\right)"," ",0,"1/3*sqrt(3)*sqrt(2*sqrt(3) - 3)*arctan(1/6*(sqrt(3)*(x^2 - 4*x - 2) - 6*x - 6)*sqrt(2*sqrt(3) - 3)/sqrt(x^3 + 1))","A",0
114,1,59,0,1.463550," ","integrate((1-x-3^(1/2))/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \sqrt{2 \, \sqrt{3} - 3} \arctan\left(\frac{\sqrt{-x^{3} + 1} {\left(\sqrt{3} {\left(x^{2} + 4 \, x - 2\right)} + 6 \, x - 6\right)} \sqrt{2 \, \sqrt{3} - 3}}{6 \, {\left(x^{3} - 1\right)}}\right)"," ",0,"1/3*sqrt(3)*sqrt(2*sqrt(3) - 3)*arctan(1/6*sqrt(-x^3 + 1)*(sqrt(3)*(x^2 + 4*x - 2) + 6*x - 6)*sqrt(2*sqrt(3) - 3)/(x^3 - 1))","A",0
115,1,204,0,1.447958," ","integrate((1-x-3^(1/2))/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \sqrt{2 \, \sqrt{3} - 3} \log\left(\frac{x^{8} + 16 \, x^{7} + 112 \, x^{6} + 16 \, x^{5} + 112 \, x^{4} - 224 \, x^{3} + 64 \, x^{2} - 4 \, {\left(2 \, x^{6} + 18 \, x^{5} + 42 \, x^{4} + 8 \, x^{3} + \sqrt{3} {\left(x^{6} + 12 \, x^{5} + 18 \, x^{4} + 16 \, x^{3} - 12 \, x^{2} - 8\right)} - 24 \, x + 8\right)} \sqrt{x^{3} - 1} \sqrt{2 \, \sqrt{3} - 3} + 16 \, \sqrt{3} {\left(x^{7} + 2 \, x^{6} + 6 \, x^{5} - 5 \, x^{4} + 2 \, x^{3} - 6 \, x^{2} + 4 \, x - 4\right)} - 128 \, x + 112}{x^{8} - 8 \, x^{7} + 16 \, x^{6} + 16 \, x^{5} - 56 \, x^{4} - 32 \, x^{3} + 64 \, x^{2} + 64 \, x + 16}\right)"," ",0,"1/6*sqrt(3)*sqrt(2*sqrt(3) - 3)*log((x^8 + 16*x^7 + 112*x^6 + 16*x^5 + 112*x^4 - 224*x^3 + 64*x^2 - 4*(2*x^6 + 18*x^5 + 42*x^4 + 8*x^3 + sqrt(3)*(x^6 + 12*x^5 + 18*x^4 + 16*x^3 - 12*x^2 - 8) - 24*x + 8)*sqrt(x^3 - 1)*sqrt(2*sqrt(3) - 3) + 16*sqrt(3)*(x^7 + 2*x^6 + 6*x^5 - 5*x^4 + 2*x^3 - 6*x^2 + 4*x - 4) - 128*x + 112)/(x^8 - 8*x^7 + 16*x^6 + 16*x^5 - 56*x^4 - 32*x^3 + 64*x^2 + 64*x + 16))","B",0
116,1,206,0,0.925539," ","integrate((1+x-3^(1/2))/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \sqrt{2 \, \sqrt{3} - 3} \log\left(\frac{x^{8} - 16 \, x^{7} + 112 \, x^{6} - 16 \, x^{5} + 112 \, x^{4} + 224 \, x^{3} + 64 \, x^{2} + 4 \, {\left(2 \, x^{6} - 18 \, x^{5} + 42 \, x^{4} - 8 \, x^{3} + \sqrt{3} {\left(x^{6} - 12 \, x^{5} + 18 \, x^{4} - 16 \, x^{3} - 12 \, x^{2} - 8\right)} + 24 \, x + 8\right)} \sqrt{-x^{3} - 1} \sqrt{2 \, \sqrt{3} - 3} - 16 \, \sqrt{3} {\left(x^{7} - 2 \, x^{6} + 6 \, x^{5} + 5 \, x^{4} + 2 \, x^{3} + 6 \, x^{2} + 4 \, x + 4\right)} + 128 \, x + 112}{x^{8} + 8 \, x^{7} + 16 \, x^{6} - 16 \, x^{5} - 56 \, x^{4} + 32 \, x^{3} + 64 \, x^{2} - 64 \, x + 16}\right)"," ",0,"1/6*sqrt(3)*sqrt(2*sqrt(3) - 3)*log((x^8 - 16*x^7 + 112*x^6 - 16*x^5 + 112*x^4 + 224*x^3 + 64*x^2 + 4*(2*x^6 - 18*x^5 + 42*x^4 - 8*x^3 + sqrt(3)*(x^6 - 12*x^5 + 18*x^4 - 16*x^3 - 12*x^2 - 8) + 24*x + 8)*sqrt(-x^3 - 1)*sqrt(2*sqrt(3) - 3) - 16*sqrt(3)*(x^7 - 2*x^6 + 6*x^5 + 5*x^4 + 2*x^3 + 6*x^2 + 4*x + 4) + 128*x + 112)/(x^8 + 8*x^7 + 16*x^6 - 16*x^5 - 56*x^4 + 32*x^3 + 64*x^2 - 64*x + 16))","B",0
117,1,1236,0,4.776163," ","integrate((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 4 \, \sqrt{\frac{1}{3}} \sqrt{b x^{3} + a} {\left({\left(3 \, b^{7} x^{22} - 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} - 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} - 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} - 24576 \, a^{7} x + 2 \, \sqrt{3} {\left(b^{7} x^{22} - 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} - 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} + 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} + 7168 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} - 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} - 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} - 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} + \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} a^{\frac{1}{3}} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} + 32 \, {\left(9 \, b^{7} x^{22} - 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} + 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} + 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} + 4608 \, a^{7} x + \sqrt{3} {\left(5 \, b^{7} x^{22} - 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} - 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} - 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} - 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} - 8 \, {\left(3 \, b^{7} x^{23} - 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} - 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} - 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} - 61440 \, a^{7} x^{2} + 2 \, \sqrt{3} {\left(b^{7} x^{23} - 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} + 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} + 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} + 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(a^{\frac{1}{3}} b x^{2} - 2 \, {\left(\sqrt{3} x + 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} a + a\right)} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}}}{2 \, \sqrt{b x^{3} + a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3)))*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 4*sqrt(1/3)*sqrt(b*x^3 + a)*((3*b^7*x^22 - 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 - 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 - 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 - 24576*a^7*x + 2*sqrt(3)*(b^7*x^22 - 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 - 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 + 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 + 7168*a^7*x))*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 - 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 - 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 - 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 + sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*a^(1/3) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*b^(1/3))*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3))) + 32*(9*b^7*x^22 - 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 + 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 + 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 + 4608*a^7*x + sqrt(3)*(5*b^7*x^22 - 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 - 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 - 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 - 2560*a^7*x))*a^(2/3)*b^(1/3) - 8*(3*b^7*x^23 - 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 - 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 - 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 - 61440*a^7*x^2 + 2*sqrt(3)*(b^7*x^23 - 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 + 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 + 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 + 17920*a^7*x^2))*a^(1/3)*b^(2/3) - 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) - 3)/(a*b^(2/3)))*arctan(-1/2*sqrt(1/3)*(a^(1/3)*b*x^2 - 2*(sqrt(3)*x + 2*x)*a^(2/3)*b^(2/3) - 2*(sqrt(3)*a + a)*b^(1/3))*sqrt((2*sqrt(3) - 3)/(a*b^(2/3)))/sqrt(b*x^3 + a))]","A",0
118,1,1288,0,3.808635," ","integrate((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 32 \, {\left(9 \, b^{7} x^{22} + 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} - 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} - 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} - 4608 \, a^{7} x + \sqrt{3} {\left(5 \, b^{7} x^{22} + 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} + 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} + 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} + 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} + 8 \, {\left(3 \, b^{7} x^{23} + 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} + 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} + 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} + 61440 \, a^{7} x^{2} + 2 \, \sqrt{3} {\left(b^{7} x^{23} + 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} - 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} - 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} - 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} - 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, b^{7} x^{22} + 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} + 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} + 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} + 24576 \, a^{7} x + 2 \, \sqrt{3} {\left(b^{7} x^{22} + 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} + 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} - 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} - 7168 \, a^{7} x\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} + 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} + 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} + 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} + \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{1}{3}} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} + a} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} + a} a^{\frac{1}{3}} b x^{2} + 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} x + 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} - 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} a + a\right)} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}}}{2 \, {\left(b x^{3} - a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3)))*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 + 32*(9*b^7*x^22 + 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 - 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 - 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 - 4608*a^7*x + sqrt(3)*(5*b^7*x^22 + 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 + 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 + 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 + 2560*a^7*x))*a^(2/3)*b^(1/3) + 8*(3*b^7*x^23 + 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 + 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 + 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 + 61440*a^7*x^2 + 2*sqrt(3)*(b^7*x^23 + 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 - 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 - 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 - 17920*a^7*x^2))*a^(1/3)*b^(2/3) - 4*sqrt(1/3)*((3*b^7*x^22 + 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 + 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 + 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 + 24576*a^7*x + 2*sqrt(3)*(b^7*x^22 + 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 + 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 - 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 - 7168*a^7*x))*sqrt(-b*x^3 + a)*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 + 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 + 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 + 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 + sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 + a)*a^(1/3) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*sqrt(-b*x^3 + a)*b^(1/3))*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3))) + 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) - 3)/(a*b^(2/3)))*arctan(1/2*sqrt(1/3)*(sqrt(-b*x^3 + a)*a^(1/3)*b*x^2 + 2*sqrt(-b*x^3 + a)*(sqrt(3)*x + 2*x)*a^(2/3)*b^(2/3) - 2*sqrt(-b*x^3 + a)*(sqrt(3)*a + a)*b^(1/3))*sqrt((2*sqrt(3) - 3)/(a*b^(2/3)))/(b*x^3 - a))]","B",0
119,1,1239,0,4.055996," ","integrate((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} - 4 \, \sqrt{\frac{1}{3}} \sqrt{b x^{3} - a} {\left({\left(3 \, b^{7} x^{22} + 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} + 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} + 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} + 24576 \, a^{7} x + 2 \, \sqrt{3} {\left(b^{7} x^{22} + 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} + 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} - 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} - 7168 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} + 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} + 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} + 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} + \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} a^{\frac{1}{3}} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} + 32 \, {\left(9 \, b^{7} x^{22} + 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} - 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} - 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} - 4608 \, a^{7} x + \sqrt{3} {\left(5 \, b^{7} x^{22} + 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} + 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} + 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} + 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} + 8 \, {\left(3 \, b^{7} x^{23} + 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} + 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} + 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} + 61440 \, a^{7} x^{2} + 2 \, \sqrt{3} {\left(b^{7} x^{23} + 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} - 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} - 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} - 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(a^{\frac{1}{3}} b x^{2} + 2 \, {\left(\sqrt{3} x + 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} a + a\right)} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}}}{2 \, \sqrt{b x^{3} - a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) - 3)/(a*b^(2/3)))*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 - 4*sqrt(1/3)*sqrt(b*x^3 - a)*((3*b^7*x^22 + 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 + 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 + 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 + 24576*a^7*x + 2*sqrt(3)*(b^7*x^22 + 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 + 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 - 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 - 7168*a^7*x))*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 + 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 + 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 + 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 + sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*a^(1/3) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*b^(1/3))*sqrt((2*sqrt(3) - 3)/(a*b^(2/3))) + 32*(9*b^7*x^22 + 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 - 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 - 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 - 4608*a^7*x + sqrt(3)*(5*b^7*x^22 + 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 + 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 + 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 + 2560*a^7*x))*a^(2/3)*b^(1/3) + 8*(3*b^7*x^23 + 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 + 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 + 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 + 61440*a^7*x^2 + 2*sqrt(3)*(b^7*x^23 + 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 - 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 - 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 - 17920*a^7*x^2))*a^(1/3)*b^(2/3) + 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3)))*arctan(1/2*sqrt(1/3)*(a^(1/3)*b*x^2 + 2*(sqrt(3)*x + 2*x)*a^(2/3)*b^(2/3) - 2*(sqrt(3)*a + a)*b^(1/3))*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3)))/sqrt(b*x^3 - a))]","A",0
120,1,1299,0,4.430718," ","integrate((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 32 \, {\left(9 \, b^{7} x^{22} - 846 \, a b^{6} x^{19} + 4617 \, a^{2} b^{5} x^{16} + 5472 \, a^{3} b^{4} x^{13} + 43776 \, a^{4} b^{3} x^{10} + 98496 \, a^{5} b^{2} x^{7} + 59328 \, a^{6} b x^{4} + 4608 \, a^{7} x + \sqrt{3} {\left(5 \, b^{7} x^{22} - 505 \, a b^{6} x^{19} + 2130 \, a^{2} b^{5} x^{16} - 4928 \, a^{3} b^{4} x^{13} - 28688 \, a^{4} b^{3} x^{10} - 53760 \, a^{5} b^{2} x^{7} - 35200 \, a^{6} b x^{4} - 2560 \, a^{7} x\right)}\right)} a^{\frac{2}{3}} b^{\frac{1}{3}} - 8 \, {\left(3 \, b^{7} x^{23} - 1077 \, a b^{6} x^{20} + 13320 \, a^{2} b^{5} x^{17} - 19200 \, a^{3} b^{4} x^{14} - 111360 \, a^{4} b^{3} x^{11} - 345024 \, a^{5} b^{2} x^{8} - 328704 \, a^{6} b x^{5} - 61440 \, a^{7} x^{2} + 2 \, \sqrt{3} {\left(b^{7} x^{23} - 299 \, a b^{6} x^{20} + 4260 \, a^{2} b^{5} x^{17} + 1520 \, a^{3} b^{4} x^{14} + 26720 \, a^{4} b^{3} x^{11} + 105024 \, a^{5} b^{2} x^{8} + 93184 \, a^{6} b x^{5} + 17920 \, a^{7} x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{2}{3}} + 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, b^{7} x^{22} - 2688 \, a b^{6} x^{19} + 56952 \, a^{2} b^{5} x^{16} - 93504 \, a^{3} b^{4} x^{13} - 63552 \, a^{4} b^{3} x^{10} - 377856 \, a^{5} b^{2} x^{7} - 314880 \, a^{6} b x^{4} - 24576 \, a^{7} x + 2 \, \sqrt{3} {\left(b^{7} x^{22} - 764 \, a b^{6} x^{19} + 16860 \, a^{2} b^{5} x^{16} - 19792 \, a^{3} b^{4} x^{13} + 42368 \, a^{4} b^{3} x^{10} + 104448 \, a^{5} b^{2} x^{7} + 90880 \, a^{6} b x^{4} + 7168 \, a^{7} x\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{2}{3}} b^{\frac{2}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} - 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} - 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} - 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} + \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{1}{3}} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} - a} b^{\frac{1}{3}}\right)} \sqrt{\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} a^{\frac{1}{3}} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} - a} a^{\frac{1}{3}} b x^{2} - 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} x + 2 \, x\right)} a^{\frac{2}{3}} b^{\frac{2}{3}} - 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} a + a\right)} b^{\frac{1}{3}}\right)} \sqrt{-\frac{2 \, \sqrt{3} - 3}{a b^{\frac{2}{3}}}}}{2 \, {\left(b x^{3} + a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*a^(1/3)*sqrt((2*sqrt(3) - 3)/(a*b^(2/3)))*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 32*(9*b^7*x^22 - 846*a*b^6*x^19 + 4617*a^2*b^5*x^16 + 5472*a^3*b^4*x^13 + 43776*a^4*b^3*x^10 + 98496*a^5*b^2*x^7 + 59328*a^6*b*x^4 + 4608*a^7*x + sqrt(3)*(5*b^7*x^22 - 505*a*b^6*x^19 + 2130*a^2*b^5*x^16 - 4928*a^3*b^4*x^13 - 28688*a^4*b^3*x^10 - 53760*a^5*b^2*x^7 - 35200*a^6*b*x^4 - 2560*a^7*x))*a^(2/3)*b^(1/3) - 8*(3*b^7*x^23 - 1077*a*b^6*x^20 + 13320*a^2*b^5*x^17 - 19200*a^3*b^4*x^14 - 111360*a^4*b^3*x^11 - 345024*a^5*b^2*x^8 - 328704*a^6*b*x^5 - 61440*a^7*x^2 + 2*sqrt(3)*(b^7*x^23 - 299*a*b^6*x^20 + 4260*a^2*b^5*x^17 + 1520*a^3*b^4*x^14 + 26720*a^4*b^3*x^11 + 105024*a^5*b^2*x^8 + 93184*a^6*b*x^5 + 17920*a^7*x^2))*a^(1/3)*b^(2/3) + 4*sqrt(1/3)*((3*b^7*x^22 - 2688*a*b^6*x^19 + 56952*a^2*b^5*x^16 - 93504*a^3*b^4*x^13 - 63552*a^4*b^3*x^10 - 377856*a^5*b^2*x^7 - 314880*a^6*b*x^4 - 24576*a^7*x + 2*sqrt(3)*(b^7*x^22 - 764*a*b^6*x^19 + 16860*a^2*b^5*x^16 - 19792*a^3*b^4*x^13 + 42368*a^4*b^3*x^10 + 104448*a^5*b^2*x^7 + 90880*a^6*b*x^4 + 7168*a^7*x))*sqrt(-b*x^3 - a)*a^(2/3)*b^(2/3) + 6*(81*a*b^7*x^20 - 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 - 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 - 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 + sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 - a)*a^(1/3) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*sqrt(-b*x^3 - a)*b^(1/3))*sqrt((2*sqrt(3) - 3)/(a*b^(2/3))) - 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*a^(1/3)*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3)))*arctan(-1/2*sqrt(1/3)*(sqrt(-b*x^3 - a)*a^(1/3)*b*x^2 - 2*sqrt(-b*x^3 - a)*(sqrt(3)*x + 2*x)*a^(2/3)*b^(2/3) - 2*sqrt(-b*x^3 - a)*(sqrt(3)*a + a)*b^(1/3))*sqrt(-(2*sqrt(3) - 3)/(a*b^(2/3)))/(b*x^3 + a))]","B",0
121,1,1270,0,2.977853," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(1+(b/a)^(1/3)*x+3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 4 \, \sqrt{\frac{1}{3}} {\left(486 \, a b^{7} x^{20} - 28512 \, a^{2} b^{6} x^{17} + 86832 \, a^{3} b^{5} x^{14} - 145152 \, a^{4} b^{4} x^{11} - 238464 \, a^{5} b^{3} x^{8} - 414720 \, a^{6} b^{2} x^{5} - 82944 \, a^{7} b x^{2} + {\left(3 \, a b^{7} x^{22} - 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} - 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} - 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} - 24576 \, a^{8} x + 2 \, \sqrt{3} {\left(a b^{7} x^{22} - 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} - 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} + 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} + 7168 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 6 \, \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{b x^{3} + a} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} - 8 \, {\left(3 \, a b^{7} x^{23} - 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} - 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} - 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} - 61440 \, a^{8} x^{2} + 2 \, \sqrt{3} {\left(a b^{7} x^{23} - 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} + 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} + 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} + 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} - 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} + 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} + 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} + 4608 \, a^{8} x + \sqrt{3} {\left(5 \, a b^{7} x^{22} - 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} - 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} - 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} - 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(b x^{2} - 2 \, {\left(\sqrt{3} a x + 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} a + a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, \sqrt{b x^{3} + a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b)*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 4*sqrt(1/3)*(486*a*b^7*x^20 - 28512*a^2*b^6*x^17 + 86832*a^3*b^5*x^14 - 145152*a^4*b^4*x^11 - 238464*a^5*b^3*x^8 - 414720*a^6*b^2*x^5 - 82944*a^7*b*x^2 + (3*a*b^7*x^22 - 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 - 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 - 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 - 24576*a^8*x + 2*sqrt(3)*(a*b^7*x^22 - 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 - 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 + 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 + 7168*a^8*x))*(b/a)^(2/3) + 6*sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*(b/a)^(1/3))*sqrt(b*x^3 + a)*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b) - 8*(3*a*b^7*x^23 - 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 - 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 - 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 - 61440*a^8*x^2 + 2*sqrt(3)*(a*b^7*x^23 - 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 + 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 + 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 + 17920*a^8*x^2))*(b/a)^(2/3) - 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8) + 32*(9*a*b^7*x^22 - 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 + 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 + 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 + 4608*a^8*x + sqrt(3)*(5*a*b^7*x^22 - 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 - 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 - 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 - 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b)*arctan(-1/2*sqrt(1/3)*(b*x^2 - 2*(sqrt(3)*a*x + 2*a*x)*(b/a)^(2/3) - 2*(sqrt(3)*a + a)*(b/a)^(1/3))*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b)/sqrt(b*x^3 + a))]","A",0
122,1,1324,0,3.230033," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(1-(b/a)^(1/3)*x+3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} - 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, a b^{7} x^{22} + 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} + 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} + 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} + 24576 \, a^{8} x + 2 \, \sqrt{3} {\left(a b^{7} x^{22} + 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} + 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} - 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} - 7168 \, a^{8} x\right)}\right)} \sqrt{-b x^{3} + a} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} + a} \left(\frac{b}{a}\right)^{\frac{1}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} + 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} + 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} + 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} + \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} + a}\right)} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} + 8 \, {\left(3 \, a b^{7} x^{23} + 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} + 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} + 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} + 61440 \, a^{8} x^{2} + 2 \, \sqrt{3} {\left(a b^{7} x^{23} + 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} - 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} - 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} - 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} + 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} - 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} - 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} - 4608 \, a^{8} x + \sqrt{3} {\left(5 \, a b^{7} x^{22} + 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} + 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} + 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} + 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} + a} b x^{2} + 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} a x + 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, \sqrt{-b x^{3} + a} {\left(\sqrt{3} a + a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, {\left(b x^{3} - a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b)*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 - 4*sqrt(1/3)*((3*a*b^7*x^22 + 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 + 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 + 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 + 24576*a^8*x + 2*sqrt(3)*(a*b^7*x^22 + 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 + 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 - 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 - 7168*a^8*x))*sqrt(-b*x^3 + a)*(b/a)^(2/3) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*sqrt(-b*x^3 + a)*(b/a)^(1/3) + 6*(81*a*b^7*x^20 + 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 + 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 + 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 + sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 + a))*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b) + 8*(3*a*b^7*x^23 + 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 + 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 + 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 + 61440*a^8*x^2 + 2*sqrt(3)*(a*b^7*x^23 + 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 - 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 - 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 - 17920*a^8*x^2))*(b/a)^(2/3) + 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8) + 32*(9*a*b^7*x^22 + 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 - 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 - 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 - 4608*a^8*x + sqrt(3)*(5*a*b^7*x^22 + 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 + 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 + 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 + 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b)*arctan(1/2*sqrt(1/3)*(sqrt(-b*x^3 + a)*b*x^2 + 2*sqrt(-b*x^3 + a)*(sqrt(3)*a*x + 2*a*x)*(b/a)^(2/3) - 2*sqrt(-b*x^3 + a)*(sqrt(3)*a + a)*(b/a)^(1/3))*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b)/(b*x^3 - a))]","B",0
123,1,1273,0,2.633957," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(1-(b/a)^(1/3)*x+3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} + 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} + 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} - 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} - 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} - 4 \, \sqrt{\frac{1}{3}} {\left(486 \, a b^{7} x^{20} + 28512 \, a^{2} b^{6} x^{17} + 86832 \, a^{3} b^{5} x^{14} + 145152 \, a^{4} b^{4} x^{11} - 238464 \, a^{5} b^{3} x^{8} + 414720 \, a^{6} b^{2} x^{5} - 82944 \, a^{7} b x^{2} + {\left(3 \, a b^{7} x^{22} + 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} + 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} + 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} + 24576 \, a^{8} x + 2 \, \sqrt{3} {\left(a b^{7} x^{22} + 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} + 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} - 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} - 7168 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 6 \, \sqrt{3} {\left(47 \, a b^{7} x^{20} + 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} + 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} - 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)} + 2 \, {\left(30 \, a b^{7} x^{21} + 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} + 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} - 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} - 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} + 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} + 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} + 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} + 1024 \, a^{8}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{b x^{3} - a} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} + 8 \, {\left(3 \, a b^{7} x^{23} + 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} + 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} + 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} + 61440 \, a^{8} x^{2} + 2 \, \sqrt{3} {\left(a b^{7} x^{23} + 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} - 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} - 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} - 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} + 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} - 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} - 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} - 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} + 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} - 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} - 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} - 4608 \, a^{8} x + \sqrt{3} {\left(5 \, a b^{7} x^{22} + 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} + 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} + 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} + 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} - 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} - 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} + 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} + 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), \sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b x^{2} + 2 \, {\left(\sqrt{3} a x + 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} a + a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, \sqrt{b x^{3} - a}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b)*log((b^8*x^24 + 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 + 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 - 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 - 1089536*a^7*b*x^3 + 28672*a^8 - 4*sqrt(1/3)*(486*a*b^7*x^20 + 28512*a^2*b^6*x^17 + 86832*a^3*b^5*x^14 + 145152*a^4*b^4*x^11 - 238464*a^5*b^3*x^8 + 414720*a^6*b^2*x^5 - 82944*a^7*b*x^2 + (3*a*b^7*x^22 + 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 + 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 + 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 + 24576*a^8*x + 2*sqrt(3)*(a*b^7*x^22 + 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 + 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 - 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 - 7168*a^8*x))*(b/a)^(2/3) + 6*sqrt(3)*(47*a*b^7*x^20 + 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 + 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 - 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2) + 2*(30*a*b^7*x^21 + 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 + 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 - 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 - 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 + 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 + 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 + 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 + 1024*a^8))*(b/a)^(1/3))*sqrt(b*x^3 - a)*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b) + 8*(3*a*b^7*x^23 + 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 + 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 + 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 + 61440*a^8*x^2 + 2*sqrt(3)*(a*b^7*x^23 + 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 - 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 - 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 - 17920*a^8*x^2))*(b/a)^(2/3) + 32*sqrt(3)*(35*a*b^7*x^21 + 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 - 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 - 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 - 512*a^8) + 32*(9*a*b^7*x^22 + 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 - 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 - 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 - 4608*a^8*x + sqrt(3)*(5*a*b^7*x^22 + 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 + 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 + 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 + 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 - 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 - 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 + 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 + 40960*a^7*b*x^3 + 4096*a^8)), sqrt(1/3)*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b)*arctan(1/2*sqrt(1/3)*(b*x^2 + 2*(sqrt(3)*a*x + 2*a*x)*(b/a)^(2/3) - 2*(sqrt(3)*a + a)*(b/a)^(1/3))*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b)/sqrt(b*x^3 - a))]","A",0
124,1,1335,0,2.608803," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(1+(b/a)^(1/3)*x+3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{3}} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \log\left(\frac{b^{8} x^{24} - 1840 \, a b^{7} x^{21} + 67264 \, a^{2} b^{6} x^{18} - 58624 \, a^{3} b^{5} x^{15} + 504064 \, a^{4} b^{4} x^{12} + 2140160 \, a^{5} b^{3} x^{9} + 3100672 \, a^{6} b^{2} x^{6} + 1089536 \, a^{7} b x^{3} + 28672 \, a^{8} + 4 \, \sqrt{\frac{1}{3}} {\left({\left(3 \, a b^{7} x^{22} - 2688 \, a^{2} b^{6} x^{19} + 56952 \, a^{3} b^{5} x^{16} - 93504 \, a^{4} b^{4} x^{13} - 63552 \, a^{5} b^{3} x^{10} - 377856 \, a^{6} b^{2} x^{7} - 314880 \, a^{7} b x^{4} - 24576 \, a^{8} x + 2 \, \sqrt{3} {\left(a b^{7} x^{22} - 764 \, a^{2} b^{6} x^{19} + 16860 \, a^{3} b^{5} x^{16} - 19792 \, a^{4} b^{4} x^{13} + 42368 \, a^{5} b^{3} x^{10} + 104448 \, a^{6} b^{2} x^{7} + 90880 \, a^{7} b x^{4} + 7168 \, a^{8} x\right)}\right)} \sqrt{-b x^{3} - a} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, {\left(30 \, a b^{7} x^{21} - 5010 \, a^{2} b^{6} x^{18} + 44640 \, a^{3} b^{5} x^{15} - 21360 \, a^{4} b^{4} x^{12} + 79872 \, a^{5} b^{3} x^{9} + 233856 \, a^{6} b^{2} x^{6} + 86016 \, a^{7} b x^{3} + 3072 \, a^{8} + \sqrt{3} {\left(17 \, a b^{7} x^{21} - 2920 \, a^{2} b^{6} x^{18} + 24864 \, a^{3} b^{5} x^{15} - 26576 \, a^{4} b^{4} x^{12} - 56000 \, a^{5} b^{3} x^{9} - 115968 \, a^{6} b^{2} x^{6} - 56320 \, a^{7} b x^{3} - 1024 \, a^{8}\right)}\right)} \sqrt{-b x^{3} - a} \left(\frac{b}{a}\right)^{\frac{1}{3}} + 6 \, {\left(81 \, a b^{7} x^{20} - 4752 \, a^{2} b^{6} x^{17} + 14472 \, a^{3} b^{5} x^{14} - 24192 \, a^{4} b^{4} x^{11} - 39744 \, a^{5} b^{3} x^{8} - 69120 \, a^{6} b^{2} x^{5} - 13824 \, a^{7} b x^{2} + \sqrt{3} {\left(47 \, a b^{7} x^{20} - 2724 \, a^{2} b^{6} x^{17} + 8976 \, a^{3} b^{5} x^{14} - 4928 \, a^{4} b^{4} x^{11} + 32448 \, a^{5} b^{3} x^{8} + 37632 \, a^{6} b^{2} x^{5} + 8192 \, a^{7} b x^{2}\right)}\right)} \sqrt{-b x^{3} - a}\right)} \sqrt{\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} - 8 \, {\left(3 \, a b^{7} x^{23} - 1077 \, a^{2} b^{6} x^{20} + 13320 \, a^{3} b^{5} x^{17} - 19200 \, a^{4} b^{4} x^{14} - 111360 \, a^{5} b^{3} x^{11} - 345024 \, a^{6} b^{2} x^{8} - 328704 \, a^{7} b x^{5} - 61440 \, a^{8} x^{2} + 2 \, \sqrt{3} {\left(a b^{7} x^{23} - 299 \, a^{2} b^{6} x^{20} + 4260 \, a^{3} b^{5} x^{17} + 1520 \, a^{4} b^{4} x^{14} + 26720 \, a^{5} b^{3} x^{11} + 105024 \, a^{6} b^{2} x^{8} + 93184 \, a^{7} b x^{5} + 17920 \, a^{8} x^{2}\right)}\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 32 \, \sqrt{3} {\left(35 \, a b^{7} x^{21} - 1141 \, a^{2} b^{6} x^{18} + 2544 \, a^{3} b^{5} x^{15} + 6760 \, a^{4} b^{4} x^{12} + 39520 \, a^{5} b^{3} x^{9} + 55680 \, a^{6} b^{2} x^{6} + 19712 \, a^{7} b x^{3} + 512 \, a^{8}\right)} + 32 \, {\left(9 \, a b^{7} x^{22} - 846 \, a^{2} b^{6} x^{19} + 4617 \, a^{3} b^{5} x^{16} + 5472 \, a^{4} b^{4} x^{13} + 43776 \, a^{5} b^{3} x^{10} + 98496 \, a^{6} b^{2} x^{7} + 59328 \, a^{7} b x^{4} + 4608 \, a^{8} x + \sqrt{3} {\left(5 \, a b^{7} x^{22} - 505 \, a^{2} b^{6} x^{19} + 2130 \, a^{3} b^{5} x^{16} - 4928 \, a^{4} b^{4} x^{13} - 28688 \, a^{5} b^{3} x^{10} - 53760 \, a^{6} b^{2} x^{7} - 35200 \, a^{7} b x^{4} - 2560 \, a^{8} x\right)}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b^{8} x^{24} + 80 \, a b^{7} x^{21} + 2368 \, a^{2} b^{6} x^{18} + 30080 \, a^{3} b^{5} x^{15} + 121984 \, a^{4} b^{4} x^{12} - 240640 \, a^{5} b^{3} x^{9} + 151552 \, a^{6} b^{2} x^{6} - 40960 \, a^{7} b x^{3} + 4096 \, a^{8}}\right), -\sqrt{\frac{1}{3}} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\sqrt{-b x^{3} - a} b x^{2} - 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} a x + 2 \, a x\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, \sqrt{-b x^{3} - a} {\left(\sqrt{3} a + a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(2 \, \sqrt{3} - 3\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{b}}}{2 \, {\left(b x^{3} + a\right)}}\right)\right]"," ",0,"[1/2*sqrt(1/3)*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b)*log((b^8*x^24 - 1840*a*b^7*x^21 + 67264*a^2*b^6*x^18 - 58624*a^3*b^5*x^15 + 504064*a^4*b^4*x^12 + 2140160*a^5*b^3*x^9 + 3100672*a^6*b^2*x^6 + 1089536*a^7*b*x^3 + 28672*a^8 + 4*sqrt(1/3)*((3*a*b^7*x^22 - 2688*a^2*b^6*x^19 + 56952*a^3*b^5*x^16 - 93504*a^4*b^4*x^13 - 63552*a^5*b^3*x^10 - 377856*a^6*b^2*x^7 - 314880*a^7*b*x^4 - 24576*a^8*x + 2*sqrt(3)*(a*b^7*x^22 - 764*a^2*b^6*x^19 + 16860*a^3*b^5*x^16 - 19792*a^4*b^4*x^13 + 42368*a^5*b^3*x^10 + 104448*a^6*b^2*x^7 + 90880*a^7*b*x^4 + 7168*a^8*x))*sqrt(-b*x^3 - a)*(b/a)^(2/3) - 2*(30*a*b^7*x^21 - 5010*a^2*b^6*x^18 + 44640*a^3*b^5*x^15 - 21360*a^4*b^4*x^12 + 79872*a^5*b^3*x^9 + 233856*a^6*b^2*x^6 + 86016*a^7*b*x^3 + 3072*a^8 + sqrt(3)*(17*a*b^7*x^21 - 2920*a^2*b^6*x^18 + 24864*a^3*b^5*x^15 - 26576*a^4*b^4*x^12 - 56000*a^5*b^3*x^9 - 115968*a^6*b^2*x^6 - 56320*a^7*b*x^3 - 1024*a^8))*sqrt(-b*x^3 - a)*(b/a)^(1/3) + 6*(81*a*b^7*x^20 - 4752*a^2*b^6*x^17 + 14472*a^3*b^5*x^14 - 24192*a^4*b^4*x^11 - 39744*a^5*b^3*x^8 - 69120*a^6*b^2*x^5 - 13824*a^7*b*x^2 + sqrt(3)*(47*a*b^7*x^20 - 2724*a^2*b^6*x^17 + 8976*a^3*b^5*x^14 - 4928*a^4*b^4*x^11 + 32448*a^5*b^3*x^8 + 37632*a^6*b^2*x^5 + 8192*a^7*b*x^2))*sqrt(-b*x^3 - a))*sqrt((2*sqrt(3) - 3)*(b/a)^(1/3)/b) - 8*(3*a*b^7*x^23 - 1077*a^2*b^6*x^20 + 13320*a^3*b^5*x^17 - 19200*a^4*b^4*x^14 - 111360*a^5*b^3*x^11 - 345024*a^6*b^2*x^8 - 328704*a^7*b*x^5 - 61440*a^8*x^2 + 2*sqrt(3)*(a*b^7*x^23 - 299*a^2*b^6*x^20 + 4260*a^3*b^5*x^17 + 1520*a^4*b^4*x^14 + 26720*a^5*b^3*x^11 + 105024*a^6*b^2*x^8 + 93184*a^7*b*x^5 + 17920*a^8*x^2))*(b/a)^(2/3) - 32*sqrt(3)*(35*a*b^7*x^21 - 1141*a^2*b^6*x^18 + 2544*a^3*b^5*x^15 + 6760*a^4*b^4*x^12 + 39520*a^5*b^3*x^9 + 55680*a^6*b^2*x^6 + 19712*a^7*b*x^3 + 512*a^8) + 32*(9*a*b^7*x^22 - 846*a^2*b^6*x^19 + 4617*a^3*b^5*x^16 + 5472*a^4*b^4*x^13 + 43776*a^5*b^3*x^10 + 98496*a^6*b^2*x^7 + 59328*a^7*b*x^4 + 4608*a^8*x + sqrt(3)*(5*a*b^7*x^22 - 505*a^2*b^6*x^19 + 2130*a^3*b^5*x^16 - 4928*a^4*b^4*x^13 - 28688*a^5*b^3*x^10 - 53760*a^6*b^2*x^7 - 35200*a^7*b*x^4 - 2560*a^8*x))*(b/a)^(1/3))/(b^8*x^24 + 80*a*b^7*x^21 + 2368*a^2*b^6*x^18 + 30080*a^3*b^5*x^15 + 121984*a^4*b^4*x^12 - 240640*a^5*b^3*x^9 + 151552*a^6*b^2*x^6 - 40960*a^7*b*x^3 + 4096*a^8)), -sqrt(1/3)*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b)*arctan(-1/2*sqrt(1/3)*(sqrt(-b*x^3 - a)*b*x^2 - 2*sqrt(-b*x^3 - a)*(sqrt(3)*a*x + 2*a*x)*(b/a)^(2/3) - 2*sqrt(-b*x^3 - a)*(sqrt(3)*a + a)*(b/a)^(1/3))*sqrt(-(2*sqrt(3) - 3)*(b/a)^(1/3)/b)/(b*x^3 + a))]","B",0
125,0,0,0,1.246310," ","integrate((1+x)/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x - \sqrt{3} + 1\right)}}{x^{4} + x^{3} - 3 \, x^{2} + 4 \, x - 2}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x - sqrt(3) + 1)/(x^4 + x^3 - 3*x^2 + 4*x - 2), x)","F",0
126,0,0,0,1.106083," ","integrate((1+x)/(1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x + \sqrt{3} + 1\right)}}{x^{4} + x^{3} - 3 \, x^{2} + 4 \, x - 2}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x + sqrt(3) + 1)/(x^4 + x^3 - 3*x^2 + 4*x - 2), x)","F",0
127,0,0,0,1.275255," ","integrate((f*x+e)/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x^{2} + {\left(e + f\right)} x - \sqrt{3} {\left(f x + e\right)} + e\right)} \sqrt{x^{3} + 1}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral((f*x^2 + (e + f)*x - sqrt(3)*(f*x + e) + e)*sqrt(x^3 + 1)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
128,0,0,0,1.487156," ","integrate((f*x+e)/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x^{2} + {\left(e - f\right)} x + \sqrt{3} {\left(f x + e\right)} - e\right)} \sqrt{-x^{3} + 1}}{x^{5} - 2 \, x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 2}, x\right)"," ",0,"integral((f*x^2 + (e - f)*x + sqrt(3)*(f*x + e) - e)*sqrt(-x^3 + 1)/(x^5 - 2*x^4 - 2*x^3 - x^2 + 2*x + 2), x)","F",0
129,0,0,0,1.182068," ","integrate((f*x+e)/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(f x^{2} + {\left(e - f\right)} x + \sqrt{3} {\left(f x + e\right)} - e\right)} \sqrt{x^{3} - 1}}{x^{5} - 2 \, x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 2}, x\right)"," ",0,"integral(-(f*x^2 + (e - f)*x + sqrt(3)*(f*x + e) - e)*sqrt(x^3 - 1)/(x^5 - 2*x^4 - 2*x^3 - x^2 + 2*x + 2), x)","F",0
130,0,0,0,1.330646," ","integrate((f*x+e)/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(f x^{2} + {\left(e + f\right)} x - \sqrt{3} {\left(f x + e\right)} + e\right)} \sqrt{-x^{3} - 1}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral(-(f*x^2 + (e + f)*x - sqrt(3)*(f*x + e) + e)*sqrt(-x^3 - 1)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
131,-2,0,0,0.000000," ","integrate((f*x+e)/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
132,0,0,0,65.956495," ","integrate((f*x+e)/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, {\left(2 \, b f x^{4} + 2 \, b e x^{3} - 2 \, a f x - 2 \, a e - \sqrt{3} {\left(b f x^{4} + b e x^{3} + 2 \, a f x + 2 \, a e\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{2}{3}} + {\left(b f x^{5} + b e x^{4} + 8 \, a f x^{2} + 8 \, a e x - \sqrt{3} {\left(b f x^{5} + b e x^{4} - 4 \, a f x^{2} - 4 \, a e x\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b f x^{6} + b e x^{5} - 10 \, a f x^{3} - 10 \, a e x^{2} - 6 \, \sqrt{3} {\left(a f x^{3} + a e x^{2}\right)}\right)} \sqrt{-b x^{3} + a} b^{\frac{2}{3}}}{b^{3} x^{9} - 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} + 8 \, a^{3}}, x\right)"," ",0,"integral((2*(2*b*f*x^4 + 2*b*e*x^3 - 2*a*f*x - 2*a*e - sqrt(3)*(b*f*x^4 + b*e*x^3 + 2*a*f*x + 2*a*e))*sqrt(-b*x^3 + a)*a^(2/3) + (b*f*x^5 + b*e*x^4 + 8*a*f*x^2 + 8*a*e*x - sqrt(3)*(b*f*x^5 + b*e*x^4 - 4*a*f*x^2 - 4*a*e*x))*sqrt(-b*x^3 + a)*a^(1/3)*b^(1/3) + (b*f*x^6 + b*e*x^5 - 10*a*f*x^3 - 10*a*e*x^2 - 6*sqrt(3)*(a*f*x^3 + a*e*x^2))*sqrt(-b*x^3 + a)*b^(2/3))/(b^3*x^9 - 21*a*b^2*x^6 + 12*a^2*b*x^3 + 8*a^3), x)","F",0
133,0,0,0,65.141418," ","integrate((f*x+e)/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{3} - a} {\left(2 \, {\left(2 \, b f x^{4} + 2 \, b e x^{3} - 2 \, a f x - 2 \, a e - \sqrt{3} {\left(b f x^{4} + b e x^{3} + 2 \, a f x + 2 \, a e\right)}\right)} a^{\frac{2}{3}} + {\left(b f x^{5} + b e x^{4} + 8 \, a f x^{2} + 8 \, a e x - \sqrt{3} {\left(b f x^{5} + b e x^{4} - 4 \, a f x^{2} - 4 \, a e x\right)}\right)} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b f x^{6} + b e x^{5} - 10 \, a f x^{3} - 10 \, a e x^{2} - 6 \, \sqrt{3} {\left(a f x^{3} + a e x^{2}\right)}\right)} b^{\frac{2}{3}}\right)}}{b^{3} x^{9} - 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} + 8 \, a^{3}}, x\right)"," ",0,"integral(-sqrt(b*x^3 - a)*(2*(2*b*f*x^4 + 2*b*e*x^3 - 2*a*f*x - 2*a*e - sqrt(3)*(b*f*x^4 + b*e*x^3 + 2*a*f*x + 2*a*e))*a^(2/3) + (b*f*x^5 + b*e*x^4 + 8*a*f*x^2 + 8*a*e*x - sqrt(3)*(b*f*x^5 + b*e*x^4 - 4*a*f*x^2 - 4*a*e*x))*a^(1/3)*b^(1/3) + (b*f*x^6 + b*e*x^5 - 10*a*f*x^3 - 10*a*e*x^2 - 6*sqrt(3)*(a*f*x^3 + a*e*x^2))*b^(2/3))/(b^3*x^9 - 21*a*b^2*x^6 + 12*a^2*b*x^3 + 8*a^3), x)","F",0
134,0,0,0,71.204163," ","integrate((f*x+e)/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, {\left(2 \, b f x^{4} + 2 \, b e x^{3} + 2 \, a f x + 2 \, a e - \sqrt{3} {\left(b f x^{4} + b e x^{3} - 2 \, a f x - 2 \, a e\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{2}{3}} - {\left(b f x^{5} + b e x^{4} - 8 \, a f x^{2} - 8 \, a e x - \sqrt{3} {\left(b f x^{5} + b e x^{4} + 4 \, a f x^{2} + 4 \, a e x\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b f x^{6} + b e x^{5} + 10 \, a f x^{3} + 10 \, a e x^{2} + 6 \, \sqrt{3} {\left(a f x^{3} + a e x^{2}\right)}\right)} \sqrt{-b x^{3} - a} b^{\frac{2}{3}}}{b^{3} x^{9} + 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} - 8 \, a^{3}}, x\right)"," ",0,"integral(-(2*(2*b*f*x^4 + 2*b*e*x^3 + 2*a*f*x + 2*a*e - sqrt(3)*(b*f*x^4 + b*e*x^3 - 2*a*f*x - 2*a*e))*sqrt(-b*x^3 - a)*a^(2/3) - (b*f*x^5 + b*e*x^4 - 8*a*f*x^2 - 8*a*e*x - sqrt(3)*(b*f*x^5 + b*e*x^4 + 4*a*f*x^2 + 4*a*e*x))*sqrt(-b*x^3 - a)*a^(1/3)*b^(1/3) + (b*f*x^6 + b*e*x^5 + 10*a*f*x^3 + 10*a*e*x^2 + 6*sqrt(3)*(a*f*x^3 + a*e*x^2))*sqrt(-b*x^3 - a)*b^(2/3))/(b^3*x^9 + 21*a*b^2*x^6 + 12*a^2*b*x^3 - 8*a^3), x)","F",0
135,0,0,0,1.157886," ","integrate(x/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x^{2} - \sqrt{3} x + x\right)}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x^2 - sqrt(3)*x + x)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
136,0,0,0,1.315297," ","integrate(x/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} + 1} {\left(x^{2} + \sqrt{3} x - x\right)}}{x^{5} - 2 \, x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 2}, x\right)"," ",0,"integral(sqrt(-x^3 + 1)*(x^2 + sqrt(3)*x - x)/(x^5 - 2*x^4 - 2*x^3 - x^2 + 2*x + 2), x)","F",0
137,0,0,0,1.067648," ","integrate(x/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} - 1} {\left(x^{2} + \sqrt{3} x - x\right)}}{x^{5} - 2 \, x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 2}, x\right)"," ",0,"integral(-sqrt(x^3 - 1)*(x^2 + sqrt(3)*x - x)/(x^5 - 2*x^4 - 2*x^3 - x^2 + 2*x + 2), x)","F",0
138,0,0,0,1.038294," ","integrate(x/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} {\left(x^{2} - \sqrt{3} x + x\right)}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*(x^2 - sqrt(3)*x + x)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
139,0,0,0,1.247303," ","integrate(x/(1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x^{2} + \sqrt{3} x + x\right)}}{x^{5} + 2 \, x^{4} - 2 \, x^{3} + x^{2} + 2 \, x - 2}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x^2 + sqrt(3)*x + x)/(x^5 + 2*x^4 - 2*x^3 + x^2 + 2*x - 2), x)","F",0
140,0,0,0,3.725083," ","integrate(x/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} {\left(2 \, {\left(2 \, b x^{4} + 2 \, a x - \sqrt{3} {\left(b x^{4} - 2 \, a x\right)}\right)} a^{\frac{2}{3}} - {\left(b x^{5} - 8 \, a x^{2} - \sqrt{3} {\left(b x^{5} + 4 \, a x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b x^{6} + 6 \, \sqrt{3} a x^{3} + 10 \, a x^{3}\right)} b^{\frac{2}{3}}\right)}}{b^{3} x^{9} + 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} - 8 \, a^{3}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*(2*(2*b*x^4 + 2*a*x - sqrt(3)*(b*x^4 - 2*a*x))*a^(2/3) - (b*x^5 - 8*a*x^2 - sqrt(3)*(b*x^5 + 4*a*x^2))*a^(1/3)*b^(1/3) + (b*x^6 + 6*sqrt(3)*a*x^3 + 10*a*x^3)*b^(2/3))/(b^3*x^9 + 21*a*b^2*x^6 + 12*a^2*b*x^3 - 8*a^3), x)","F",0
141,0,0,0,3.185689," ","integrate(x/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, {\left(2 \, b x^{4} - 2 \, a x - \sqrt{3} {\left(b x^{4} + 2 \, a x\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{2}{3}} + {\left(b x^{5} + 8 \, a x^{2} - \sqrt{3} {\left(b x^{5} - 4 \, a x^{2}\right)}\right)} \sqrt{-b x^{3} + a} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b x^{6} - 6 \, \sqrt{3} a x^{3} - 10 \, a x^{3}\right)} \sqrt{-b x^{3} + a} b^{\frac{2}{3}}}{b^{3} x^{9} - 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} + 8 \, a^{3}}, x\right)"," ",0,"integral((2*(2*b*x^4 - 2*a*x - sqrt(3)*(b*x^4 + 2*a*x))*sqrt(-b*x^3 + a)*a^(2/3) + (b*x^5 + 8*a*x^2 - sqrt(3)*(b*x^5 - 4*a*x^2))*sqrt(-b*x^3 + a)*a^(1/3)*b^(1/3) + (b*x^6 - 6*sqrt(3)*a*x^3 - 10*a*x^3)*sqrt(-b*x^3 + a)*b^(2/3))/(b^3*x^9 - 21*a*b^2*x^6 + 12*a^2*b*x^3 + 8*a^3), x)","F",0
142,0,0,0,3.085498," ","integrate(x/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x^{3} - a} {\left(2 \, {\left(2 \, b x^{4} - 2 \, a x - \sqrt{3} {\left(b x^{4} + 2 \, a x\right)}\right)} a^{\frac{2}{3}} + {\left(b x^{5} + 8 \, a x^{2} - \sqrt{3} {\left(b x^{5} - 4 \, a x^{2}\right)}\right)} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b x^{6} - 6 \, \sqrt{3} a x^{3} - 10 \, a x^{3}\right)} b^{\frac{2}{3}}\right)}}{b^{3} x^{9} - 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} + 8 \, a^{3}}, x\right)"," ",0,"integral(-sqrt(b*x^3 - a)*(2*(2*b*x^4 - 2*a*x - sqrt(3)*(b*x^4 + 2*a*x))*a^(2/3) + (b*x^5 + 8*a*x^2 - sqrt(3)*(b*x^5 - 4*a*x^2))*a^(1/3)*b^(1/3) + (b*x^6 - 6*sqrt(3)*a*x^3 - 10*a*x^3)*b^(2/3))/(b^3*x^9 - 21*a*b^2*x^6 + 12*a^2*b*x^3 + 8*a^3), x)","F",0
143,0,0,0,3.132589," ","integrate(x/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, {\left(2 \, b x^{4} + 2 \, a x - \sqrt{3} {\left(b x^{4} - 2 \, a x\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{2}{3}} - {\left(b x^{5} - 8 \, a x^{2} - \sqrt{3} {\left(b x^{5} + 4 \, a x^{2}\right)}\right)} \sqrt{-b x^{3} - a} a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(b x^{6} + 6 \, \sqrt{3} a x^{3} + 10 \, a x^{3}\right)} \sqrt{-b x^{3} - a} b^{\frac{2}{3}}}{b^{3} x^{9} + 21 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} - 8 \, a^{3}}, x\right)"," ",0,"integral(-(2*(2*b*x^4 + 2*a*x - sqrt(3)*(b*x^4 - 2*a*x))*sqrt(-b*x^3 - a)*a^(2/3) - (b*x^5 - 8*a*x^2 - sqrt(3)*(b*x^5 + 4*a*x^2))*sqrt(-b*x^3 - a)*a^(1/3)*b^(1/3) + (b*x^6 + 6*sqrt(3)*a*x^3 + 10*a*x^3)*sqrt(-b*x^3 - a)*b^(2/3))/(b^3*x^9 + 21*a*b^2*x^6 + 12*a^2*b*x^3 - 8*a^3), x)","F",0
144,-1,0,0,0.000000," ","integrate((1+x+3^(1/2))/(d*x+c)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-2,0,0,0.000000," ","integrate((1-x+3^(1/2))/(d*x+c)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
146,0,0,0,9.924066," ","integrate((1-x+3^(1/2))/(d*x+c)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} - 1} {\left(x - \sqrt{3} - 1\right)}}{d x^{4} + c x^{3} - d x - c}, x\right)"," ",0,"integral(-sqrt(x^3 - 1)*(x - sqrt(3) - 1)/(d*x^4 + c*x^3 - d*x - c), x)","F",0
147,-1,0,0,0.000000," ","integrate((1+x+3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((1+x-3^(1/2))/(d*x+c)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-2,0,0,0.000000," ","integrate((1-x-3^(1/2))/(d*x+c)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
150,0,0,0,11.258158," ","integrate((1-x-3^(1/2))/(d*x+c)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} - 1} {\left(x + \sqrt{3} - 1\right)}}{d x^{4} + c x^{3} - d x - c}, x\right)"," ",0,"integral(-sqrt(x^3 - 1)*(x + sqrt(3) - 1)/(d*x^4 + c*x^3 - d*x - c), x)","F",0
151,-1,0,0,0.000000," ","integrate((1+x-3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,0,0,0,0.913834," ","integrate((1+x+3^(1/2))/x/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x + \sqrt{3} + 1\right)}}{x^{4} + x}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x + sqrt(3) + 1)/(x^4 + x), x)","F",0
153,0,0,0,1.353018," ","integrate((1-x+3^(1/2))/x/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} + 1} {\left(x - \sqrt{3} - 1\right)}}{x^{4} - x}, x\right)"," ",0,"integral(sqrt(-x^3 + 1)*(x - sqrt(3) - 1)/(x^4 - x), x)","F",0
154,0,0,0,1.094951," ","integrate((1-x+3^(1/2))/x/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} - 1} {\left(x - \sqrt{3} - 1\right)}}{x^{4} - x}, x\right)"," ",0,"integral(-sqrt(x^3 - 1)*(x - sqrt(3) - 1)/(x^4 - x), x)","F",0
155,0,0,0,1.108430," ","integrate((1+x+3^(1/2))/x/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} {\left(x + \sqrt{3} + 1\right)}}{x^{4} + x}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*(x + sqrt(3) + 1)/(x^4 + x), x)","F",0
156,0,0,0,1.178255," ","integrate((1+x-3^(1/2))/x/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(x - \sqrt{3} + 1\right)}}{x^{4} + x}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(x - sqrt(3) + 1)/(x^4 + x), x)","F",0
157,0,0,0,1.093456," ","integrate((1-x-3^(1/2))/x/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{3} + 1} {\left(x + \sqrt{3} - 1\right)}}{x^{4} - x}, x\right)"," ",0,"integral(sqrt(-x^3 + 1)*(x + sqrt(3) - 1)/(x^4 - x), x)","F",0
158,0,0,0,0.914989," ","integrate((1-x-3^(1/2))/x/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{3} - 1} {\left(x + \sqrt{3} - 1\right)}}{x^{4} - x}, x\right)"," ",0,"integral(-sqrt(x^3 - 1)*(x + sqrt(3) - 1)/(x^4 - x), x)","F",0
159,0,0,0,1.273237," ","integrate((1+x-3^(1/2))/x/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} {\left(x - \sqrt{3} + 1\right)}}{x^{4} + x}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*(x - sqrt(3) + 1)/(x^4 + x), x)","F",0
160,0,0,0,1.103254," ","integrate(x/(3+x)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} x}{x^{4} + 3 \, x^{3} + x + 3}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*x/(x^4 + 3*x^3 + x + 3), x)","F",0
161,0,0,0,0.710774," ","integrate(x/(3+x)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x}{x^{4} + 3 \, x^{3} - x - 3}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x/(x^4 + 3*x^3 - x - 3), x)","F",0
162,0,0,0,0.880870," ","integrate(x/(3+x)/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1} x}{x^{4} + 3 \, x^{3} - x - 3}, x\right)"," ",0,"integral(sqrt(x^3 - 1)*x/(x^4 + 3*x^3 - x - 3), x)","F",0
163,0,0,0,1.128391," ","integrate(x/(3+x)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} x}{x^{4} + 3 \, x^{3} + x + 3}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*x/(x^4 + 3*x^3 + x + 3), x)","F",0
164,-1,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,0,0,0,1.394278," ","integrate((f*x+e)/x/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1} {\left(f x + e\right)}}{x^{4} + x}, x\right)"," ",0,"integral(sqrt(x^3 + 1)*(f*x + e)/(x^4 + x), x)","F",0
169,0,0,0,1.403304," ","integrate((f*x+e)/x/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} {\left(f x + e\right)}}{x^{4} - x}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*(f*x + e)/(x^4 - x), x)","F",0
170,0,0,0,1.291349," ","integrate((f*x+e)/x/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1} {\left(f x + e\right)}}{x^{4} - x}, x\right)"," ",0,"integral(sqrt(x^3 - 1)*(f*x + e)/(x^4 - x), x)","F",0
171,0,0,0,0.921647," ","integrate((f*x+e)/x/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} {\left(f x + e\right)}}{x^{4} + x}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*(f*x + e)/(x^4 + x), x)","F",0
172,-2,0,0,0.000000," ","integrate((-d*x+c)/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (residue poly has multiple non-linear factors)","F(-2)",0
173,-1,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(d^3*x^3-c^3)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,1,490,0,1.247523," ","integrate(x^2*(b*x+a)^n*(d*x^3+c),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{3} c n^{3} + 30 \, a^{3} b^{3} c n^{2} + 148 \, a^{3} b^{3} c n + 240 \, a^{3} b^{3} c - 120 \, a^{6} d + {\left(b^{6} d n^{5} + 15 \, b^{6} d n^{4} + 85 \, b^{6} d n^{3} + 225 \, b^{6} d n^{2} + 274 \, b^{6} d n + 120 \, b^{6} d\right)} x^{6} + {\left(a b^{5} d n^{5} + 10 \, a b^{5} d n^{4} + 35 \, a b^{5} d n^{3} + 50 \, a b^{5} d n^{2} + 24 \, a b^{5} d n\right)} x^{5} - 5 \, {\left(a^{2} b^{4} d n^{4} + 6 \, a^{2} b^{4} d n^{3} + 11 \, a^{2} b^{4} d n^{2} + 6 \, a^{2} b^{4} d n\right)} x^{4} + {\left(b^{6} c n^{5} + 18 \, b^{6} c n^{4} + 240 \, b^{6} c + {\left(121 \, b^{6} c + 20 \, a^{3} b^{3} d\right)} n^{3} + 12 \, {\left(31 \, b^{6} c + 5 \, a^{3} b^{3} d\right)} n^{2} + 4 \, {\left(127 \, b^{6} c + 10 \, a^{3} b^{3} d\right)} n\right)} x^{3} + {\left(a b^{5} c n^{5} + 16 \, a b^{5} c n^{4} + 89 \, a b^{5} c n^{3} + 2 \, {\left(97 \, a b^{5} c - 30 \, a^{4} b^{2} d\right)} n^{2} + 60 \, {\left(2 \, a b^{5} c - a^{4} b^{2} d\right)} n\right)} x^{2} - 2 \, {\left(a^{2} b^{4} c n^{4} + 15 \, a^{2} b^{4} c n^{3} + 74 \, a^{2} b^{4} c n^{2} + 60 \, {\left(2 \, a^{2} b^{4} c - a^{5} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{6} n^{6} + 21 \, b^{6} n^{5} + 175 \, b^{6} n^{4} + 735 \, b^{6} n^{3} + 1624 \, b^{6} n^{2} + 1764 \, b^{6} n + 720 \, b^{6}}"," ",0,"(2*a^3*b^3*c*n^3 + 30*a^3*b^3*c*n^2 + 148*a^3*b^3*c*n + 240*a^3*b^3*c - 120*a^6*d + (b^6*d*n^5 + 15*b^6*d*n^4 + 85*b^6*d*n^3 + 225*b^6*d*n^2 + 274*b^6*d*n + 120*b^6*d)*x^6 + (a*b^5*d*n^5 + 10*a*b^5*d*n^4 + 35*a*b^5*d*n^3 + 50*a*b^5*d*n^2 + 24*a*b^5*d*n)*x^5 - 5*(a^2*b^4*d*n^4 + 6*a^2*b^4*d*n^3 + 11*a^2*b^4*d*n^2 + 6*a^2*b^4*d*n)*x^4 + (b^6*c*n^5 + 18*b^6*c*n^4 + 240*b^6*c + (121*b^6*c + 20*a^3*b^3*d)*n^3 + 12*(31*b^6*c + 5*a^3*b^3*d)*n^2 + 4*(127*b^6*c + 10*a^3*b^3*d)*n)*x^3 + (a*b^5*c*n^5 + 16*a*b^5*c*n^4 + 89*a*b^5*c*n^3 + 2*(97*a*b^5*c - 30*a^4*b^2*d)*n^2 + 60*(2*a*b^5*c - a^4*b^2*d)*n)*x^2 - 2*(a^2*b^4*c*n^4 + 15*a^2*b^4*c*n^3 + 74*a^2*b^4*c*n^2 + 60*(2*a^2*b^4*c - a^5*b*d)*n)*x)*(b*x + a)^n/(b^6*n^6 + 21*b^6*n^5 + 175*b^6*n^4 + 735*b^6*n^3 + 1624*b^6*n^2 + 1764*b^6*n + 720*b^6)","B",0
175,1,348,0,1.618104," ","integrate(x*(b*x+a)^n*(d*x^3+c),x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{3} c n^{3} + 12 \, a^{2} b^{3} c n^{2} + 47 \, a^{2} b^{3} c n + 60 \, a^{2} b^{3} c - 24 \, a^{5} d - {\left(b^{5} d n^{4} + 10 \, b^{5} d n^{3} + 35 \, b^{5} d n^{2} + 50 \, b^{5} d n + 24 \, b^{5} d\right)} x^{5} - {\left(a b^{4} d n^{4} + 6 \, a b^{4} d n^{3} + 11 \, a b^{4} d n^{2} + 6 \, a b^{4} d n\right)} x^{4} + 4 \, {\left(a^{2} b^{3} d n^{3} + 3 \, a^{2} b^{3} d n^{2} + 2 \, a^{2} b^{3} d n\right)} x^{3} - {\left(b^{5} c n^{4} + 13 \, b^{5} c n^{3} + 60 \, b^{5} c + {\left(59 \, b^{5} c + 12 \, a^{3} b^{2} d\right)} n^{2} + {\left(107 \, b^{5} c + 12 \, a^{3} b^{2} d\right)} n\right)} x^{2} - {\left(a b^{4} c n^{4} + 12 \, a b^{4} c n^{3} + 47 \, a b^{4} c n^{2} + 12 \, {\left(5 \, a b^{4} c - 2 \, a^{4} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"-(a^2*b^3*c*n^3 + 12*a^2*b^3*c*n^2 + 47*a^2*b^3*c*n + 60*a^2*b^3*c - 24*a^5*d - (b^5*d*n^4 + 10*b^5*d*n^3 + 35*b^5*d*n^2 + 50*b^5*d*n + 24*b^5*d)*x^5 - (a*b^4*d*n^4 + 6*a*b^4*d*n^3 + 11*a*b^4*d*n^2 + 6*a*b^4*d*n)*x^4 + 4*(a^2*b^3*d*n^3 + 3*a^2*b^3*d*n^2 + 2*a^2*b^3*d*n)*x^3 - (b^5*c*n^4 + 13*b^5*c*n^3 + 60*b^5*c + (59*b^5*c + 12*a^3*b^2*d)*n^2 + (107*b^5*c + 12*a^3*b^2*d)*n)*x^2 - (a*b^4*c*n^4 + 12*a*b^4*c*n^3 + 47*a*b^4*c*n^2 + 12*(5*a*b^4*c - 2*a^4*b*d)*n)*x)*(b*x + a)^n/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
176,1,222,0,0.786751," ","integrate((b*x+a)^n*(d*x^3+c),x, algorithm=""fricas"")","\frac{{\left(a b^{3} c n^{3} + 9 \, a b^{3} c n^{2} + 26 \, a b^{3} c n + 24 \, a b^{3} c - 6 \, a^{4} d + {\left(b^{4} d n^{3} + 6 \, b^{4} d n^{2} + 11 \, b^{4} d n + 6 \, b^{4} d\right)} x^{4} + {\left(a b^{3} d n^{3} + 3 \, a b^{3} d n^{2} + 2 \, a b^{3} d n\right)} x^{3} - 3 \, {\left(a^{2} b^{2} d n^{2} + a^{2} b^{2} d n\right)} x^{2} + {\left(b^{4} c n^{3} + 9 \, b^{4} c n^{2} + 24 \, b^{4} c + 2 \, {\left(13 \, b^{4} c + 3 \, a^{3} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"(a*b^3*c*n^3 + 9*a*b^3*c*n^2 + 26*a*b^3*c*n + 24*a*b^3*c - 6*a^4*d + (b^4*d*n^3 + 6*b^4*d*n^2 + 11*b^4*d*n + 6*b^4*d)*x^4 + (a*b^3*d*n^3 + 3*a*b^3*d*n^2 + 2*a*b^3*d*n)*x^3 - 3*(a^2*b^2*d*n^2 + a^2*b^2*d*n)*x^2 + (b^4*c*n^3 + 9*b^4*c*n^2 + 24*b^4*c + 2*(13*b^4*c + 3*a^3*b*d)*n)*x)*(b*x + a)^n/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
177,0,0,0,0.914361," ","integrate((b*x+a)^n*(d*x^3+c)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d*x^3 + c)*(b*x + a)^n/x, x)","F",0
178,1,1565,0,0.997148," ","integrate(x^2*(b*x+a)^n*(d*x^3+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{6} c^{2} n^{6} + 78 \, a^{3} b^{6} c^{2} n^{5} + 1250 \, a^{3} b^{6} c^{2} n^{4} + 120960 \, a^{3} b^{6} c^{2} - 120960 \, a^{6} b^{3} c d + 40320 \, a^{9} d^{2} + {\left(b^{9} d^{2} n^{8} + 36 \, b^{9} d^{2} n^{7} + 546 \, b^{9} d^{2} n^{6} + 4536 \, b^{9} d^{2} n^{5} + 22449 \, b^{9} d^{2} n^{4} + 67284 \, b^{9} d^{2} n^{3} + 118124 \, b^{9} d^{2} n^{2} + 109584 \, b^{9} d^{2} n + 40320 \, b^{9} d^{2}\right)} x^{9} + {\left(a b^{8} d^{2} n^{8} + 28 \, a b^{8} d^{2} n^{7} + 322 \, a b^{8} d^{2} n^{6} + 1960 \, a b^{8} d^{2} n^{5} + 6769 \, a b^{8} d^{2} n^{4} + 13132 \, a b^{8} d^{2} n^{3} + 13068 \, a b^{8} d^{2} n^{2} + 5040 \, a b^{8} d^{2} n\right)} x^{8} - 8 \, {\left(a^{2} b^{7} d^{2} n^{7} + 21 \, a^{2} b^{7} d^{2} n^{6} + 175 \, a^{2} b^{7} d^{2} n^{5} + 735 \, a^{2} b^{7} d^{2} n^{4} + 1624 \, a^{2} b^{7} d^{2} n^{3} + 1764 \, a^{2} b^{7} d^{2} n^{2} + 720 \, a^{2} b^{7} d^{2} n\right)} x^{7} + 2 \, {\left(b^{9} c d n^{8} + 39 \, b^{9} c d n^{7} + 60480 \, b^{9} c d + 4 \, {\left(159 \, b^{9} c d + 7 \, a^{3} b^{6} d^{2}\right)} n^{6} + 6 \, {\left(939 \, b^{9} c d + 70 \, a^{3} b^{6} d^{2}\right)} n^{5} + {\left(29469 \, b^{9} c d + 2380 \, a^{3} b^{6} d^{2}\right)} n^{4} + 9 \, {\left(10279 \, b^{9} c d + 700 \, a^{3} b^{6} d^{2}\right)} n^{3} + 2 \, {\left(84307 \, b^{9} c d + 3836 \, a^{3} b^{6} d^{2}\right)} n^{2} + 24 \, {\left(6709 \, b^{9} c d + 140 \, a^{3} b^{6} d^{2}\right)} n\right)} x^{6} + 2 \, {\left(a b^{8} c d n^{8} + 34 \, a b^{8} c d n^{7} + 466 \, a b^{8} c d n^{6} + 56 \, {\left(59 \, a b^{8} c d - 3 \, a^{4} b^{5} d^{2}\right)} n^{5} + {\left(12949 \, a b^{8} c d - 1680 \, a^{4} b^{5} d^{2}\right)} n^{4} + 2 \, {\left(13883 \, a b^{8} c d - 2940 \, a^{4} b^{5} d^{2}\right)} n^{3} + 24 \, {\left(1241 \, a b^{8} c d - 350 \, a^{4} b^{5} d^{2}\right)} n^{2} + 4032 \, {\left(3 \, a b^{8} c d - a^{4} b^{5} d^{2}\right)} n\right)} x^{5} - 10 \, {\left(a^{2} b^{7} c d n^{7} + 30 \, a^{2} b^{7} c d n^{6} + 346 \, a^{2} b^{7} c d n^{5} + 24 \, {\left(80 \, a^{2} b^{7} c d - 7 \, a^{5} b^{4} d^{2}\right)} n^{4} + {\left(5269 \, a^{2} b^{7} c d - 1008 \, a^{5} b^{4} d^{2}\right)} n^{3} + 6 \, {\left(1115 \, a^{2} b^{7} c d - 308 \, a^{5} b^{4} d^{2}\right)} n^{2} + 1008 \, {\left(3 \, a^{2} b^{7} c d - a^{5} b^{4} d^{2}\right)} n\right)} x^{4} + 30 \, {\left(351 \, a^{3} b^{6} c^{2} - 8 \, a^{6} b^{3} c d\right)} n^{3} + {\left(b^{9} c^{2} n^{8} + 42 \, b^{9} c^{2} n^{7} + 120960 \, b^{9} c^{2} + 8 \, {\left(93 \, b^{9} c^{2} + 5 \, a^{3} b^{6} c d\right)} n^{6} + 18 \, {\left(401 \, b^{9} c^{2} + 60 \, a^{3} b^{6} c d\right)} n^{5} + {\left(41619 \, b^{9} c^{2} + 10600 \, a^{3} b^{6} c d\right)} n^{4} + 12 \, {\left(12039 \, b^{9} c^{2} + 3750 \, a^{3} b^{6} c d - 560 \, a^{6} b^{3} d^{2}\right)} n^{3} + 4 \, {\left(72569 \, b^{9} c^{2} + 18940 \, a^{3} b^{6} c d - 5040 \, a^{6} b^{3} d^{2}\right)} n^{2} + 48 \, {\left(6289 \, b^{9} c^{2} + 840 \, a^{3} b^{6} c d - 280 \, a^{6} b^{3} d^{2}\right)} n\right)} x^{3} + 4 \, {\left(12287 \, a^{3} b^{6} c^{2} - 1440 \, a^{6} b^{3} c d\right)} n^{2} + {\left(a b^{8} c^{2} n^{8} + 40 \, a b^{8} c^{2} n^{7} + 664 \, a b^{8} c^{2} n^{6} + 10 \, {\left(589 \, a b^{8} c^{2} - 12 \, a^{4} b^{5} c d\right)} n^{5} + {\left(29839 \, a b^{8} c^{2} - 3000 \, a^{4} b^{5} c d\right)} n^{4} + 10 \, {\left(8479 \, a b^{8} c^{2} - 2580 \, a^{4} b^{5} c d\right)} n^{3} + 24 \, {\left(5029 \, a b^{8} c^{2} - 3475 \, a^{4} b^{5} c d + 840 \, a^{7} b^{2} d^{2}\right)} n^{2} + 20160 \, {\left(3 \, a b^{8} c^{2} - 3 \, a^{4} b^{5} c d + a^{7} b^{2} d^{2}\right)} n\right)} x^{2} + 48 \, {\left(2509 \, a^{3} b^{6} c^{2} - 955 \, a^{6} b^{3} c d\right)} n - 2 \, {\left(a^{2} b^{7} c^{2} n^{7} + 39 \, a^{2} b^{7} c^{2} n^{6} + 625 \, a^{2} b^{7} c^{2} n^{5} + 15 \, {\left(351 \, a^{2} b^{7} c^{2} - 8 \, a^{5} b^{4} c d\right)} n^{4} + 2 \, {\left(12287 \, a^{2} b^{7} c^{2} - 1440 \, a^{5} b^{4} c d\right)} n^{3} + 24 \, {\left(2509 \, a^{2} b^{7} c^{2} - 955 \, a^{5} b^{4} c d\right)} n^{2} + 20160 \, {\left(3 \, a^{2} b^{7} c^{2} - 3 \, a^{5} b^{4} c d + a^{8} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{9} n^{9} + 45 \, b^{9} n^{8} + 870 \, b^{9} n^{7} + 9450 \, b^{9} n^{6} + 63273 \, b^{9} n^{5} + 269325 \, b^{9} n^{4} + 723680 \, b^{9} n^{3} + 1172700 \, b^{9} n^{2} + 1026576 \, b^{9} n + 362880 \, b^{9}}"," ",0,"(2*a^3*b^6*c^2*n^6 + 78*a^3*b^6*c^2*n^5 + 1250*a^3*b^6*c^2*n^4 + 120960*a^3*b^6*c^2 - 120960*a^6*b^3*c*d + 40320*a^9*d^2 + (b^9*d^2*n^8 + 36*b^9*d^2*n^7 + 546*b^9*d^2*n^6 + 4536*b^9*d^2*n^5 + 22449*b^9*d^2*n^4 + 67284*b^9*d^2*n^3 + 118124*b^9*d^2*n^2 + 109584*b^9*d^2*n + 40320*b^9*d^2)*x^9 + (a*b^8*d^2*n^8 + 28*a*b^8*d^2*n^7 + 322*a*b^8*d^2*n^6 + 1960*a*b^8*d^2*n^5 + 6769*a*b^8*d^2*n^4 + 13132*a*b^8*d^2*n^3 + 13068*a*b^8*d^2*n^2 + 5040*a*b^8*d^2*n)*x^8 - 8*(a^2*b^7*d^2*n^7 + 21*a^2*b^7*d^2*n^6 + 175*a^2*b^7*d^2*n^5 + 735*a^2*b^7*d^2*n^4 + 1624*a^2*b^7*d^2*n^3 + 1764*a^2*b^7*d^2*n^2 + 720*a^2*b^7*d^2*n)*x^7 + 2*(b^9*c*d*n^8 + 39*b^9*c*d*n^7 + 60480*b^9*c*d + 4*(159*b^9*c*d + 7*a^3*b^6*d^2)*n^6 + 6*(939*b^9*c*d + 70*a^3*b^6*d^2)*n^5 + (29469*b^9*c*d + 2380*a^3*b^6*d^2)*n^4 + 9*(10279*b^9*c*d + 700*a^3*b^6*d^2)*n^3 + 2*(84307*b^9*c*d + 3836*a^3*b^6*d^2)*n^2 + 24*(6709*b^9*c*d + 140*a^3*b^6*d^2)*n)*x^6 + 2*(a*b^8*c*d*n^8 + 34*a*b^8*c*d*n^7 + 466*a*b^8*c*d*n^6 + 56*(59*a*b^8*c*d - 3*a^4*b^5*d^2)*n^5 + (12949*a*b^8*c*d - 1680*a^4*b^5*d^2)*n^4 + 2*(13883*a*b^8*c*d - 2940*a^4*b^5*d^2)*n^3 + 24*(1241*a*b^8*c*d - 350*a^4*b^5*d^2)*n^2 + 4032*(3*a*b^8*c*d - a^4*b^5*d^2)*n)*x^5 - 10*(a^2*b^7*c*d*n^7 + 30*a^2*b^7*c*d*n^6 + 346*a^2*b^7*c*d*n^5 + 24*(80*a^2*b^7*c*d - 7*a^5*b^4*d^2)*n^4 + (5269*a^2*b^7*c*d - 1008*a^5*b^4*d^2)*n^3 + 6*(1115*a^2*b^7*c*d - 308*a^5*b^4*d^2)*n^2 + 1008*(3*a^2*b^7*c*d - a^5*b^4*d^2)*n)*x^4 + 30*(351*a^3*b^6*c^2 - 8*a^6*b^3*c*d)*n^3 + (b^9*c^2*n^8 + 42*b^9*c^2*n^7 + 120960*b^9*c^2 + 8*(93*b^9*c^2 + 5*a^3*b^6*c*d)*n^6 + 18*(401*b^9*c^2 + 60*a^3*b^6*c*d)*n^5 + (41619*b^9*c^2 + 10600*a^3*b^6*c*d)*n^4 + 12*(12039*b^9*c^2 + 3750*a^3*b^6*c*d - 560*a^6*b^3*d^2)*n^3 + 4*(72569*b^9*c^2 + 18940*a^3*b^6*c*d - 5040*a^6*b^3*d^2)*n^2 + 48*(6289*b^9*c^2 + 840*a^3*b^6*c*d - 280*a^6*b^3*d^2)*n)*x^3 + 4*(12287*a^3*b^6*c^2 - 1440*a^6*b^3*c*d)*n^2 + (a*b^8*c^2*n^8 + 40*a*b^8*c^2*n^7 + 664*a*b^8*c^2*n^6 + 10*(589*a*b^8*c^2 - 12*a^4*b^5*c*d)*n^5 + (29839*a*b^8*c^2 - 3000*a^4*b^5*c*d)*n^4 + 10*(8479*a*b^8*c^2 - 2580*a^4*b^5*c*d)*n^3 + 24*(5029*a*b^8*c^2 - 3475*a^4*b^5*c*d + 840*a^7*b^2*d^2)*n^2 + 20160*(3*a*b^8*c^2 - 3*a^4*b^5*c*d + a^7*b^2*d^2)*n)*x^2 + 48*(2509*a^3*b^6*c^2 - 955*a^6*b^3*c*d)*n - 2*(a^2*b^7*c^2*n^7 + 39*a^2*b^7*c^2*n^6 + 625*a^2*b^7*c^2*n^5 + 15*(351*a^2*b^7*c^2 - 8*a^5*b^4*c*d)*n^4 + 2*(12287*a^2*b^7*c^2 - 1440*a^5*b^4*c*d)*n^3 + 24*(2509*a^2*b^7*c^2 - 955*a^5*b^4*c*d)*n^2 + 20160*(3*a^2*b^7*c^2 - 3*a^5*b^4*c*d + a^8*b*d^2)*n)*x)*(b*x + a)^n/(b^9*n^9 + 45*b^9*n^8 + 870*b^9*n^7 + 9450*b^9*n^6 + 63273*b^9*n^5 + 269325*b^9*n^4 + 723680*b^9*n^3 + 1172700*b^9*n^2 + 1026576*b^9*n + 362880*b^9)","B",0
179,1,1216,0,0.855442," ","integrate(x*(b*x+a)^n*(d*x^3+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{6} c^{2} n^{6} + 33 \, a^{2} b^{6} c^{2} n^{5} + 445 \, a^{2} b^{6} c^{2} n^{4} + 20160 \, a^{2} b^{6} c^{2} - 16128 \, a^{5} b^{3} c d + 5040 \, a^{8} d^{2} - {\left(b^{8} d^{2} n^{7} + 28 \, b^{8} d^{2} n^{6} + 322 \, b^{8} d^{2} n^{5} + 1960 \, b^{8} d^{2} n^{4} + 6769 \, b^{8} d^{2} n^{3} + 13132 \, b^{8} d^{2} n^{2} + 13068 \, b^{8} d^{2} n + 5040 \, b^{8} d^{2}\right)} x^{8} - {\left(a b^{7} d^{2} n^{7} + 21 \, a b^{7} d^{2} n^{6} + 175 \, a b^{7} d^{2} n^{5} + 735 \, a b^{7} d^{2} n^{4} + 1624 \, a b^{7} d^{2} n^{3} + 1764 \, a b^{7} d^{2} n^{2} + 720 \, a b^{7} d^{2} n\right)} x^{7} + 7 \, {\left(a^{2} b^{6} d^{2} n^{6} + 15 \, a^{2} b^{6} d^{2} n^{5} + 85 \, a^{2} b^{6} d^{2} n^{4} + 225 \, a^{2} b^{6} d^{2} n^{3} + 274 \, a^{2} b^{6} d^{2} n^{2} + 120 \, a^{2} b^{6} d^{2} n\right)} x^{6} - 2 \, {\left(b^{8} c d n^{7} + 31 \, b^{8} c d n^{6} + 8064 \, b^{8} c d + {\left(391 \, b^{8} c d + 21 \, a^{3} b^{5} d^{2}\right)} n^{5} + {\left(2581 \, b^{8} c d + 210 \, a^{3} b^{5} d^{2}\right)} n^{4} + {\left(9544 \, b^{8} c d + 735 \, a^{3} b^{5} d^{2}\right)} n^{3} + 2 \, {\left(9782 \, b^{8} c d + 525 \, a^{3} b^{5} d^{2}\right)} n^{2} + 72 \, {\left(282 \, b^{8} c d + 7 \, a^{3} b^{5} d^{2}\right)} n\right)} x^{5} - 2 \, {\left(a b^{7} c d n^{7} + 27 \, a b^{7} c d n^{6} + 283 \, a b^{7} c d n^{5} + 21 \, {\left(69 \, a b^{7} c d - 5 \, a^{4} b^{4} d^{2}\right)} n^{4} + 2 \, {\left(1874 \, a b^{7} c d - 315 \, a^{4} b^{4} d^{2}\right)} n^{3} + 3 \, {\left(1524 \, a b^{7} c d - 385 \, a^{4} b^{4} d^{2}\right)} n^{2} + 126 \, {\left(16 \, a b^{7} c d - 5 \, a^{4} b^{4} d^{2}\right)} n\right)} x^{4} + 3 \, {\left(1045 \, a^{2} b^{6} c^{2} - 16 \, a^{5} b^{3} c d\right)} n^{3} + 8 \, {\left(a^{2} b^{6} c d n^{6} + 24 \, a^{2} b^{6} c d n^{5} + 211 \, a^{2} b^{6} c d n^{4} + 3 \, {\left(272 \, a^{2} b^{6} c d - 35 \, a^{5} b^{3} d^{2}\right)} n^{3} + 5 \, {\left(260 \, a^{2} b^{6} c d - 63 \, a^{5} b^{3} d^{2}\right)} n^{2} + 42 \, {\left(16 \, a^{2} b^{6} c d - 5 \, a^{5} b^{3} d^{2}\right)} n\right)} x^{3} + 2 \, {\left(6077 \, a^{2} b^{6} c^{2} - 504 \, a^{5} b^{3} c d\right)} n^{2} - {\left(b^{8} c^{2} n^{7} + 34 \, b^{8} c^{2} n^{6} + 20160 \, b^{8} c^{2} + 2 \, {\left(239 \, b^{8} c^{2} + 12 \, a^{3} b^{5} c d\right)} n^{5} + 4 \, {\left(895 \, b^{8} c^{2} + 132 \, a^{3} b^{5} c d\right)} n^{4} + {\left(15289 \, b^{8} c^{2} + 4008 \, a^{3} b^{5} c d\right)} n^{3} + 2 \, {\left(18353 \, b^{8} c^{2} + 5784 \, a^{3} b^{5} c d - 1260 \, a^{6} b^{2} d^{2}\right)} n^{2} + 72 \, {\left(621 \, b^{8} c^{2} + 112 \, a^{3} b^{5} c d - 35 \, a^{6} b^{2} d^{2}\right)} n\right)} x^{2} + 24 \, {\left(1023 \, a^{2} b^{6} c^{2} - 292 \, a^{5} b^{3} c d\right)} n - {\left(a b^{7} c^{2} n^{7} + 33 \, a b^{7} c^{2} n^{6} + 445 \, a b^{7} c^{2} n^{5} + 3 \, {\left(1045 \, a b^{7} c^{2} - 16 \, a^{4} b^{4} c d\right)} n^{4} + 2 \, {\left(6077 \, a b^{7} c^{2} - 504 \, a^{4} b^{4} c d\right)} n^{3} + 24 \, {\left(1023 \, a b^{7} c^{2} - 292 \, a^{4} b^{4} c d\right)} n^{2} + 1008 \, {\left(20 \, a b^{7} c^{2} - 16 \, a^{4} b^{4} c d + 5 \, a^{7} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{8} n^{8} + 36 \, b^{8} n^{7} + 546 \, b^{8} n^{6} + 4536 \, b^{8} n^{5} + 22449 \, b^{8} n^{4} + 67284 \, b^{8} n^{3} + 118124 \, b^{8} n^{2} + 109584 \, b^{8} n + 40320 \, b^{8}}"," ",0,"-(a^2*b^6*c^2*n^6 + 33*a^2*b^6*c^2*n^5 + 445*a^2*b^6*c^2*n^4 + 20160*a^2*b^6*c^2 - 16128*a^5*b^3*c*d + 5040*a^8*d^2 - (b^8*d^2*n^7 + 28*b^8*d^2*n^6 + 322*b^8*d^2*n^5 + 1960*b^8*d^2*n^4 + 6769*b^8*d^2*n^3 + 13132*b^8*d^2*n^2 + 13068*b^8*d^2*n + 5040*b^8*d^2)*x^8 - (a*b^7*d^2*n^7 + 21*a*b^7*d^2*n^6 + 175*a*b^7*d^2*n^5 + 735*a*b^7*d^2*n^4 + 1624*a*b^7*d^2*n^3 + 1764*a*b^7*d^2*n^2 + 720*a*b^7*d^2*n)*x^7 + 7*(a^2*b^6*d^2*n^6 + 15*a^2*b^6*d^2*n^5 + 85*a^2*b^6*d^2*n^4 + 225*a^2*b^6*d^2*n^3 + 274*a^2*b^6*d^2*n^2 + 120*a^2*b^6*d^2*n)*x^6 - 2*(b^8*c*d*n^7 + 31*b^8*c*d*n^6 + 8064*b^8*c*d + (391*b^8*c*d + 21*a^3*b^5*d^2)*n^5 + (2581*b^8*c*d + 210*a^3*b^5*d^2)*n^4 + (9544*b^8*c*d + 735*a^3*b^5*d^2)*n^3 + 2*(9782*b^8*c*d + 525*a^3*b^5*d^2)*n^2 + 72*(282*b^8*c*d + 7*a^3*b^5*d^2)*n)*x^5 - 2*(a*b^7*c*d*n^7 + 27*a*b^7*c*d*n^6 + 283*a*b^7*c*d*n^5 + 21*(69*a*b^7*c*d - 5*a^4*b^4*d^2)*n^4 + 2*(1874*a*b^7*c*d - 315*a^4*b^4*d^2)*n^3 + 3*(1524*a*b^7*c*d - 385*a^4*b^4*d^2)*n^2 + 126*(16*a*b^7*c*d - 5*a^4*b^4*d^2)*n)*x^4 + 3*(1045*a^2*b^6*c^2 - 16*a^5*b^3*c*d)*n^3 + 8*(a^2*b^6*c*d*n^6 + 24*a^2*b^6*c*d*n^5 + 211*a^2*b^6*c*d*n^4 + 3*(272*a^2*b^6*c*d - 35*a^5*b^3*d^2)*n^3 + 5*(260*a^2*b^6*c*d - 63*a^5*b^3*d^2)*n^2 + 42*(16*a^2*b^6*c*d - 5*a^5*b^3*d^2)*n)*x^3 + 2*(6077*a^2*b^6*c^2 - 504*a^5*b^3*c*d)*n^2 - (b^8*c^2*n^7 + 34*b^8*c^2*n^6 + 20160*b^8*c^2 + 2*(239*b^8*c^2 + 12*a^3*b^5*c*d)*n^5 + 4*(895*b^8*c^2 + 132*a^3*b^5*c*d)*n^4 + (15289*b^8*c^2 + 4008*a^3*b^5*c*d)*n^3 + 2*(18353*b^8*c^2 + 5784*a^3*b^5*c*d - 1260*a^6*b^2*d^2)*n^2 + 72*(621*b^8*c^2 + 112*a^3*b^5*c*d - 35*a^6*b^2*d^2)*n)*x^2 + 24*(1023*a^2*b^6*c^2 - 292*a^5*b^3*c*d)*n - (a*b^7*c^2*n^7 + 33*a*b^7*c^2*n^6 + 445*a*b^7*c^2*n^5 + 3*(1045*a*b^7*c^2 - 16*a^4*b^4*c*d)*n^4 + 2*(6077*a*b^7*c^2 - 504*a^4*b^4*c*d)*n^3 + 24*(1023*a*b^7*c^2 - 292*a^4*b^4*c*d)*n^2 + 1008*(20*a*b^7*c^2 - 16*a^4*b^4*c*d + 5*a^7*b*d^2)*n)*x)*(b*x + a)^n/(b^8*n^8 + 36*b^8*n^7 + 546*b^8*n^6 + 4536*b^8*n^5 + 22449*b^8*n^4 + 67284*b^8*n^3 + 118124*b^8*n^2 + 109584*b^8*n + 40320*b^8)","B",0
180,1,893,0,0.647669," ","integrate((b*x+a)^n*(d*x^3+c)^2,x, algorithm=""fricas"")","\frac{{\left(a b^{6} c^{2} n^{6} + 27 \, a b^{6} c^{2} n^{5} + 295 \, a b^{6} c^{2} n^{4} + 5040 \, a b^{6} c^{2} - 2520 \, a^{4} b^{3} c d + 720 \, a^{7} d^{2} + {\left(b^{7} d^{2} n^{6} + 21 \, b^{7} d^{2} n^{5} + 175 \, b^{7} d^{2} n^{4} + 735 \, b^{7} d^{2} n^{3} + 1624 \, b^{7} d^{2} n^{2} + 1764 \, b^{7} d^{2} n + 720 \, b^{7} d^{2}\right)} x^{7} + {\left(a b^{6} d^{2} n^{6} + 15 \, a b^{6} d^{2} n^{5} + 85 \, a b^{6} d^{2} n^{4} + 225 \, a b^{6} d^{2} n^{3} + 274 \, a b^{6} d^{2} n^{2} + 120 \, a b^{6} d^{2} n\right)} x^{6} - 6 \, {\left(a^{2} b^{5} d^{2} n^{5} + 10 \, a^{2} b^{5} d^{2} n^{4} + 35 \, a^{2} b^{5} d^{2} n^{3} + 50 \, a^{2} b^{5} d^{2} n^{2} + 24 \, a^{2} b^{5} d^{2} n\right)} x^{5} + 2 \, {\left(b^{7} c d n^{6} + 24 \, b^{7} c d n^{5} + 1260 \, b^{7} c d + {\left(226 \, b^{7} c d + 15 \, a^{3} b^{4} d^{2}\right)} n^{4} + 6 \, {\left(176 \, b^{7} c d + 15 \, a^{3} b^{4} d^{2}\right)} n^{3} + 5 \, {\left(509 \, b^{7} c d + 33 \, a^{3} b^{4} d^{2}\right)} n^{2} + 18 \, {\left(164 \, b^{7} c d + 5 \, a^{3} b^{4} d^{2}\right)} n\right)} x^{4} + 3 \, {\left(555 \, a b^{6} c^{2} - 4 \, a^{4} b^{3} c d\right)} n^{3} + 2 \, {\left(a b^{6} c d n^{6} + 21 \, a b^{6} c d n^{5} + 163 \, a b^{6} c d n^{4} + 3 \, {\left(189 \, a b^{6} c d - 20 \, a^{4} b^{3} d^{2}\right)} n^{3} + 4 \, {\left(211 \, a b^{6} c d - 45 \, a^{4} b^{3} d^{2}\right)} n^{2} + 60 \, {\left(7 \, a b^{6} c d - 2 \, a^{4} b^{3} d^{2}\right)} n\right)} x^{3} + 8 \, {\left(638 \, a b^{6} c^{2} - 27 \, a^{4} b^{3} c d\right)} n^{2} - 6 \, {\left(a^{2} b^{5} c d n^{5} + 19 \, a^{2} b^{5} c d n^{4} + 125 \, a^{2} b^{5} c d n^{3} + {\left(317 \, a^{2} b^{5} c d - 60 \, a^{5} b^{2} d^{2}\right)} n^{2} + 30 \, {\left(7 \, a^{2} b^{5} c d - 2 \, a^{5} b^{2} d^{2}\right)} n\right)} x^{2} + 12 \, {\left(669 \, a b^{6} c^{2} - 107 \, a^{4} b^{3} c d\right)} n + {\left(b^{7} c^{2} n^{6} + 27 \, b^{7} c^{2} n^{5} + 5040 \, b^{7} c^{2} + {\left(295 \, b^{7} c^{2} + 12 \, a^{3} b^{4} c d\right)} n^{4} + 9 \, {\left(185 \, b^{7} c^{2} + 24 \, a^{3} b^{4} c d\right)} n^{3} + 4 \, {\left(1276 \, b^{7} c^{2} + 321 \, a^{3} b^{4} c d\right)} n^{2} + 36 \, {\left(223 \, b^{7} c^{2} + 70 \, a^{3} b^{4} c d - 20 \, a^{6} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{7} n^{7} + 28 \, b^{7} n^{6} + 322 \, b^{7} n^{5} + 1960 \, b^{7} n^{4} + 6769 \, b^{7} n^{3} + 13132 \, b^{7} n^{2} + 13068 \, b^{7} n + 5040 \, b^{7}}"," ",0,"(a*b^6*c^2*n^6 + 27*a*b^6*c^2*n^5 + 295*a*b^6*c^2*n^4 + 5040*a*b^6*c^2 - 2520*a^4*b^3*c*d + 720*a^7*d^2 + (b^7*d^2*n^6 + 21*b^7*d^2*n^5 + 175*b^7*d^2*n^4 + 735*b^7*d^2*n^3 + 1624*b^7*d^2*n^2 + 1764*b^7*d^2*n + 720*b^7*d^2)*x^7 + (a*b^6*d^2*n^6 + 15*a*b^6*d^2*n^5 + 85*a*b^6*d^2*n^4 + 225*a*b^6*d^2*n^3 + 274*a*b^6*d^2*n^2 + 120*a*b^6*d^2*n)*x^6 - 6*(a^2*b^5*d^2*n^5 + 10*a^2*b^5*d^2*n^4 + 35*a^2*b^5*d^2*n^3 + 50*a^2*b^5*d^2*n^2 + 24*a^2*b^5*d^2*n)*x^5 + 2*(b^7*c*d*n^6 + 24*b^7*c*d*n^5 + 1260*b^7*c*d + (226*b^7*c*d + 15*a^3*b^4*d^2)*n^4 + 6*(176*b^7*c*d + 15*a^3*b^4*d^2)*n^3 + 5*(509*b^7*c*d + 33*a^3*b^4*d^2)*n^2 + 18*(164*b^7*c*d + 5*a^3*b^4*d^2)*n)*x^4 + 3*(555*a*b^6*c^2 - 4*a^4*b^3*c*d)*n^3 + 2*(a*b^6*c*d*n^6 + 21*a*b^6*c*d*n^5 + 163*a*b^6*c*d*n^4 + 3*(189*a*b^6*c*d - 20*a^4*b^3*d^2)*n^3 + 4*(211*a*b^6*c*d - 45*a^4*b^3*d^2)*n^2 + 60*(7*a*b^6*c*d - 2*a^4*b^3*d^2)*n)*x^3 + 8*(638*a*b^6*c^2 - 27*a^4*b^3*c*d)*n^2 - 6*(a^2*b^5*c*d*n^5 + 19*a^2*b^5*c*d*n^4 + 125*a^2*b^5*c*d*n^3 + (317*a^2*b^5*c*d - 60*a^5*b^2*d^2)*n^2 + 30*(7*a^2*b^5*c*d - 2*a^5*b^2*d^2)*n)*x^2 + 12*(669*a*b^6*c^2 - 107*a^4*b^3*c*d)*n + (b^7*c^2*n^6 + 27*b^7*c^2*n^5 + 5040*b^7*c^2 + (295*b^7*c^2 + 12*a^3*b^4*c*d)*n^4 + 9*(185*b^7*c^2 + 24*a^3*b^4*c*d)*n^3 + 4*(1276*b^7*c^2 + 321*a^3*b^4*c*d)*n^2 + 36*(223*b^7*c^2 + 70*a^3*b^4*c*d - 20*a^6*b*d^2)*n)*x)*(b*x + a)^n/(b^7*n^7 + 28*b^7*n^6 + 322*b^7*n^5 + 1960*b^7*n^4 + 6769*b^7*n^3 + 13132*b^7*n^2 + 13068*b^7*n + 5040*b^7)","B",0
181,0,0,0,0.549536," ","integrate((b*x+a)^n*(d*x^3+c)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{6} + 2 \, c d x^{3} + c^{2}\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^3 + c^2)*(b*x + a)^n/x, x)","F",0
182,1,3564,0,0.941586," ","integrate(x^2*(b*x+a)^n*(d*x^3+c)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{9} c^{3} n^{9} + 144 \, a^{3} b^{9} c^{3} n^{8} + 4548 \, a^{3} b^{9} c^{3} n^{7} + 159667200 \, a^{3} b^{9} c^{3} - 239500800 \, a^{6} b^{6} c^{2} d + 159667200 \, a^{9} b^{3} c d^{2} - 39916800 \, a^{12} d^{3} + {\left(b^{12} d^{3} n^{11} + 66 \, b^{12} d^{3} n^{10} + 1925 \, b^{12} d^{3} n^{9} + 32670 \, b^{12} d^{3} n^{8} + 357423 \, b^{12} d^{3} n^{7} + 2637558 \, b^{12} d^{3} n^{6} + 13339535 \, b^{12} d^{3} n^{5} + 45995730 \, b^{12} d^{3} n^{4} + 105258076 \, b^{12} d^{3} n^{3} + 150917976 \, b^{12} d^{3} n^{2} + 120543840 \, b^{12} d^{3} n + 39916800 \, b^{12} d^{3}\right)} x^{12} + {\left(a b^{11} d^{3} n^{11} + 55 \, a b^{11} d^{3} n^{10} + 1320 \, a b^{11} d^{3} n^{9} + 18150 \, a b^{11} d^{3} n^{8} + 157773 \, a b^{11} d^{3} n^{7} + 902055 \, a b^{11} d^{3} n^{6} + 3416930 \, a b^{11} d^{3} n^{5} + 8409500 \, a b^{11} d^{3} n^{4} + 12753576 \, a b^{11} d^{3} n^{3} + 10628640 \, a b^{11} d^{3} n^{2} + 3628800 \, a b^{11} d^{3} n\right)} x^{11} - 11 \, {\left(a^{2} b^{10} d^{3} n^{10} + 45 \, a^{2} b^{10} d^{3} n^{9} + 870 \, a^{2} b^{10} d^{3} n^{8} + 9450 \, a^{2} b^{10} d^{3} n^{7} + 63273 \, a^{2} b^{10} d^{3} n^{6} + 269325 \, a^{2} b^{10} d^{3} n^{5} + 723680 \, a^{2} b^{10} d^{3} n^{4} + 1172700 \, a^{2} b^{10} d^{3} n^{3} + 1026576 \, a^{2} b^{10} d^{3} n^{2} + 362880 \, a^{2} b^{10} d^{3} n\right)} x^{10} + {\left(3 \, b^{12} c d^{2} n^{11} + 207 \, b^{12} c d^{2} n^{10} + 159667200 \, b^{12} c d^{2} + 2 \, {\left(3144 \, b^{12} c d^{2} + 55 \, a^{3} b^{9} d^{3}\right)} n^{9} + 18 \, {\left(6151 \, b^{12} c d^{2} + 220 \, a^{3} b^{9} d^{3}\right)} n^{8} + 3 \, {\left(417309 \, b^{12} c d^{2} + 20020 \, a^{3} b^{9} d^{3}\right)} n^{7} + 567 \, {\left(16777 \, b^{12} c d^{2} + 880 \, a^{3} b^{9} d^{3}\right)} n^{6} + 6 \, {\left(8226277 \, b^{12} c d^{2} + 411565 \, a^{3} b^{9} d^{3}\right)} n^{5} + 36 \, {\left(4833097 \, b^{12} c d^{2} + 205590 \, a^{3} b^{9} d^{3}\right)} n^{4} + 40 \, {\left(10142427 \, b^{12} c d^{2} + 324841 \, a^{3} b^{9} d^{3}\right)} n^{3} + 288 \, {\left(2051288 \, b^{12} c d^{2} + 41855 \, a^{3} b^{9} d^{3}\right)} n^{2} + 5760 \, {\left(82941 \, b^{12} c d^{2} + 770 \, a^{3} b^{9} d^{3}\right)} n\right)} x^{9} + 3 \, {\left(a b^{11} c d^{2} n^{11} + 61 \, a b^{11} c d^{2} n^{10} + 1608 \, a b^{11} c d^{2} n^{9} + 6 \, {\left(4007 \, a b^{11} c d^{2} - 55 \, a^{4} b^{8} d^{3}\right)} n^{8} + 21 \, {\left(10713 \, a b^{11} c d^{2} - 440 \, a^{4} b^{8} d^{3}\right)} n^{7} + 21 \, {\left(65289 \, a b^{11} c d^{2} - 5060 \, a^{4} b^{8} d^{3}\right)} n^{6} + 2 \, {\left(2742001 \, a b^{11} c d^{2} - 323400 \, a^{4} b^{8} d^{3}\right)} n^{5} + 2 \, {\left(7062574 \, a b^{11} c d^{2} - 1116885 \, a^{4} b^{8} d^{3}\right)} n^{4} + 264 \, {\left(84209 \, a b^{11} c d^{2} - 16415 \, a^{4} b^{8} d^{3}\right)} n^{3} + 360 \, {\left(52984 \, a b^{11} c d^{2} - 11979 \, a^{4} b^{8} d^{3}\right)} n^{2} + 1663200 \, {\left(4 \, a b^{11} c d^{2} - a^{4} b^{8} d^{3}\right)} n\right)} x^{8} - 24 \, {\left(a^{2} b^{10} c d^{2} n^{10} + 54 \, a^{2} b^{10} c d^{2} n^{9} + 1230 \, a^{2} b^{10} c d^{2} n^{8} + 6 \, {\left(2572 \, a^{2} b^{10} c d^{2} - 55 \, a^{5} b^{7} d^{3}\right)} n^{7} + 21 \, {\left(5569 \, a^{2} b^{10} c d^{2} - 330 \, a^{5} b^{7} d^{3}\right)} n^{6} + 42 \, {\left(13153 \, a^{2} b^{10} c d^{2} - 1375 \, a^{5} b^{7} d^{3}\right)} n^{5} + 10 \, {\left(161702 \, a^{2} b^{10} c d^{2} - 24255 \, a^{5} b^{7} d^{3}\right)} n^{4} + 24 \, {\left(116917 \, a^{2} b^{10} c d^{2} - 22330 \, a^{5} b^{7} d^{3}\right)} n^{3} + 360 \, {\left(7192 \, a^{2} b^{10} c d^{2} - 1617 \, a^{5} b^{7} d^{3}\right)} n^{2} + 237600 \, {\left(4 \, a^{2} b^{10} c d^{2} - a^{5} b^{7} d^{3}\right)} n\right)} x^{7} + 72 \, {\left(1148 \, a^{3} b^{9} c^{3} - 5 \, a^{6} b^{6} c^{2} d\right)} n^{6} + 3 \, {\left(b^{12} c^{2} d n^{11} + 72 \, b^{12} c^{2} d n^{10} + 79833600 \, b^{12} c^{2} d + {\left(2285 \, b^{12} c^{2} d + 56 \, a^{3} b^{9} c d^{2}\right)} n^{9} + 12 \, {\left(3505 \, b^{12} c^{2} d + 224 \, a^{3} b^{9} c d^{2}\right)} n^{8} + 3 \, {\left(165701 \, b^{12} c^{2} d + 17584 \, a^{3} b^{9} c d^{2}\right)} n^{7} + 48 \, {\left(82167 \, b^{12} c^{2} d + 11410 \, a^{3} b^{9} c d^{2} - 385 \, a^{6} b^{6} d^{3}\right)} n^{6} + {\left(21326135 \, b^{12} c^{2} d + 3263064 \, a^{3} b^{9} c d^{2} - 277200 \, a^{6} b^{6} d^{3}\right)} n^{5} + 12 \, {\left(6509445 \, b^{12} c^{2} d + 946456 \, a^{3} b^{9} c d^{2} - 130900 \, a^{6} b^{6} d^{3}\right)} n^{4} + 4 \, {\left(47131699 \, b^{12} c^{2} d + 5602072 \, a^{3} b^{9} c d^{2} - 1039500 \, a^{6} b^{6} d^{3}\right)} n^{3} + 96 \, {\left(2946397 \, b^{12} c^{2} d + 236320 \, a^{3} b^{9} c d^{2} - 52745 \, a^{6} b^{6} d^{3}\right)} n^{2} + 2880 \, {\left(81401 \, b^{12} c^{2} d + 3080 \, a^{3} b^{9} c d^{2} - 770 \, a^{6} b^{6} d^{3}\right)} n\right)} x^{6} + 6 \, {\left(158683 \, a^{3} b^{9} c^{3} - 3420 \, a^{6} b^{6} c^{2} d\right)} n^{5} + 3 \, {\left(a b^{11} c^{2} d n^{11} + 67 \, a b^{11} c^{2} d n^{10} + 1950 \, a b^{11} c^{2} d n^{9} + 6 \, {\left(5385 \, a b^{11} c^{2} d - 56 \, a^{4} b^{8} c d^{2}\right)} n^{8} + 3 \, {\left(111851 \, a b^{11} c^{2} d - 4816 \, a^{4} b^{8} c d^{2}\right)} n^{7} + 3 \, {\left(755417 \, a b^{11} c^{2} d - 81424 \, a^{4} b^{8} c d^{2}\right)} n^{6} + 560 \, {\left(17848 \, a b^{11} c^{2} d - 3687 \, a^{4} b^{8} c d^{2} + 198 \, a^{7} b^{5} d^{3}\right)} n^{5} + 4 \, {\left(7034735 \, a b^{11} c^{2} d - 2313696 \, a^{4} b^{8} c d^{2} + 277200 \, a^{7} b^{5} d^{3}\right)} n^{4} + 96 \, {\left(498251 \, a b^{11} c^{2} d - 227822 \, a^{4} b^{8} c d^{2} + 40425 \, a^{7} b^{5} d^{3}\right)} n^{3} + 576 \, {\left(75857 \, a b^{11} c^{2} d - 43568 \, a^{4} b^{8} c d^{2} + 9625 \, a^{7} b^{5} d^{3}\right)} n^{2} + 2661120 \, {\left(6 \, a b^{11} c^{2} d - 4 \, a^{4} b^{8} c d^{2} + a^{7} b^{5} d^{3}\right)} n\right)} x^{5} + 72 \, {\left(100058 \, a^{3} b^{9} c^{3} - 6725 \, a^{6} b^{6} c^{2} d\right)} n^{4} - 15 \, {\left(a^{2} b^{10} c^{2} d n^{10} + 63 \, a^{2} b^{10} c^{2} d n^{9} + 1698 \, a^{2} b^{10} c^{2} d n^{8} + 6 \, {\left(4253 \, a^{2} b^{10} c^{2} d - 56 \, a^{5} b^{7} c d^{2}\right)} n^{7} + 3 \, {\left(77827 \, a^{2} b^{10} c^{2} d - 4368 \, a^{5} b^{7} c d^{2}\right)} n^{6} + 3 \, {\left(444109 \, a^{2} b^{10} c^{2} d - 63952 \, a^{5} b^{7} c d^{2}\right)} n^{5} + 4 \, {\left(1166393 \, a^{2} b^{10} c^{2} d - 324324 \, a^{5} b^{7} c d^{2} + 27720 \, a^{8} b^{4} d^{3}\right)} n^{4} + 12 \, {\left(789721 \, a^{2} b^{10} c^{2} d - 338800 \, a^{5} b^{7} c d^{2} + 55440 \, a^{8} b^{4} d^{3}\right)} n^{3} + 144 \, {\left(68927 \, a^{2} b^{10} c^{2} d - 38948 \, a^{5} b^{7} c d^{2} + 8470 \, a^{8} b^{4} d^{3}\right)} n^{2} + 665280 \, {\left(6 \, a^{2} b^{10} c^{2} d - 4 \, a^{5} b^{7} c d^{2} + a^{8} b^{4} d^{3}\right)} n\right)} x^{4} + 8 \, {\left(4473299 \, a^{3} b^{9} c^{3} - 756675 \, a^{6} b^{6} c^{2} d + 15120 \, a^{9} b^{3} c d^{2}\right)} n^{3} + {\left(b^{12} c^{3} n^{11} + 75 \, b^{12} c^{3} n^{10} + 159667200 \, b^{12} c^{3} + 4 \, {\left(623 \, b^{12} c^{3} + 15 \, a^{3} b^{9} c^{2} d\right)} n^{9} + 18 \, {\left(2683 \, b^{12} c^{3} + 200 \, a^{3} b^{9} c^{2} d\right)} n^{8} + 3 \, {\left(201527 \, b^{12} c^{3} + 30360 \, a^{3} b^{9} c^{2} d\right)} n^{7} + 9 \, {\left(568099 \, b^{12} c^{3} + 139760 \, a^{3} b^{9} c^{2} d - 2240 \, a^{6} b^{6} c d^{2}\right)} n^{6} + 2 \, {\left(14825779 \, b^{12} c^{3} + 5117670 \, a^{3} b^{9} c^{2} d - 362880 \, a^{6} b^{6} c d^{2}\right)} n^{5} + 12 \, {\left(9759623 \, b^{12} c^{3} + 4102800 \, a^{3} b^{9} c^{2} d - 777840 \, a^{6} b^{6} c d^{2}\right)} n^{4} + 8 \, {\left(38232551 \, b^{12} c^{3} + 16529190 \, a^{3} b^{9} c^{2} d - 6229440 \, a^{6} b^{6} c d^{2} + 831600 \, a^{9} b^{3} d^{3}\right)} n^{3} + 576 \, {\left(861864 \, b^{12} c^{3} + 298435 \, a^{3} b^{9} c^{2} d - 163940 \, a^{6} b^{6} c d^{2} + 34650 \, a^{9} b^{3} d^{3}\right)} n^{2} + 5760 \, {\left(76781 \, b^{12} c^{3} + 13860 \, a^{3} b^{9} c^{2} d - 9240 \, a^{6} b^{6} c d^{2} + 2310 \, a^{9} b^{3} d^{3}\right)} n\right)} x^{3} + 144 \, {\left(780996 \, a^{3} b^{9} c^{3} - 293635 \, a^{6} b^{6} c^{2} d + 27720 \, a^{9} b^{3} c d^{2}\right)} n^{2} + {\left(a b^{11} c^{3} n^{11} + 73 \, a b^{11} c^{3} n^{10} + 2346 \, a b^{11} c^{3} n^{9} + 6 \, {\left(7267 \, a b^{11} c^{3} - 30 \, a^{4} b^{8} c^{2} d\right)} n^{8} + 3 \, {\left(172459 \, a b^{11} c^{3} - 3480 \, a^{4} b^{8} c^{2} d\right)} n^{7} + 3 \, {\left(1359379 \, a b^{11} c^{3} - 84120 \, a^{4} b^{8} c^{2} d\right)} n^{6} + 4 \, {\left(5373821 \, a b^{11} c^{3} - 817200 \, a^{4} b^{8} c^{2} d + 15120 \, a^{7} b^{5} c d^{2}\right)} n^{5} + 4 \, {\left(18531227 \, a b^{11} c^{3} - 6042105 \, a^{4} b^{8} c^{2} d + 514080 \, a^{7} b^{5} c d^{2}\right)} n^{4} + 72 \, {\left(2189036 \, a b^{11} c^{3} - 1380055 \, a^{4} b^{8} c^{2} d + 331800 \, a^{7} b^{5} c d^{2}\right)} n^{3} + 1440 \, {\left(125842 \, a b^{11} c^{3} - 137481 \, a^{4} b^{8} c^{2} d + 70644 \, a^{7} b^{5} c d^{2} - 13860 \, a^{10} b^{2} d^{3}\right)} n^{2} + 19958400 \, {\left(4 \, a b^{11} c^{3} - 6 \, a^{4} b^{8} c^{2} d + 4 \, a^{7} b^{5} c d^{2} - a^{10} b^{2} d^{3}\right)} n\right)} x^{2} + 2880 \, {\left(70402 \, a^{3} b^{9} c^{3} - 54321 \, a^{6} b^{6} c^{2} d + 15204 \, a^{9} b^{3} c d^{2}\right)} n - 2 \, {\left(a^{2} b^{10} c^{3} n^{10} + 72 \, a^{2} b^{10} c^{3} n^{9} + 2274 \, a^{2} b^{10} c^{3} n^{8} + 36 \, {\left(1148 \, a^{2} b^{10} c^{3} - 5 \, a^{5} b^{7} c^{2} d\right)} n^{7} + 3 \, {\left(158683 \, a^{2} b^{10} c^{3} - 3420 \, a^{5} b^{7} c^{2} d\right)} n^{6} + 36 \, {\left(100058 \, a^{2} b^{10} c^{3} - 6725 \, a^{5} b^{7} c^{2} d\right)} n^{5} + 4 \, {\left(4473299 \, a^{2} b^{10} c^{3} - 756675 \, a^{5} b^{7} c^{2} d + 15120 \, a^{8} b^{4} c d^{2}\right)} n^{4} + 72 \, {\left(780996 \, a^{2} b^{10} c^{3} - 293635 \, a^{5} b^{7} c^{2} d + 27720 \, a^{8} b^{4} c d^{2}\right)} n^{3} + 1440 \, {\left(70402 \, a^{2} b^{10} c^{3} - 54321 \, a^{5} b^{7} c^{2} d + 15204 \, a^{8} b^{4} c d^{2}\right)} n^{2} + 19958400 \, {\left(4 \, a^{2} b^{10} c^{3} - 6 \, a^{5} b^{7} c^{2} d + 4 \, a^{8} b^{4} c d^{2} - a^{11} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{12} n^{12} + 78 \, b^{12} n^{11} + 2717 \, b^{12} n^{10} + 55770 \, b^{12} n^{9} + 749463 \, b^{12} n^{8} + 6926634 \, b^{12} n^{7} + 44990231 \, b^{12} n^{6} + 206070150 \, b^{12} n^{5} + 657206836 \, b^{12} n^{4} + 1414014888 \, b^{12} n^{3} + 1931559552 \, b^{12} n^{2} + 1486442880 \, b^{12} n + 479001600 \, b^{12}}"," ",0,"(2*a^3*b^9*c^3*n^9 + 144*a^3*b^9*c^3*n^8 + 4548*a^3*b^9*c^3*n^7 + 159667200*a^3*b^9*c^3 - 239500800*a^6*b^6*c^2*d + 159667200*a^9*b^3*c*d^2 - 39916800*a^12*d^3 + (b^12*d^3*n^11 + 66*b^12*d^3*n^10 + 1925*b^12*d^3*n^9 + 32670*b^12*d^3*n^8 + 357423*b^12*d^3*n^7 + 2637558*b^12*d^3*n^6 + 13339535*b^12*d^3*n^5 + 45995730*b^12*d^3*n^4 + 105258076*b^12*d^3*n^3 + 150917976*b^12*d^3*n^2 + 120543840*b^12*d^3*n + 39916800*b^12*d^3)*x^12 + (a*b^11*d^3*n^11 + 55*a*b^11*d^3*n^10 + 1320*a*b^11*d^3*n^9 + 18150*a*b^11*d^3*n^8 + 157773*a*b^11*d^3*n^7 + 902055*a*b^11*d^3*n^6 + 3416930*a*b^11*d^3*n^5 + 8409500*a*b^11*d^3*n^4 + 12753576*a*b^11*d^3*n^3 + 10628640*a*b^11*d^3*n^2 + 3628800*a*b^11*d^3*n)*x^11 - 11*(a^2*b^10*d^3*n^10 + 45*a^2*b^10*d^3*n^9 + 870*a^2*b^10*d^3*n^8 + 9450*a^2*b^10*d^3*n^7 + 63273*a^2*b^10*d^3*n^6 + 269325*a^2*b^10*d^3*n^5 + 723680*a^2*b^10*d^3*n^4 + 1172700*a^2*b^10*d^3*n^3 + 1026576*a^2*b^10*d^3*n^2 + 362880*a^2*b^10*d^3*n)*x^10 + (3*b^12*c*d^2*n^11 + 207*b^12*c*d^2*n^10 + 159667200*b^12*c*d^2 + 2*(3144*b^12*c*d^2 + 55*a^3*b^9*d^3)*n^9 + 18*(6151*b^12*c*d^2 + 220*a^3*b^9*d^3)*n^8 + 3*(417309*b^12*c*d^2 + 20020*a^3*b^9*d^3)*n^7 + 567*(16777*b^12*c*d^2 + 880*a^3*b^9*d^3)*n^6 + 6*(8226277*b^12*c*d^2 + 411565*a^3*b^9*d^3)*n^5 + 36*(4833097*b^12*c*d^2 + 205590*a^3*b^9*d^3)*n^4 + 40*(10142427*b^12*c*d^2 + 324841*a^3*b^9*d^3)*n^3 + 288*(2051288*b^12*c*d^2 + 41855*a^3*b^9*d^3)*n^2 + 5760*(82941*b^12*c*d^2 + 770*a^3*b^9*d^3)*n)*x^9 + 3*(a*b^11*c*d^2*n^11 + 61*a*b^11*c*d^2*n^10 + 1608*a*b^11*c*d^2*n^9 + 6*(4007*a*b^11*c*d^2 - 55*a^4*b^8*d^3)*n^8 + 21*(10713*a*b^11*c*d^2 - 440*a^4*b^8*d^3)*n^7 + 21*(65289*a*b^11*c*d^2 - 5060*a^4*b^8*d^3)*n^6 + 2*(2742001*a*b^11*c*d^2 - 323400*a^4*b^8*d^3)*n^5 + 2*(7062574*a*b^11*c*d^2 - 1116885*a^4*b^8*d^3)*n^4 + 264*(84209*a*b^11*c*d^2 - 16415*a^4*b^8*d^3)*n^3 + 360*(52984*a*b^11*c*d^2 - 11979*a^4*b^8*d^3)*n^2 + 1663200*(4*a*b^11*c*d^2 - a^4*b^8*d^3)*n)*x^8 - 24*(a^2*b^10*c*d^2*n^10 + 54*a^2*b^10*c*d^2*n^9 + 1230*a^2*b^10*c*d^2*n^8 + 6*(2572*a^2*b^10*c*d^2 - 55*a^5*b^7*d^3)*n^7 + 21*(5569*a^2*b^10*c*d^2 - 330*a^5*b^7*d^3)*n^6 + 42*(13153*a^2*b^10*c*d^2 - 1375*a^5*b^7*d^3)*n^5 + 10*(161702*a^2*b^10*c*d^2 - 24255*a^5*b^7*d^3)*n^4 + 24*(116917*a^2*b^10*c*d^2 - 22330*a^5*b^7*d^3)*n^3 + 360*(7192*a^2*b^10*c*d^2 - 1617*a^5*b^7*d^3)*n^2 + 237600*(4*a^2*b^10*c*d^2 - a^5*b^7*d^3)*n)*x^7 + 72*(1148*a^3*b^9*c^3 - 5*a^6*b^6*c^2*d)*n^6 + 3*(b^12*c^2*d*n^11 + 72*b^12*c^2*d*n^10 + 79833600*b^12*c^2*d + (2285*b^12*c^2*d + 56*a^3*b^9*c*d^2)*n^9 + 12*(3505*b^12*c^2*d + 224*a^3*b^9*c*d^2)*n^8 + 3*(165701*b^12*c^2*d + 17584*a^3*b^9*c*d^2)*n^7 + 48*(82167*b^12*c^2*d + 11410*a^3*b^9*c*d^2 - 385*a^6*b^6*d^3)*n^6 + (21326135*b^12*c^2*d + 3263064*a^3*b^9*c*d^2 - 277200*a^6*b^6*d^3)*n^5 + 12*(6509445*b^12*c^2*d + 946456*a^3*b^9*c*d^2 - 130900*a^6*b^6*d^3)*n^4 + 4*(47131699*b^12*c^2*d + 5602072*a^3*b^9*c*d^2 - 1039500*a^6*b^6*d^3)*n^3 + 96*(2946397*b^12*c^2*d + 236320*a^3*b^9*c*d^2 - 52745*a^6*b^6*d^3)*n^2 + 2880*(81401*b^12*c^2*d + 3080*a^3*b^9*c*d^2 - 770*a^6*b^6*d^3)*n)*x^6 + 6*(158683*a^3*b^9*c^3 - 3420*a^6*b^6*c^2*d)*n^5 + 3*(a*b^11*c^2*d*n^11 + 67*a*b^11*c^2*d*n^10 + 1950*a*b^11*c^2*d*n^9 + 6*(5385*a*b^11*c^2*d - 56*a^4*b^8*c*d^2)*n^8 + 3*(111851*a*b^11*c^2*d - 4816*a^4*b^8*c*d^2)*n^7 + 3*(755417*a*b^11*c^2*d - 81424*a^4*b^8*c*d^2)*n^6 + 560*(17848*a*b^11*c^2*d - 3687*a^4*b^8*c*d^2 + 198*a^7*b^5*d^3)*n^5 + 4*(7034735*a*b^11*c^2*d - 2313696*a^4*b^8*c*d^2 + 277200*a^7*b^5*d^3)*n^4 + 96*(498251*a*b^11*c^2*d - 227822*a^4*b^8*c*d^2 + 40425*a^7*b^5*d^3)*n^3 + 576*(75857*a*b^11*c^2*d - 43568*a^4*b^8*c*d^2 + 9625*a^7*b^5*d^3)*n^2 + 2661120*(6*a*b^11*c^2*d - 4*a^4*b^8*c*d^2 + a^7*b^5*d^3)*n)*x^5 + 72*(100058*a^3*b^9*c^3 - 6725*a^6*b^6*c^2*d)*n^4 - 15*(a^2*b^10*c^2*d*n^10 + 63*a^2*b^10*c^2*d*n^9 + 1698*a^2*b^10*c^2*d*n^8 + 6*(4253*a^2*b^10*c^2*d - 56*a^5*b^7*c*d^2)*n^7 + 3*(77827*a^2*b^10*c^2*d - 4368*a^5*b^7*c*d^2)*n^6 + 3*(444109*a^2*b^10*c^2*d - 63952*a^5*b^7*c*d^2)*n^5 + 4*(1166393*a^2*b^10*c^2*d - 324324*a^5*b^7*c*d^2 + 27720*a^8*b^4*d^3)*n^4 + 12*(789721*a^2*b^10*c^2*d - 338800*a^5*b^7*c*d^2 + 55440*a^8*b^4*d^3)*n^3 + 144*(68927*a^2*b^10*c^2*d - 38948*a^5*b^7*c*d^2 + 8470*a^8*b^4*d^3)*n^2 + 665280*(6*a^2*b^10*c^2*d - 4*a^5*b^7*c*d^2 + a^8*b^4*d^3)*n)*x^4 + 8*(4473299*a^3*b^9*c^3 - 756675*a^6*b^6*c^2*d + 15120*a^9*b^3*c*d^2)*n^3 + (b^12*c^3*n^11 + 75*b^12*c^3*n^10 + 159667200*b^12*c^3 + 4*(623*b^12*c^3 + 15*a^3*b^9*c^2*d)*n^9 + 18*(2683*b^12*c^3 + 200*a^3*b^9*c^2*d)*n^8 + 3*(201527*b^12*c^3 + 30360*a^3*b^9*c^2*d)*n^7 + 9*(568099*b^12*c^3 + 139760*a^3*b^9*c^2*d - 2240*a^6*b^6*c*d^2)*n^6 + 2*(14825779*b^12*c^3 + 5117670*a^3*b^9*c^2*d - 362880*a^6*b^6*c*d^2)*n^5 + 12*(9759623*b^12*c^3 + 4102800*a^3*b^9*c^2*d - 777840*a^6*b^6*c*d^2)*n^4 + 8*(38232551*b^12*c^3 + 16529190*a^3*b^9*c^2*d - 6229440*a^6*b^6*c*d^2 + 831600*a^9*b^3*d^3)*n^3 + 576*(861864*b^12*c^3 + 298435*a^3*b^9*c^2*d - 163940*a^6*b^6*c*d^2 + 34650*a^9*b^3*d^3)*n^2 + 5760*(76781*b^12*c^3 + 13860*a^3*b^9*c^2*d - 9240*a^6*b^6*c*d^2 + 2310*a^9*b^3*d^3)*n)*x^3 + 144*(780996*a^3*b^9*c^3 - 293635*a^6*b^6*c^2*d + 27720*a^9*b^3*c*d^2)*n^2 + (a*b^11*c^3*n^11 + 73*a*b^11*c^3*n^10 + 2346*a*b^11*c^3*n^9 + 6*(7267*a*b^11*c^3 - 30*a^4*b^8*c^2*d)*n^8 + 3*(172459*a*b^11*c^3 - 3480*a^4*b^8*c^2*d)*n^7 + 3*(1359379*a*b^11*c^3 - 84120*a^4*b^8*c^2*d)*n^6 + 4*(5373821*a*b^11*c^3 - 817200*a^4*b^8*c^2*d + 15120*a^7*b^5*c*d^2)*n^5 + 4*(18531227*a*b^11*c^3 - 6042105*a^4*b^8*c^2*d + 514080*a^7*b^5*c*d^2)*n^4 + 72*(2189036*a*b^11*c^3 - 1380055*a^4*b^8*c^2*d + 331800*a^7*b^5*c*d^2)*n^3 + 1440*(125842*a*b^11*c^3 - 137481*a^4*b^8*c^2*d + 70644*a^7*b^5*c*d^2 - 13860*a^10*b^2*d^3)*n^2 + 19958400*(4*a*b^11*c^3 - 6*a^4*b^8*c^2*d + 4*a^7*b^5*c*d^2 - a^10*b^2*d^3)*n)*x^2 + 2880*(70402*a^3*b^9*c^3 - 54321*a^6*b^6*c^2*d + 15204*a^9*b^3*c*d^2)*n - 2*(a^2*b^10*c^3*n^10 + 72*a^2*b^10*c^3*n^9 + 2274*a^2*b^10*c^3*n^8 + 36*(1148*a^2*b^10*c^3 - 5*a^5*b^7*c^2*d)*n^7 + 3*(158683*a^2*b^10*c^3 - 3420*a^5*b^7*c^2*d)*n^6 + 36*(100058*a^2*b^10*c^3 - 6725*a^5*b^7*c^2*d)*n^5 + 4*(4473299*a^2*b^10*c^3 - 756675*a^5*b^7*c^2*d + 15120*a^8*b^4*c*d^2)*n^4 + 72*(780996*a^2*b^10*c^3 - 293635*a^5*b^7*c^2*d + 27720*a^8*b^4*c*d^2)*n^3 + 1440*(70402*a^2*b^10*c^3 - 54321*a^5*b^7*c^2*d + 15204*a^8*b^4*c*d^2)*n^2 + 19958400*(4*a^2*b^10*c^3 - 6*a^5*b^7*c^2*d + 4*a^8*b^4*c*d^2 - a^11*b*d^3)*n)*x)*(b*x + a)^n/(b^12*n^12 + 78*b^12*n^11 + 2717*b^12*n^10 + 55770*b^12*n^9 + 749463*b^12*n^8 + 6926634*b^12*n^7 + 44990231*b^12*n^6 + 206070150*b^12*n^5 + 657206836*b^12*n^4 + 1414014888*b^12*n^3 + 1931559552*b^12*n^2 + 1486442880*b^12*n + 479001600*b^12)","B",0
183,1,2919,0,0.974132," ","integrate(x*(b*x+a)^n*(d*x^3+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{9} c^{3} n^{9} + 63 \, a^{2} b^{9} c^{3} n^{8} + 1734 \, a^{2} b^{9} c^{3} n^{7} + 19958400 \, a^{2} b^{9} c^{3} - 23950080 \, a^{5} b^{6} c^{2} d + 14968800 \, a^{8} b^{3} c d^{2} - 3628800 \, a^{11} d^{3} - {\left(b^{11} d^{3} n^{10} + 55 \, b^{11} d^{3} n^{9} + 1320 \, b^{11} d^{3} n^{8} + 18150 \, b^{11} d^{3} n^{7} + 157773 \, b^{11} d^{3} n^{6} + 902055 \, b^{11} d^{3} n^{5} + 3416930 \, b^{11} d^{3} n^{4} + 8409500 \, b^{11} d^{3} n^{3} + 12753576 \, b^{11} d^{3} n^{2} + 10628640 \, b^{11} d^{3} n + 3628800 \, b^{11} d^{3}\right)} x^{11} - {\left(a b^{10} d^{3} n^{10} + 45 \, a b^{10} d^{3} n^{9} + 870 \, a b^{10} d^{3} n^{8} + 9450 \, a b^{10} d^{3} n^{7} + 63273 \, a b^{10} d^{3} n^{6} + 269325 \, a b^{10} d^{3} n^{5} + 723680 \, a b^{10} d^{3} n^{4} + 1172700 \, a b^{10} d^{3} n^{3} + 1026576 \, a b^{10} d^{3} n^{2} + 362880 \, a b^{10} d^{3} n\right)} x^{10} + 10 \, {\left(a^{2} b^{9} d^{3} n^{9} + 36 \, a^{2} b^{9} d^{3} n^{8} + 546 \, a^{2} b^{9} d^{3} n^{7} + 4536 \, a^{2} b^{9} d^{3} n^{6} + 22449 \, a^{2} b^{9} d^{3} n^{5} + 67284 \, a^{2} b^{9} d^{3} n^{4} + 118124 \, a^{2} b^{9} d^{3} n^{3} + 109584 \, a^{2} b^{9} d^{3} n^{2} + 40320 \, a^{2} b^{9} d^{3} n\right)} x^{9} - 3 \, {\left(b^{11} c d^{2} n^{10} + 58 \, b^{11} c d^{2} n^{9} + 4989600 \, b^{11} c d^{2} + 3 \, {\left(487 \, b^{11} c d^{2} + 10 \, a^{3} b^{8} d^{3}\right)} n^{8} + 6 \, {\left(3497 \, b^{11} c d^{2} + 140 \, a^{3} b^{8} d^{3}\right)} n^{7} + 21 \, {\left(9027 \, b^{11} c d^{2} + 460 \, a^{3} b^{8} d^{3}\right)} n^{6} + 294 \, {\left(3813 \, b^{11} c d^{2} + 200 \, a^{3} b^{8} d^{3}\right)} n^{5} + {\left(4371359 \, b^{11} c d^{2} + 203070 \, a^{3} b^{8} d^{3}\right)} n^{4} + 2 \, {\left(5512429 \, b^{11} c d^{2} + 196980 \, a^{3} b^{8} d^{3}\right)} n^{3} + 36 \, {\left(473867 \, b^{11} c d^{2} + 10890 \, a^{3} b^{8} d^{3}\right)} n^{2} + 360 \, {\left(40123 \, b^{11} c d^{2} + 420 \, a^{3} b^{8} d^{3}\right)} n\right)} x^{8} - 3 \, {\left(a b^{10} c d^{2} n^{10} + 51 \, a b^{10} c d^{2} n^{9} + 1104 \, a b^{10} c d^{2} n^{8} + 6 \, {\left(2209 \, a b^{10} c d^{2} - 40 \, a^{4} b^{7} d^{3}\right)} n^{7} + 21 \, {\left(4609 \, a b^{10} c d^{2} - 240 \, a^{4} b^{7} d^{3}\right)} n^{6} + 21 \, {\left(21119 \, a b^{10} c d^{2} - 2000 \, a^{4} b^{7} d^{3}\right)} n^{5} + 2 \, {\left(633433 \, a b^{10} c d^{2} - 88200 \, a^{4} b^{7} d^{3}\right)} n^{4} + 12 \, {\left(179733 \, a b^{10} c d^{2} - 32480 \, a^{4} b^{7} d^{3}\right)} n^{3} + 360 \, {\left(5449 \, a b^{10} c d^{2} - 1176 \, a^{4} b^{7} d^{3}\right)} n^{2} + 21600 \, {\left(33 \, a b^{10} c d^{2} - 8 \, a^{4} b^{7} d^{3}\right)} n\right)} x^{7} + 18 \, {\left(1519 \, a^{2} b^{9} c^{3} - 4 \, a^{5} b^{6} c^{2} d\right)} n^{6} + 21 \, {\left(a^{2} b^{9} c d^{2} n^{9} + 45 \, a^{2} b^{9} c d^{2} n^{8} + 834 \, a^{2} b^{9} c d^{2} n^{7} + 30 \, {\left(275 \, a^{2} b^{9} c d^{2} - 8 \, a^{5} b^{6} d^{3}\right)} n^{6} + 3 \, {\left(15763 \, a^{2} b^{9} c d^{2} - 1200 \, a^{5} b^{6} d^{3}\right)} n^{5} + 15 \, {\left(10651 \, a^{2} b^{9} c d^{2} - 1360 \, a^{5} b^{6} d^{3}\right)} n^{4} + 4 \, {\left(77069 \, a^{2} b^{9} c d^{2} - 13500 \, a^{5} b^{6} d^{3}\right)} n^{3} + 60 \, {\left(5119 \, a^{2} b^{9} c d^{2} - 1096 \, a^{5} b^{6} d^{3}\right)} n^{2} + 3600 \, {\left(33 \, a^{2} b^{9} c d^{2} - 8 \, a^{5} b^{6} d^{3}\right)} n\right)} x^{6} + 3 \, {\left(90643 \, a^{2} b^{9} c^{3} - 1224 \, a^{5} b^{6} c^{2} d\right)} n^{5} - 3 \, {\left(b^{11} c^{2} d n^{10} + 61 \, b^{11} c^{2} d n^{9} + 7983360 \, b^{11} c^{2} d + 6 \, {\left(270 \, b^{11} c^{2} d + 7 \, a^{3} b^{8} c d^{2}\right)} n^{8} + 210 \, {\left(117 \, b^{11} c^{2} d + 8 \, a^{3} b^{8} c d^{2}\right)} n^{7} + 3 \, {\left(78191 \, b^{11} c^{2} d + 8876 \, a^{3} b^{8} c d^{2}\right)} n^{6} + 3 \, {\left(488231 \, b^{11} c^{2} d + 71120 \, a^{3} b^{8} c d^{2} - 3360 \, a^{6} b^{5} d^{3}\right)} n^{5} + 2 \, {\left(3008035 \, b^{11} c^{2} d + 459669 \, a^{3} b^{8} c d^{2} - 50400 \, a^{6} b^{5} d^{3}\right)} n^{4} + 20 \, {\left(795769 \, b^{11} c^{2} d + 105672 \, a^{3} b^{8} c d^{2} - 17640 \, a^{6} b^{5} d^{3}\right)} n^{3} + 72 \, {\left(356683 \, b^{11} c^{2} d + 33061 \, a^{3} b^{8} c d^{2} - 7000 \, a^{6} b^{5} d^{3}\right)} n^{2} + 288 \, {\left(78167 \, b^{11} c^{2} d + 3465 \, a^{3} b^{8} c d^{2} - 840 \, a^{6} b^{5} d^{3}\right)} n\right)} x^{5} + 9 \, {\left(196343 \, a^{2} b^{9} c^{3} - 8600 \, a^{5} b^{6} c^{2} d\right)} n^{4} - 3 \, {\left(a b^{10} c^{2} d n^{10} + 57 \, a b^{10} c^{2} d n^{9} + 1392 \, a b^{10} c^{2} d n^{8} + 6 \, {\left(3167 \, a b^{10} c^{2} d - 35 \, a^{4} b^{7} c d^{2}\right)} n^{7} + 15 \, {\left(10571 \, a b^{10} c^{2} d - 504 \, a^{4} b^{7} c d^{2}\right)} n^{6} + 3 \, {\left(276811 \, a b^{10} c^{2} d - 34300 \, a^{4} b^{7} c d^{2}\right)} n^{5} + 2 \, {\left(1347169 \, a b^{10} c^{2} d - 327600 \, a^{4} b^{7} c d^{2} + 25200 \, a^{7} b^{4} d^{3}\right)} n^{4} + 42 \, {\left(122334 \, a b^{10} c^{2} d - 47045 \, a^{4} b^{7} c d^{2} + 7200 \, a^{7} b^{4} d^{3}\right)} n^{3} + 72 \, {\left(71237 \, a b^{10} c^{2} d - 36995 \, a^{4} b^{7} c d^{2} + 7700 \, a^{7} b^{4} d^{3}\right)} n^{2} + 7560 \, {\left(264 \, a b^{10} c^{2} d - 165 \, a^{4} b^{7} c d^{2} + 40 \, a^{7} b^{4} d^{3}\right)} n\right)} x^{4} + 8 \, {\left(936802 \, a^{2} b^{9} c^{3} - 107865 \, a^{5} b^{6} c^{2} d + 1890 \, a^{8} b^{3} c d^{2}\right)} n^{3} + 12 \, {\left(a^{2} b^{9} c^{2} d n^{9} + 54 \, a^{2} b^{9} c^{2} d n^{8} + 1230 \, a^{2} b^{9} c^{2} d n^{7} + 6 \, {\left(2552 \, a^{2} b^{9} c^{2} d - 35 \, a^{5} b^{6} c d^{2}\right)} n^{6} + 33 \, {\left(3413 \, a^{2} b^{9} c^{2} d - 210 \, a^{5} b^{6} c d^{2}\right)} n^{5} + 6 \, {\left(82091 \, a^{2} b^{9} c^{2} d - 13685 \, a^{5} b^{6} c d^{2}\right)} n^{4} + 10 \, {\left(121670 \, a^{2} b^{9} c^{2} d - 40887 \, a^{5} b^{6} c d^{2} + 5040 \, a^{8} b^{3} d^{3}\right)} n^{3} + 24 \, {\left(61997 \, a^{2} b^{9} c^{2} d - 31220 \, a^{5} b^{6} c d^{2} + 6300 \, a^{8} b^{3} d^{3}\right)} n^{2} + 2520 \, {\left(264 \, a^{2} b^{9} c^{2} d - 165 \, a^{5} b^{6} c d^{2} + 40 \, a^{8} b^{3} d^{3}\right)} n\right)} x^{3} + 36 \, {\left(554953 \, a^{2} b^{9} c^{3} - 149048 \, a^{5} b^{6} c^{2} d + 12600 \, a^{8} b^{3} c d^{2}\right)} n^{2} - {\left(b^{11} c^{3} n^{10} + 64 \, b^{11} c^{3} n^{9} + 19958400 \, b^{11} c^{3} + 3 \, {\left(599 \, b^{11} c^{3} + 12 \, a^{3} b^{8} c^{2} d\right)} n^{8} + 12 \, {\left(2423 \, b^{11} c^{3} + 156 \, a^{3} b^{8} c^{2} d\right)} n^{7} + 3 \, {\left(99757 \, b^{11} c^{3} + 13512 \, a^{3} b^{8} c^{2} d\right)} n^{6} + 24 \, {\left(84959 \, b^{11} c^{3} + 19590 \, a^{3} b^{8} c^{2} d - 315 \, a^{6} b^{5} c d^{2}\right)} n^{5} + {\left(9261503 \, b^{11} c^{3} + 3114324 \, a^{3} b^{8} c^{2} d - 234360 \, a^{6} b^{5} c d^{2}\right)} n^{4} + 4 \, {\left(6868181 \, b^{11} c^{3} + 2875752 \, a^{3} b^{8} c^{2} d - 621810 \, a^{6} b^{5} c d^{2}\right)} n^{3} + 36 \, {\left(1397573 \, b^{11} c^{3} + 577644 \, a^{3} b^{8} c^{2} d - 270690 \, a^{6} b^{5} c d^{2} + 50400 \, a^{9} b^{2} d^{3}\right)} n^{2} + 720 \, {\left(69851 \, b^{11} c^{3} + 16632 \, a^{3} b^{8} c^{2} d - 10395 \, a^{6} b^{5} c d^{2} + 2520 \, a^{9} b^{2} d^{3}\right)} n\right)} x^{2} + 144 \, {\left(210655 \, a^{2} b^{9} c^{3} - 122502 \, a^{5} b^{6} c^{2} d + 31395 \, a^{8} b^{3} c d^{2}\right)} n - {\left(a b^{10} c^{3} n^{10} + 63 \, a b^{10} c^{3} n^{9} + 1734 \, a b^{10} c^{3} n^{8} + 18 \, {\left(1519 \, a b^{10} c^{3} - 4 \, a^{4} b^{7} c^{2} d\right)} n^{7} + 3 \, {\left(90643 \, a b^{10} c^{3} - 1224 \, a^{4} b^{7} c^{2} d\right)} n^{6} + 9 \, {\left(196343 \, a b^{10} c^{3} - 8600 \, a^{4} b^{7} c^{2} d\right)} n^{5} + 8 \, {\left(936802 \, a b^{10} c^{3} - 107865 \, a^{4} b^{7} c^{2} d + 1890 \, a^{7} b^{4} c d^{2}\right)} n^{4} + 36 \, {\left(554953 \, a b^{10} c^{3} - 149048 \, a^{4} b^{7} c^{2} d + 12600 \, a^{7} b^{4} c d^{2}\right)} n^{3} + 144 \, {\left(210655 \, a b^{10} c^{3} - 122502 \, a^{4} b^{7} c^{2} d + 31395 \, a^{7} b^{4} c d^{2}\right)} n^{2} + 90720 \, {\left(220 \, a b^{10} c^{3} - 264 \, a^{4} b^{7} c^{2} d + 165 \, a^{7} b^{4} c d^{2} - 40 \, a^{10} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{11} n^{11} + 66 \, b^{11} n^{10} + 1925 \, b^{11} n^{9} + 32670 \, b^{11} n^{8} + 357423 \, b^{11} n^{7} + 2637558 \, b^{11} n^{6} + 13339535 \, b^{11} n^{5} + 45995730 \, b^{11} n^{4} + 105258076 \, b^{11} n^{3} + 150917976 \, b^{11} n^{2} + 120543840 \, b^{11} n + 39916800 \, b^{11}}"," ",0,"-(a^2*b^9*c^3*n^9 + 63*a^2*b^9*c^3*n^8 + 1734*a^2*b^9*c^3*n^7 + 19958400*a^2*b^9*c^3 - 23950080*a^5*b^6*c^2*d + 14968800*a^8*b^3*c*d^2 - 3628800*a^11*d^3 - (b^11*d^3*n^10 + 55*b^11*d^3*n^9 + 1320*b^11*d^3*n^8 + 18150*b^11*d^3*n^7 + 157773*b^11*d^3*n^6 + 902055*b^11*d^3*n^5 + 3416930*b^11*d^3*n^4 + 8409500*b^11*d^3*n^3 + 12753576*b^11*d^3*n^2 + 10628640*b^11*d^3*n + 3628800*b^11*d^3)*x^11 - (a*b^10*d^3*n^10 + 45*a*b^10*d^3*n^9 + 870*a*b^10*d^3*n^8 + 9450*a*b^10*d^3*n^7 + 63273*a*b^10*d^3*n^6 + 269325*a*b^10*d^3*n^5 + 723680*a*b^10*d^3*n^4 + 1172700*a*b^10*d^3*n^3 + 1026576*a*b^10*d^3*n^2 + 362880*a*b^10*d^3*n)*x^10 + 10*(a^2*b^9*d^3*n^9 + 36*a^2*b^9*d^3*n^8 + 546*a^2*b^9*d^3*n^7 + 4536*a^2*b^9*d^3*n^6 + 22449*a^2*b^9*d^3*n^5 + 67284*a^2*b^9*d^3*n^4 + 118124*a^2*b^9*d^3*n^3 + 109584*a^2*b^9*d^3*n^2 + 40320*a^2*b^9*d^3*n)*x^9 - 3*(b^11*c*d^2*n^10 + 58*b^11*c*d^2*n^9 + 4989600*b^11*c*d^2 + 3*(487*b^11*c*d^2 + 10*a^3*b^8*d^3)*n^8 + 6*(3497*b^11*c*d^2 + 140*a^3*b^8*d^3)*n^7 + 21*(9027*b^11*c*d^2 + 460*a^3*b^8*d^3)*n^6 + 294*(3813*b^11*c*d^2 + 200*a^3*b^8*d^3)*n^5 + (4371359*b^11*c*d^2 + 203070*a^3*b^8*d^3)*n^4 + 2*(5512429*b^11*c*d^2 + 196980*a^3*b^8*d^3)*n^3 + 36*(473867*b^11*c*d^2 + 10890*a^3*b^8*d^3)*n^2 + 360*(40123*b^11*c*d^2 + 420*a^3*b^8*d^3)*n)*x^8 - 3*(a*b^10*c*d^2*n^10 + 51*a*b^10*c*d^2*n^9 + 1104*a*b^10*c*d^2*n^8 + 6*(2209*a*b^10*c*d^2 - 40*a^4*b^7*d^3)*n^7 + 21*(4609*a*b^10*c*d^2 - 240*a^4*b^7*d^3)*n^6 + 21*(21119*a*b^10*c*d^2 - 2000*a^4*b^7*d^3)*n^5 + 2*(633433*a*b^10*c*d^2 - 88200*a^4*b^7*d^3)*n^4 + 12*(179733*a*b^10*c*d^2 - 32480*a^4*b^7*d^3)*n^3 + 360*(5449*a*b^10*c*d^2 - 1176*a^4*b^7*d^3)*n^2 + 21600*(33*a*b^10*c*d^2 - 8*a^4*b^7*d^3)*n)*x^7 + 18*(1519*a^2*b^9*c^3 - 4*a^5*b^6*c^2*d)*n^6 + 21*(a^2*b^9*c*d^2*n^9 + 45*a^2*b^9*c*d^2*n^8 + 834*a^2*b^9*c*d^2*n^7 + 30*(275*a^2*b^9*c*d^2 - 8*a^5*b^6*d^3)*n^6 + 3*(15763*a^2*b^9*c*d^2 - 1200*a^5*b^6*d^3)*n^5 + 15*(10651*a^2*b^9*c*d^2 - 1360*a^5*b^6*d^3)*n^4 + 4*(77069*a^2*b^9*c*d^2 - 13500*a^5*b^6*d^3)*n^3 + 60*(5119*a^2*b^9*c*d^2 - 1096*a^5*b^6*d^3)*n^2 + 3600*(33*a^2*b^9*c*d^2 - 8*a^5*b^6*d^3)*n)*x^6 + 3*(90643*a^2*b^9*c^3 - 1224*a^5*b^6*c^2*d)*n^5 - 3*(b^11*c^2*d*n^10 + 61*b^11*c^2*d*n^9 + 7983360*b^11*c^2*d + 6*(270*b^11*c^2*d + 7*a^3*b^8*c*d^2)*n^8 + 210*(117*b^11*c^2*d + 8*a^3*b^8*c*d^2)*n^7 + 3*(78191*b^11*c^2*d + 8876*a^3*b^8*c*d^2)*n^6 + 3*(488231*b^11*c^2*d + 71120*a^3*b^8*c*d^2 - 3360*a^6*b^5*d^3)*n^5 + 2*(3008035*b^11*c^2*d + 459669*a^3*b^8*c*d^2 - 50400*a^6*b^5*d^3)*n^4 + 20*(795769*b^11*c^2*d + 105672*a^3*b^8*c*d^2 - 17640*a^6*b^5*d^3)*n^3 + 72*(356683*b^11*c^2*d + 33061*a^3*b^8*c*d^2 - 7000*a^6*b^5*d^3)*n^2 + 288*(78167*b^11*c^2*d + 3465*a^3*b^8*c*d^2 - 840*a^6*b^5*d^3)*n)*x^5 + 9*(196343*a^2*b^9*c^3 - 8600*a^5*b^6*c^2*d)*n^4 - 3*(a*b^10*c^2*d*n^10 + 57*a*b^10*c^2*d*n^9 + 1392*a*b^10*c^2*d*n^8 + 6*(3167*a*b^10*c^2*d - 35*a^4*b^7*c*d^2)*n^7 + 15*(10571*a*b^10*c^2*d - 504*a^4*b^7*c*d^2)*n^6 + 3*(276811*a*b^10*c^2*d - 34300*a^4*b^7*c*d^2)*n^5 + 2*(1347169*a*b^10*c^2*d - 327600*a^4*b^7*c*d^2 + 25200*a^7*b^4*d^3)*n^4 + 42*(122334*a*b^10*c^2*d - 47045*a^4*b^7*c*d^2 + 7200*a^7*b^4*d^3)*n^3 + 72*(71237*a*b^10*c^2*d - 36995*a^4*b^7*c*d^2 + 7700*a^7*b^4*d^3)*n^2 + 7560*(264*a*b^10*c^2*d - 165*a^4*b^7*c*d^2 + 40*a^7*b^4*d^3)*n)*x^4 + 8*(936802*a^2*b^9*c^3 - 107865*a^5*b^6*c^2*d + 1890*a^8*b^3*c*d^2)*n^3 + 12*(a^2*b^9*c^2*d*n^9 + 54*a^2*b^9*c^2*d*n^8 + 1230*a^2*b^9*c^2*d*n^7 + 6*(2552*a^2*b^9*c^2*d - 35*a^5*b^6*c*d^2)*n^6 + 33*(3413*a^2*b^9*c^2*d - 210*a^5*b^6*c*d^2)*n^5 + 6*(82091*a^2*b^9*c^2*d - 13685*a^5*b^6*c*d^2)*n^4 + 10*(121670*a^2*b^9*c^2*d - 40887*a^5*b^6*c*d^2 + 5040*a^8*b^3*d^3)*n^3 + 24*(61997*a^2*b^9*c^2*d - 31220*a^5*b^6*c*d^2 + 6300*a^8*b^3*d^3)*n^2 + 2520*(264*a^2*b^9*c^2*d - 165*a^5*b^6*c*d^2 + 40*a^8*b^3*d^3)*n)*x^3 + 36*(554953*a^2*b^9*c^3 - 149048*a^5*b^6*c^2*d + 12600*a^8*b^3*c*d^2)*n^2 - (b^11*c^3*n^10 + 64*b^11*c^3*n^9 + 19958400*b^11*c^3 + 3*(599*b^11*c^3 + 12*a^3*b^8*c^2*d)*n^8 + 12*(2423*b^11*c^3 + 156*a^3*b^8*c^2*d)*n^7 + 3*(99757*b^11*c^3 + 13512*a^3*b^8*c^2*d)*n^6 + 24*(84959*b^11*c^3 + 19590*a^3*b^8*c^2*d - 315*a^6*b^5*c*d^2)*n^5 + (9261503*b^11*c^3 + 3114324*a^3*b^8*c^2*d - 234360*a^6*b^5*c*d^2)*n^4 + 4*(6868181*b^11*c^3 + 2875752*a^3*b^8*c^2*d - 621810*a^6*b^5*c*d^2)*n^3 + 36*(1397573*b^11*c^3 + 577644*a^3*b^8*c^2*d - 270690*a^6*b^5*c*d^2 + 50400*a^9*b^2*d^3)*n^2 + 720*(69851*b^11*c^3 + 16632*a^3*b^8*c^2*d - 10395*a^6*b^5*c*d^2 + 2520*a^9*b^2*d^3)*n)*x^2 + 144*(210655*a^2*b^9*c^3 - 122502*a^5*b^6*c^2*d + 31395*a^8*b^3*c*d^2)*n - (a*b^10*c^3*n^10 + 63*a*b^10*c^3*n^9 + 1734*a*b^10*c^3*n^8 + 18*(1519*a*b^10*c^3 - 4*a^4*b^7*c^2*d)*n^7 + 3*(90643*a*b^10*c^3 - 1224*a^4*b^7*c^2*d)*n^6 + 9*(196343*a*b^10*c^3 - 8600*a^4*b^7*c^2*d)*n^5 + 8*(936802*a*b^10*c^3 - 107865*a^4*b^7*c^2*d + 1890*a^7*b^4*c*d^2)*n^4 + 36*(554953*a*b^10*c^3 - 149048*a^4*b^7*c^2*d + 12600*a^7*b^4*c*d^2)*n^3 + 144*(210655*a*b^10*c^3 - 122502*a^4*b^7*c^2*d + 31395*a^7*b^4*c*d^2)*n^2 + 90720*(220*a*b^10*c^3 - 264*a^4*b^7*c^2*d + 165*a^7*b^4*c*d^2 - 40*a^10*b*d^3)*n)*x)*(b*x + a)^n/(b^11*n^11 + 66*b^11*n^10 + 1925*b^11*n^9 + 32670*b^11*n^8 + 357423*b^11*n^7 + 2637558*b^11*n^6 + 13339535*b^11*n^5 + 45995730*b^11*n^4 + 105258076*b^11*n^3 + 150917976*b^11*n^2 + 120543840*b^11*n + 39916800*b^11)","B",0
184,1,2313,0,0.837022," ","integrate((b*x+a)^n*(d*x^3+c)^3,x, algorithm=""fricas"")","\frac{{\left(a b^{9} c^{3} n^{9} + 54 \, a b^{9} c^{3} n^{8} + 1266 \, a b^{9} c^{3} n^{7} + 3628800 \, a b^{9} c^{3} - 2721600 \, a^{4} b^{6} c^{2} d + 1555200 \, a^{7} b^{3} c d^{2} - 362880 \, a^{10} d^{3} + {\left(b^{10} d^{3} n^{9} + 45 \, b^{10} d^{3} n^{8} + 870 \, b^{10} d^{3} n^{7} + 9450 \, b^{10} d^{3} n^{6} + 63273 \, b^{10} d^{3} n^{5} + 269325 \, b^{10} d^{3} n^{4} + 723680 \, b^{10} d^{3} n^{3} + 1172700 \, b^{10} d^{3} n^{2} + 1026576 \, b^{10} d^{3} n + 362880 \, b^{10} d^{3}\right)} x^{10} + {\left(a b^{9} d^{3} n^{9} + 36 \, a b^{9} d^{3} n^{8} + 546 \, a b^{9} d^{3} n^{7} + 4536 \, a b^{9} d^{3} n^{6} + 22449 \, a b^{9} d^{3} n^{5} + 67284 \, a b^{9} d^{3} n^{4} + 118124 \, a b^{9} d^{3} n^{3} + 109584 \, a b^{9} d^{3} n^{2} + 40320 \, a b^{9} d^{3} n\right)} x^{9} - 9 \, {\left(a^{2} b^{8} d^{3} n^{8} + 28 \, a^{2} b^{8} d^{3} n^{7} + 322 \, a^{2} b^{8} d^{3} n^{6} + 1960 \, a^{2} b^{8} d^{3} n^{5} + 6769 \, a^{2} b^{8} d^{3} n^{4} + 13132 \, a^{2} b^{8} d^{3} n^{3} + 13068 \, a^{2} b^{8} d^{3} n^{2} + 5040 \, a^{2} b^{8} d^{3} n\right)} x^{8} + 3 \, {\left(b^{10} c d^{2} n^{9} + 48 \, b^{10} c d^{2} n^{8} + 518400 \, b^{10} c d^{2} + 24 \, {\left(41 \, b^{10} c d^{2} + a^{3} b^{7} d^{3}\right)} n^{7} + 6 \, {\left(1877 \, b^{10} c d^{2} + 84 \, a^{3} b^{7} d^{3}\right)} n^{6} + 21 \, {\left(3759 \, b^{10} c d^{2} + 200 \, a^{3} b^{7} d^{3}\right)} n^{5} + 42 \, {\left(8321 \, b^{10} c d^{2} + 420 \, a^{3} b^{7} d^{3}\right)} n^{4} + 4 \, {\left(242639 \, b^{10} c d^{2} + 9744 \, a^{3} b^{7} d^{3}\right)} n^{3} + 72 \, {\left(22439 \, b^{10} c d^{2} + 588 \, a^{3} b^{7} d^{3}\right)} n^{2} + 1440 \, {\left(1003 \, b^{10} c d^{2} + 12 \, a^{3} b^{7} d^{3}\right)} n\right)} x^{7} + 18 \, {\left(938 \, a b^{9} c^{3} - a^{4} b^{6} c^{2} d\right)} n^{6} + 3 \, {\left(a b^{9} c d^{2} n^{9} + 42 \, a b^{9} c d^{2} n^{8} + 732 \, a b^{9} c d^{2} n^{7} + 6 \, {\left(1145 \, a b^{9} c d^{2} - 28 \, a^{4} b^{6} d^{3}\right)} n^{6} + 9 \, {\left(4191 \, a b^{9} c d^{2} - 280 \, a^{4} b^{6} d^{3}\right)} n^{5} + 24 \, {\left(5132 \, a b^{9} c d^{2} - 595 \, a^{4} b^{6} d^{3}\right)} n^{4} + 4 \, {\left(57887 \, a b^{9} c d^{2} - 9450 \, a^{4} b^{6} d^{3}\right)} n^{3} + 48 \, {\left(4715 \, a b^{9} c d^{2} - 959 \, a^{4} b^{6} d^{3}\right)} n^{2} + 2880 \, {\left(30 \, a b^{9} c d^{2} - 7 \, a^{4} b^{6} d^{3}\right)} n\right)} x^{6} + 3 \, {\left(46963 \, a b^{9} c^{3} - 270 \, a^{4} b^{6} c^{2} d\right)} n^{5} - 18 \, {\left(a^{2} b^{8} c d^{2} n^{8} + 37 \, a^{2} b^{8} c d^{2} n^{7} + 547 \, a^{2} b^{8} c d^{2} n^{6} + {\left(4135 \, a^{2} b^{8} c d^{2} - 168 \, a^{5} b^{5} d^{3}\right)} n^{5} + 4 \, {\left(4261 \, a^{2} b^{8} c d^{2} - 420 \, a^{5} b^{5} d^{3}\right)} n^{4} + 4 \, {\left(9487 \, a^{2} b^{8} c d^{2} - 1470 \, a^{5} b^{5} d^{3}\right)} n^{3} + 48 \, {\left(871 \, a^{2} b^{8} c d^{2} - 175 \, a^{5} b^{5} d^{3}\right)} n^{2} + 576 \, {\left(30 \, a^{2} b^{8} c d^{2} - 7 \, a^{5} b^{5} d^{3}\right)} n\right)} x^{5} + 18 \, {\left(42287 \, a b^{9} c^{3} - 835 \, a^{4} b^{6} c^{2} d\right)} n^{4} + 3 \, {\left(b^{10} c^{2} d n^{9} + 51 \, b^{10} c^{2} d n^{8} + 907200 \, b^{10} c^{2} d + 6 \, {\left(186 \, b^{10} c^{2} d + 5 \, a^{3} b^{7} c d^{2}\right)} n^{7} + 6 \, {\left(2281 \, b^{10} c^{2} d + 165 \, a^{3} b^{7} c d^{2}\right)} n^{6} + 3 \, {\left(34343 \, b^{10} c^{2} d + 4150 \, a^{3} b^{7} c d^{2}\right)} n^{5} + 3 \, {\left(163313 \, b^{10} c^{2} d + 24750 \, a^{3} b^{7} c d^{2} - 1680 \, a^{6} b^{4} d^{3}\right)} n^{4} + 2 \, {\left(728587 \, b^{10} c^{2} d + 107160 \, a^{3} b^{7} c d^{2} - 15120 \, a^{6} b^{4} d^{3}\right)} n^{3} + 36 \, {\left(71689 \, b^{10} c^{2} d + 7810 \, a^{3} b^{7} c d^{2} - 1540 \, a^{6} b^{4} d^{3}\right)} n^{2} + 360 \, {\left(6751 \, b^{10} c^{2} d + 360 \, a^{3} b^{7} c d^{2} - 84 \, a^{6} b^{4} d^{3}\right)} n\right)} x^{4} + 2 \, {\left(1327882 \, a b^{9} c^{3} - 73575 \, a^{4} b^{6} c^{2} d + 1080 \, a^{7} b^{3} c d^{2}\right)} n^{3} + 3 \, {\left(a b^{9} c^{2} d n^{9} + 48 \, a b^{9} c^{2} d n^{8} + 972 \, a b^{9} c^{2} d n^{7} + 30 \, {\left(359 \, a b^{9} c^{2} d - 4 \, a^{4} b^{6} c d^{2}\right)} n^{6} + 3 \, {\left(23573 \, a b^{9} c^{2} d - 1200 \, a^{4} b^{6} c d^{2}\right)} n^{5} + 6 \, {\left(46297 \, a b^{9} c^{2} d - 6500 \, a^{4} b^{6} c d^{2}\right)} n^{4} + 4 \, {\left(155957 \, a b^{9} c^{2} d - 45000 \, a^{4} b^{6} c d^{2} + 5040 \, a^{7} b^{3} d^{3}\right)} n^{3} + 120 \, {\left(5911 \, a b^{9} c^{2} d - 2644 \, a^{4} b^{6} c d^{2} + 504 \, a^{7} b^{3} d^{3}\right)} n^{2} + 2880 \, {\left(105 \, a b^{9} c^{2} d - 60 \, a^{4} b^{6} c d^{2} + 14 \, a^{7} b^{3} d^{3}\right)} n\right)} x^{3} + 72 \, {\left(79913 \, a b^{9} c^{3} - 11131 \, a^{4} b^{6} c^{2} d + 810 \, a^{7} b^{3} c d^{2}\right)} n^{2} - 9 \, {\left(a^{2} b^{8} c^{2} d n^{8} + 46 \, a^{2} b^{8} c^{2} d n^{7} + 880 \, a^{2} b^{8} c^{2} d n^{6} + 10 \, {\left(901 \, a^{2} b^{8} c^{2} d - 12 \, a^{5} b^{5} c d^{2}\right)} n^{5} + {\left(52699 \, a^{2} b^{8} c^{2} d - 3360 \, a^{5} b^{5} c d^{2}\right)} n^{4} + 8 \, {\left(21548 \, a^{2} b^{8} c^{2} d - 4035 \, a^{5} b^{5} c d^{2}\right)} n^{3} + 60 \, {\left(4651 \, a^{2} b^{8} c^{2} d - 1924 \, a^{5} b^{5} c d^{2} + 336 \, a^{8} b^{2} d^{3}\right)} n^{2} + 1440 \, {\left(105 \, a^{2} b^{8} c^{2} d - 60 \, a^{5} b^{5} c d^{2} + 14 \, a^{8} b^{2} d^{3}\right)} n\right)} x^{2} + 360 \, {\left(19444 \, a b^{9} c^{3} - 6393 \, a^{4} b^{6} c^{2} d + 1452 \, a^{7} b^{3} c d^{2}\right)} n + {\left(b^{10} c^{3} n^{9} + 54 \, b^{10} c^{3} n^{8} + 3628800 \, b^{10} c^{3} + 6 \, {\left(211 \, b^{10} c^{3} + 3 \, a^{3} b^{7} c^{2} d\right)} n^{7} + 18 \, {\left(938 \, b^{10} c^{3} + 45 \, a^{3} b^{7} c^{2} d\right)} n^{6} + 3 \, {\left(46963 \, b^{10} c^{3} + 5010 \, a^{3} b^{7} c^{2} d\right)} n^{5} + 18 \, {\left(42287 \, b^{10} c^{3} + 8175 \, a^{3} b^{7} c^{2} d - 120 \, a^{6} b^{4} c d^{2}\right)} n^{4} + 4 \, {\left(663941 \, b^{10} c^{3} + 200358 \, a^{3} b^{7} c^{2} d - 14580 \, a^{6} b^{4} c d^{2}\right)} n^{3} + 72 \, {\left(79913 \, b^{10} c^{3} + 31965 \, a^{3} b^{7} c^{2} d - 7260 \, a^{6} b^{4} c d^{2}\right)} n^{2} + 1440 \, {\left(4861 \, b^{10} c^{3} + 1890 \, a^{3} b^{7} c^{2} d - 1080 \, a^{6} b^{4} c d^{2} + 252 \, a^{9} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{10} n^{10} + 55 \, b^{10} n^{9} + 1320 \, b^{10} n^{8} + 18150 \, b^{10} n^{7} + 157773 \, b^{10} n^{6} + 902055 \, b^{10} n^{5} + 3416930 \, b^{10} n^{4} + 8409500 \, b^{10} n^{3} + 12753576 \, b^{10} n^{2} + 10628640 \, b^{10} n + 3628800 \, b^{10}}"," ",0,"(a*b^9*c^3*n^9 + 54*a*b^9*c^3*n^8 + 1266*a*b^9*c^3*n^7 + 3628800*a*b^9*c^3 - 2721600*a^4*b^6*c^2*d + 1555200*a^7*b^3*c*d^2 - 362880*a^10*d^3 + (b^10*d^3*n^9 + 45*b^10*d^3*n^8 + 870*b^10*d^3*n^7 + 9450*b^10*d^3*n^6 + 63273*b^10*d^3*n^5 + 269325*b^10*d^3*n^4 + 723680*b^10*d^3*n^3 + 1172700*b^10*d^3*n^2 + 1026576*b^10*d^3*n + 362880*b^10*d^3)*x^10 + (a*b^9*d^3*n^9 + 36*a*b^9*d^3*n^8 + 546*a*b^9*d^3*n^7 + 4536*a*b^9*d^3*n^6 + 22449*a*b^9*d^3*n^5 + 67284*a*b^9*d^3*n^4 + 118124*a*b^9*d^3*n^3 + 109584*a*b^9*d^3*n^2 + 40320*a*b^9*d^3*n)*x^9 - 9*(a^2*b^8*d^3*n^8 + 28*a^2*b^8*d^3*n^7 + 322*a^2*b^8*d^3*n^6 + 1960*a^2*b^8*d^3*n^5 + 6769*a^2*b^8*d^3*n^4 + 13132*a^2*b^8*d^3*n^3 + 13068*a^2*b^8*d^3*n^2 + 5040*a^2*b^8*d^3*n)*x^8 + 3*(b^10*c*d^2*n^9 + 48*b^10*c*d^2*n^8 + 518400*b^10*c*d^2 + 24*(41*b^10*c*d^2 + a^3*b^7*d^3)*n^7 + 6*(1877*b^10*c*d^2 + 84*a^3*b^7*d^3)*n^6 + 21*(3759*b^10*c*d^2 + 200*a^3*b^7*d^3)*n^5 + 42*(8321*b^10*c*d^2 + 420*a^3*b^7*d^3)*n^4 + 4*(242639*b^10*c*d^2 + 9744*a^3*b^7*d^3)*n^3 + 72*(22439*b^10*c*d^2 + 588*a^3*b^7*d^3)*n^2 + 1440*(1003*b^10*c*d^2 + 12*a^3*b^7*d^3)*n)*x^7 + 18*(938*a*b^9*c^3 - a^4*b^6*c^2*d)*n^6 + 3*(a*b^9*c*d^2*n^9 + 42*a*b^9*c*d^2*n^8 + 732*a*b^9*c*d^2*n^7 + 6*(1145*a*b^9*c*d^2 - 28*a^4*b^6*d^3)*n^6 + 9*(4191*a*b^9*c*d^2 - 280*a^4*b^6*d^3)*n^5 + 24*(5132*a*b^9*c*d^2 - 595*a^4*b^6*d^3)*n^4 + 4*(57887*a*b^9*c*d^2 - 9450*a^4*b^6*d^3)*n^3 + 48*(4715*a*b^9*c*d^2 - 959*a^4*b^6*d^3)*n^2 + 2880*(30*a*b^9*c*d^2 - 7*a^4*b^6*d^3)*n)*x^6 + 3*(46963*a*b^9*c^3 - 270*a^4*b^6*c^2*d)*n^5 - 18*(a^2*b^8*c*d^2*n^8 + 37*a^2*b^8*c*d^2*n^7 + 547*a^2*b^8*c*d^2*n^6 + (4135*a^2*b^8*c*d^2 - 168*a^5*b^5*d^3)*n^5 + 4*(4261*a^2*b^8*c*d^2 - 420*a^5*b^5*d^3)*n^4 + 4*(9487*a^2*b^8*c*d^2 - 1470*a^5*b^5*d^3)*n^3 + 48*(871*a^2*b^8*c*d^2 - 175*a^5*b^5*d^3)*n^2 + 576*(30*a^2*b^8*c*d^2 - 7*a^5*b^5*d^3)*n)*x^5 + 18*(42287*a*b^9*c^3 - 835*a^4*b^6*c^2*d)*n^4 + 3*(b^10*c^2*d*n^9 + 51*b^10*c^2*d*n^8 + 907200*b^10*c^2*d + 6*(186*b^10*c^2*d + 5*a^3*b^7*c*d^2)*n^7 + 6*(2281*b^10*c^2*d + 165*a^3*b^7*c*d^2)*n^6 + 3*(34343*b^10*c^2*d + 4150*a^3*b^7*c*d^2)*n^5 + 3*(163313*b^10*c^2*d + 24750*a^3*b^7*c*d^2 - 1680*a^6*b^4*d^3)*n^4 + 2*(728587*b^10*c^2*d + 107160*a^3*b^7*c*d^2 - 15120*a^6*b^4*d^3)*n^3 + 36*(71689*b^10*c^2*d + 7810*a^3*b^7*c*d^2 - 1540*a^6*b^4*d^3)*n^2 + 360*(6751*b^10*c^2*d + 360*a^3*b^7*c*d^2 - 84*a^6*b^4*d^3)*n)*x^4 + 2*(1327882*a*b^9*c^3 - 73575*a^4*b^6*c^2*d + 1080*a^7*b^3*c*d^2)*n^3 + 3*(a*b^9*c^2*d*n^9 + 48*a*b^9*c^2*d*n^8 + 972*a*b^9*c^2*d*n^7 + 30*(359*a*b^9*c^2*d - 4*a^4*b^6*c*d^2)*n^6 + 3*(23573*a*b^9*c^2*d - 1200*a^4*b^6*c*d^2)*n^5 + 6*(46297*a*b^9*c^2*d - 6500*a^4*b^6*c*d^2)*n^4 + 4*(155957*a*b^9*c^2*d - 45000*a^4*b^6*c*d^2 + 5040*a^7*b^3*d^3)*n^3 + 120*(5911*a*b^9*c^2*d - 2644*a^4*b^6*c*d^2 + 504*a^7*b^3*d^3)*n^2 + 2880*(105*a*b^9*c^2*d - 60*a^4*b^6*c*d^2 + 14*a^7*b^3*d^3)*n)*x^3 + 72*(79913*a*b^9*c^3 - 11131*a^4*b^6*c^2*d + 810*a^7*b^3*c*d^2)*n^2 - 9*(a^2*b^8*c^2*d*n^8 + 46*a^2*b^8*c^2*d*n^7 + 880*a^2*b^8*c^2*d*n^6 + 10*(901*a^2*b^8*c^2*d - 12*a^5*b^5*c*d^2)*n^5 + (52699*a^2*b^8*c^2*d - 3360*a^5*b^5*c*d^2)*n^4 + 8*(21548*a^2*b^8*c^2*d - 4035*a^5*b^5*c*d^2)*n^3 + 60*(4651*a^2*b^8*c^2*d - 1924*a^5*b^5*c*d^2 + 336*a^8*b^2*d^3)*n^2 + 1440*(105*a^2*b^8*c^2*d - 60*a^5*b^5*c*d^2 + 14*a^8*b^2*d^3)*n)*x^2 + 360*(19444*a*b^9*c^3 - 6393*a^4*b^6*c^2*d + 1452*a^7*b^3*c*d^2)*n + (b^10*c^3*n^9 + 54*b^10*c^3*n^8 + 3628800*b^10*c^3 + 6*(211*b^10*c^3 + 3*a^3*b^7*c^2*d)*n^7 + 18*(938*b^10*c^3 + 45*a^3*b^7*c^2*d)*n^6 + 3*(46963*b^10*c^3 + 5010*a^3*b^7*c^2*d)*n^5 + 18*(42287*b^10*c^3 + 8175*a^3*b^7*c^2*d - 120*a^6*b^4*c*d^2)*n^4 + 4*(663941*b^10*c^3 + 200358*a^3*b^7*c^2*d - 14580*a^6*b^4*c*d^2)*n^3 + 72*(79913*b^10*c^3 + 31965*a^3*b^7*c^2*d - 7260*a^6*b^4*c*d^2)*n^2 + 1440*(4861*b^10*c^3 + 1890*a^3*b^7*c^2*d - 1080*a^6*b^4*c*d^2 + 252*a^9*b*d^3)*n)*x)*(b*x + a)^n/(b^10*n^10 + 55*b^10*n^9 + 1320*b^10*n^8 + 18150*b^10*n^7 + 157773*b^10*n^6 + 902055*b^10*n^5 + 3416930*b^10*n^4 + 8409500*b^10*n^3 + 12753576*b^10*n^2 + 10628640*b^10*n + 3628800*b^10)","B",0
185,0,0,0,1.087104," ","integrate((b*x+a)^n*(d*x^3+c)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{9} + 3 \, c d^{2} x^{6} + 3 \, c^{2} d x^{3} + c^{3}\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d^3*x^9 + 3*c*d^2*x^6 + 3*c^2*d*x^3 + c^3)*(b*x + a)^n/x, x)","F",0
186,0,0,0,0.817467," ","integrate(x^5*(f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{5}}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n*x^5/(b*x^3 + a), x)","F",0
187,0,0,0,0.888251," ","integrate(x^4*(f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{4}}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n*x^4/(b*x^3 + a), x)","F",0
188,0,0,0,0.883184," ","integrate(x^3*(f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{3}}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n*x^3/(b*x^3 + a), x)","F",0
189,0,0,0,0.750403," ","integrate(x^2*(f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{2}}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n*x^2/(b*x^3 + a), x)","F",0
190,0,0,0,0.959959," ","integrate(x*(f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n*x/(b*x^3 + a), x)","F",0
191,0,0,0,0.807201," ","integrate((f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n/(b*x^3 + a), x)","F",0
192,0,0,0,0.784415," ","integrate((f*x+e)^n/x/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{b x^{4} + a x}, x\right)"," ",0,"integral((f*x + e)^n/(b*x^4 + a*x), x)","F",0
193,0,0,0,0.852619," ","integrate((f*x+e)^n/x^2/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{b x^{5} + a x^{2}}, x\right)"," ",0,"integral((f*x + e)^n/(b*x^5 + a*x^2), x)","F",0
194,0,0,0,0.708484," ","integrate(x^2*(d*x+c)^(1+n)/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{n + 1} x^{2}}{b x^{3} + a}, x\right)"," ",0,"integral((d*x + c)^(n + 1)*x^2/(b*x^3 + a), x)","F",0
195,0,0,0,0.897899," ","integrate(x^m*(f*x+e)^n/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{m}}{b x^{3} + a}, x\right)"," ",0,"integral((f*x + e)^n*x^m/(b*x^3 + a), x)","F",0
196,0,0,0,46.816011," ","integrate((d*x^3+c)^(1/2)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{b x + a}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(b*x + a), x)","F",0
197,0,0,0,0.856956," ","integrate((e^3*x^3+d^3)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + d^{3}\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((e^3*x^3 + d^3)^p/(e*x + d), x)","F",0
198,1,19,0,0.805099," ","integrate((-x^2-2*x+2)/(x^2+2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{x^{2} - 2 \, x}{2 \, \sqrt{x^{3} + 1}}\right)"," ",0,"-arctan(1/2*(x^2 - 2*x)/sqrt(x^3 + 1))","A",0
199,1,28,0,0.828145," ","integrate((-x^2+2*x+2)/(x^2+2)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{3} + 1} {\left(x^{2} + 2 \, x\right)}}{2 \, {\left(x^{3} - 1\right)}}\right)"," ",0,"-arctan(1/2*sqrt(-x^3 + 1)*(x^2 + 2*x)/(x^3 - 1))","A",0
200,1,25,0,0.721445," ","integrate((-x^2+2*x+2)/(x^2+2)/(x^3-1)^(1/2),x, algorithm=""fricas"")","\log\left(\frac{x^{2} + 2 \, x + 2 \, \sqrt{x^{3} - 1}}{x^{2} + 2}\right)"," ",0,"log((x^2 + 2*x + 2*sqrt(x^3 - 1))/(x^2 + 2))","A",0
201,1,28,0,0.820678," ","integrate((-x^2-2*x+2)/(x^2+2)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\log\left(-\frac{x^{2} - 2 \, x - 2 \, \sqrt{-x^{3} - 1}}{x^{2} + 2}\right)"," ",0,"log(-(x^2 - 2*x - 2*sqrt(-x^3 - 1))/(x^2 + 2))","A",0
202,1,181,0,0.956507," ","integrate((-x^2-2*x+2)/(d*x+x^2+d+2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d - 1} \log\left(-\frac{2 \, {\left(3 \, d + 4\right)} x^{3} - x^{4} - {\left(d^{2} + 2 \, d + 4\right)} x^{2} - d^{2} + 4 \, \sqrt{x^{3} + 1} {\left({\left(d + 2\right)} x - x^{2} + d\right)} \sqrt{-d - 1} - 2 \, {\left(d^{2} + 2 \, d\right)} x + 4 \, d + 4}{2 \, d x^{3} + x^{4} + {\left(d^{2} + 2 \, d + 4\right)} x^{2} + d^{2} + 2 \, {\left(d^{2} + 2 \, d\right)} x + 4 \, d + 4}\right)}{2 \, {\left(d + 1\right)}}, -\frac{\arctan\left(-\frac{\sqrt{x^{3} + 1} {\left({\left(d + 2\right)} x - x^{2} + d\right)} \sqrt{d + 1}}{2 \, {\left({\left(d + 1\right)} x^{3} + d + 1\right)}}\right)}{\sqrt{d + 1}}\right]"," ",0,"[-1/2*sqrt(-d - 1)*log(-(2*(3*d + 4)*x^3 - x^4 - (d^2 + 2*d + 4)*x^2 - d^2 + 4*sqrt(x^3 + 1)*((d + 2)*x - x^2 + d)*sqrt(-d - 1) - 2*(d^2 + 2*d)*x + 4*d + 4)/(2*d*x^3 + x^4 + (d^2 + 2*d + 4)*x^2 + d^2 + 2*(d^2 + 2*d)*x + 4*d + 4))/(d + 1), -arctan(-1/2*sqrt(x^3 + 1)*((d + 2)*x - x^2 + d)*sqrt(d + 1)/((d + 1)*x^3 + d + 1))/sqrt(d + 1)]","A",0
203,1,191,0,0.977137," ","integrate((-x^2+2*x+2)/(d*x+x^2-d+2)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{2 \, {\left(3 \, d - 4\right)} x^{3} - x^{4} - {\left(d^{2} - 2 \, d + 4\right)} x^{2} - 4 \, \sqrt{-x^{3} + 1} {\left({\left(d - 2\right)} x - x^{2} - d\right)} \sqrt{d - 1} - d^{2} + 2 \, {\left(d^{2} - 2 \, d\right)} x - 4 \, d + 4}{2 \, d x^{3} + x^{4} + {\left(d^{2} - 2 \, d + 4\right)} x^{2} + d^{2} - 2 \, {\left(d^{2} - 2 \, d\right)} x - 4 \, d + 4}\right)}{2 \, \sqrt{d - 1}}, -\frac{\sqrt{-d + 1} \arctan\left(-\frac{\sqrt{-x^{3} + 1} {\left({\left(d - 2\right)} x - x^{2} - d\right)} \sqrt{-d + 1}}{2 \, {\left({\left(d - 1\right)} x^{3} - d + 1\right)}}\right)}{d - 1}\right]"," ",0,"[1/2*log(-(2*(3*d - 4)*x^3 - x^4 - (d^2 - 2*d + 4)*x^2 - 4*sqrt(-x^3 + 1)*((d - 2)*x - x^2 - d)*sqrt(d - 1) - d^2 + 2*(d^2 - 2*d)*x - 4*d + 4)/(2*d*x^3 + x^4 + (d^2 - 2*d + 4)*x^2 + d^2 - 2*(d^2 - 2*d)*x - 4*d + 4))/sqrt(d - 1), -sqrt(-d + 1)*arctan(-1/2*sqrt(-x^3 + 1)*((d - 2)*x - x^2 - d)*sqrt(-d + 1)/((d - 1)*x^3 - d + 1))/(d - 1)]","A",0
204,1,187,0,0.940726," ","integrate((-x^2+2*x+2)/(d*x+x^2-d+2)/(x^3-1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d + 1} \log\left(-\frac{2 \, {\left(3 \, d - 4\right)} x^{3} - x^{4} - {\left(d^{2} - 2 \, d + 4\right)} x^{2} - d^{2} + 4 \, \sqrt{x^{3} - 1} {\left({\left(d - 2\right)} x - x^{2} - d\right)} \sqrt{-d + 1} + 2 \, {\left(d^{2} - 2 \, d\right)} x - 4 \, d + 4}{2 \, d x^{3} + x^{4} + {\left(d^{2} - 2 \, d + 4\right)} x^{2} + d^{2} - 2 \, {\left(d^{2} - 2 \, d\right)} x - 4 \, d + 4}\right)}{2 \, {\left(d - 1\right)}}, -\frac{\arctan\left(-\frac{\sqrt{x^{3} - 1} {\left({\left(d - 2\right)} x - x^{2} - d\right)} \sqrt{d - 1}}{2 \, {\left({\left(d - 1\right)} x^{3} - d + 1\right)}}\right)}{\sqrt{d - 1}}\right]"," ",0,"[-1/2*sqrt(-d + 1)*log(-(2*(3*d - 4)*x^3 - x^4 - (d^2 - 2*d + 4)*x^2 - d^2 + 4*sqrt(x^3 - 1)*((d - 2)*x - x^2 - d)*sqrt(-d + 1) + 2*(d^2 - 2*d)*x - 4*d + 4)/(2*d*x^3 + x^4 + (d^2 - 2*d + 4)*x^2 + d^2 - 2*(d^2 - 2*d)*x - 4*d + 4))/(d - 1), -arctan(-1/2*sqrt(x^3 - 1)*((d - 2)*x - x^2 - d)*sqrt(d - 1)/((d - 1)*x^3 - d + 1))/sqrt(d - 1)]","A",0
205,1,185,0,1.055892," ","integrate((-x^2-2*x+2)/(d*x+x^2+d+2)/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{2 \, {\left(3 \, d + 4\right)} x^{3} - x^{4} - {\left(d^{2} + 2 \, d + 4\right)} x^{2} - 4 \, \sqrt{-x^{3} - 1} {\left({\left(d + 2\right)} x - x^{2} + d\right)} \sqrt{d + 1} - d^{2} - 2 \, {\left(d^{2} + 2 \, d\right)} x + 4 \, d + 4}{2 \, d x^{3} + x^{4} + {\left(d^{2} + 2 \, d + 4\right)} x^{2} + d^{2} + 2 \, {\left(d^{2} + 2 \, d\right)} x + 4 \, d + 4}\right)}{2 \, \sqrt{d + 1}}, -\frac{\sqrt{-d - 1} \arctan\left(-\frac{\sqrt{-x^{3} - 1} {\left({\left(d + 2\right)} x - x^{2} + d\right)} \sqrt{-d - 1}}{2 \, {\left({\left(d + 1\right)} x^{3} + d + 1\right)}}\right)}{d + 1}\right]"," ",0,"[1/2*log(-(2*(3*d + 4)*x^3 - x^4 - (d^2 + 2*d + 4)*x^2 - 4*sqrt(-x^3 - 1)*((d + 2)*x - x^2 + d)*sqrt(d + 1) - d^2 - 2*(d^2 + 2*d)*x + 4*d + 4)/(2*d*x^3 + x^4 + (d^2 + 2*d + 4)*x^2 + d^2 + 2*(d^2 + 2*d)*x + 4*d + 4))/sqrt(d + 1), -sqrt(-d - 1)*arctan(-1/2*sqrt(-x^3 - 1)*((d + 2)*x - x^2 + d)*sqrt(-d - 1)/((d + 1)*x^3 + d + 1))/(d + 1)]","B",0
206,0,0,0,0.971537," ","integrate((e*x+d)^3*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{4} + a}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^4 + a), x)","F",0
207,0,0,0,1.026537," ","integrate((e*x+d)^2*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + a} {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
208,0,0,0,0.683445," ","integrate((e*x+d)*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + a} {\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*(e*x + d), x)","F",0
209,0,0,0,0.818915," ","integrate((c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + a}, x\right)"," ",0,"integral(sqrt(c*x^4 + a), x)","F",0
210,-1,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,0,0,0,1.223959," ","integrate((e*x+d)^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)/sqrt(c*x^4 + a), x)","F",0
213,0,0,0,1.431780," ","integrate((e*x+d)^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2} + 2 \, d e x + d^{2}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)/sqrt(c*x^4 + a), x)","F",0
214,0,0,0,1.682835," ","integrate((e*x+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x + d}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e*x + d)/sqrt(c*x^4 + a), x)","F",0
215,0,0,0,0.867222," ","integrate(1/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral(1/sqrt(c*x^4 + a), x)","F",0
216,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,0,0,0,1.096768," ","integrate((e*x+d)^3/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{4} + a}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^4 + a)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
220,0,0,0,1.083305," ","integrate((e*x+d)^2/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a} {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*(e^2*x^2 + 2*d*e*x + d^2)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
221,0,0,0,0.689445," ","integrate((e*x+d)/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a} {\left(e x + d\right)}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*(e*x + d)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
222,0,0,0,0.585872," ","integrate(1/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
223,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,0,0,0,0.886625," ","integrate(x^3*(d*x+c)^n/(b*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{n} x^{3}}{b x^{4} + a}, x\right)"," ",0,"integral((d*x + c)^n*x^3/(b*x^4 + a), x)","F",0
225,0,0,0,0.582500," ","integrate(x^3*(d*x+c)^(1+n)/(b*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{n + 1} x^{3}}{b x^{4} + a}, x\right)"," ",0,"integral((d*x + c)^(n + 1)*x^3/(b*x^4 + a), x)","F",0
226,-1,0,0,0.000000," ","integrate(1/(e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,1,233,0,0.707803," ","integrate(x^m*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} c m^{3} + 9 \, b^{3} c m^{2} + 23 \, b^{3} c m + 15 \, b^{3} c\right)} x^{7} + 3 \, {\left(a b^{2} c m^{3} + 11 \, a b^{2} c m^{2} + 31 \, a b^{2} c m + 21 \, a b^{2} c\right)} x^{5} + 3 \, {\left(a^{2} b c m^{3} + 13 \, a^{2} b c m^{2} + 47 \, a^{2} b c m + 35 \, a^{2} b c\right)} x^{3} + {\left(a^{3} c m^{3} + 15 \, a^{3} c m^{2} + 71 \, a^{3} c m + 105 \, a^{3} c\right)} x\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c} x^{m}}{a m^{4} + 16 \, a m^{3} + 86 \, a m^{2} + {\left(b m^{4} + 16 \, b m^{3} + 86 \, b m^{2} + 176 \, b m + 105 \, b\right)} x^{2} + 176 \, a m + 105 \, a}"," ",0,"((b^3*c*m^3 + 9*b^3*c*m^2 + 23*b^3*c*m + 15*b^3*c)*x^7 + 3*(a*b^2*c*m^3 + 11*a*b^2*c*m^2 + 31*a*b^2*c*m + 21*a*b^2*c)*x^5 + 3*(a^2*b*c*m^3 + 13*a^2*b*c*m^2 + 47*a^2*b*c*m + 35*a^2*b*c)*x^3 + (a^3*c*m^3 + 15*a^3*c*m^2 + 71*a^3*c*m + 105*a^3*c)*x)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)*x^m/(a*m^4 + 16*a*m^3 + 86*a*m^2 + (b*m^4 + 16*b*m^3 + 86*b*m^2 + 176*b*m + 105*b)*x^2 + 176*a*m + 105*a)","A",0
228,1,74,0,0.673424," ","integrate(x^5*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(10 \, b^{3} c x^{12} + 36 \, a b^{2} c x^{10} + 45 \, a^{2} b c x^{8} + 20 \, a^{3} c x^{6}\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{120 \, {\left(b x^{2} + a\right)}}"," ",0,"1/120*(10*b^3*c*x^12 + 36*a*b^2*c*x^10 + 45*a^2*b*c*x^8 + 20*a^3*c*x^6)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","A",0
229,1,74,0,0.865405," ","integrate(x^4*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(105 \, b^{3} c x^{11} + 385 \, a b^{2} c x^{9} + 495 \, a^{2} b c x^{7} + 231 \, a^{3} c x^{5}\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{1155 \, {\left(b x^{2} + a\right)}}"," ",0,"1/1155*(105*b^3*c*x^11 + 385*a*b^2*c*x^9 + 495*a^2*b*c*x^7 + 231*a^3*c*x^5)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","A",0
230,1,74,0,0.919690," ","integrate(x^3*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(4 \, b^{3} c x^{10} + 15 \, a b^{2} c x^{8} + 20 \, a^{2} b c x^{6} + 10 \, a^{3} c x^{4}\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{40 \, {\left(b x^{2} + a\right)}}"," ",0,"1/40*(4*b^3*c*x^10 + 15*a*b^2*c*x^8 + 20*a^2*b*c*x^6 + 10*a^3*c*x^4)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","A",0
231,1,74,0,0.954767," ","integrate(x^2*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(35 \, b^{3} c x^{9} + 135 \, a b^{2} c x^{7} + 189 \, a^{2} b c x^{5} + 105 \, a^{3} c x^{3}\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{315 \, {\left(b x^{2} + a\right)}}"," ",0,"1/315*(35*b^3*c*x^9 + 135*a*b^2*c*x^7 + 189*a^2*b*c*x^5 + 105*a^3*c*x^3)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","A",0
232,1,73,0,0.804353," ","integrate(x*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{3} c x^{8} + 4 \, a b^{2} c x^{6} + 6 \, a^{2} b c x^{4} + 4 \, a^{3} c x^{2}\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{8 \, {\left(b x^{2} + a\right)}}"," ",0,"1/8*(b^3*c*x^8 + 4*a*b^2*c*x^6 + 6*a^2*b*c*x^4 + 4*a^3*c*x^2)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","B",0
233,1,72,0,0.666469," ","integrate((c*(b*x^2+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, b^{3} c x^{7} + 21 \, a b^{2} c x^{5} + 35 \, a^{2} b c x^{3} + 35 \, a^{3} c x\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{35 \, {\left(b x^{2} + a\right)}}"," ",0,"1/35*(5*b^3*c*x^7 + 21*a*b^2*c*x^5 + 35*a^2*b*c*x^3 + 35*a^3*c*x)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","A",0
234,1,73,0,0.722550," ","integrate((c*(b*x^2+a)^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} c x^{6} + 9 \, a b^{2} c x^{4} + 18 \, a^{2} b c x^{2} + 12 \, a^{3} c \log\left(x\right)\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{12 \, {\left(b x^{2} + a\right)}}"," ",0,"1/12*(2*b^3*c*x^6 + 9*a*b^2*c*x^4 + 18*a^2*b*c*x^2 + 12*a^3*c*log(x))*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^2 + a)","A",0
235,1,72,0,0.483857," ","integrate((c*(b*x^2+a)^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{{\left(b^{3} c x^{6} + 5 \, a b^{2} c x^{4} + 15 \, a^{2} b c x^{2} - 5 \, a^{3} c\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{5 \, {\left(b x^{3} + a x\right)}}"," ",0,"1/5*(b^3*c*x^6 + 5*a*b^2*c*x^4 + 15*a^2*b*c*x^2 - 5*a^3*c)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^3 + a*x)","A",0
236,1,76,0,0.685334," ","integrate((c*(b*x^2+a)^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{{\left(b^{3} c x^{6} + 6 \, a b^{2} c x^{4} + 12 \, a^{2} b c x^{2} \log\left(x\right) - 2 \, a^{3} c\right)} \sqrt{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}}{4 \, {\left(b x^{4} + a x^{2}\right)}}"," ",0,"1/4*(b^3*c*x^6 + 6*a*b^2*c*x^4 + 12*a^2*b*c*x^2*log(x) - 2*a^3*c)*sqrt(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)/(b*x^4 + a*x^2)","A",0
237,1,433,0,0.835995," ","integrate(x^2*(c*(b*x^2+a)^3)^(3/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{6} b c x^{2} + a^{7} c\right)} \sqrt{\frac{c}{b}} \log\left(-\frac{2 \, b^{2} c x^{4} + 3 \, a b c x^{2} + a^{2} c - 2 \, \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} b x \sqrt{\frac{c}{b}}}{b x^{2} + a}\right) + 2 \, {\left(1280 \, b^{5} c x^{11} + 6272 \, a b^{4} c x^{9} + 12144 \, a^{2} b^{3} c x^{7} + 11432 \, a^{3} b^{2} c x^{5} + 4910 \, a^{4} b c x^{3} + 315 \, a^{5} c x\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{30720 \, {\left(b^{2} x^{2} + a b\right)}}, \frac{315 \, {\left(a^{6} b c x^{2} + a^{7} c\right)} \sqrt{-\frac{c}{b}} \arctan\left(\frac{\sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} b x \sqrt{-\frac{c}{b}}}{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}\right) + {\left(1280 \, b^{5} c x^{11} + 6272 \, a b^{4} c x^{9} + 12144 \, a^{2} b^{3} c x^{7} + 11432 \, a^{3} b^{2} c x^{5} + 4910 \, a^{4} b c x^{3} + 315 \, a^{5} c x\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{15360 \, {\left(b^{2} x^{2} + a b\right)}}\right]"," ",0,"[1/30720*(315*(a^6*b*c*x^2 + a^7*c)*sqrt(c/b)*log(-(2*b^2*c*x^4 + 3*a*b*c*x^2 + a^2*c - 2*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*b*x*sqrt(c/b))/(b*x^2 + a)) + 2*(1280*b^5*c*x^11 + 6272*a*b^4*c*x^9 + 12144*a^2*b^3*c*x^7 + 11432*a^3*b^2*c*x^5 + 4910*a^4*b*c*x^3 + 315*a^5*c*x)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b^2*x^2 + a*b), 1/15360*(315*(a^6*b*c*x^2 + a^7*c)*sqrt(-c/b)*arctan(sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*b*x*sqrt(-c/b)/(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)) + (1280*b^5*c*x^11 + 6272*a*b^4*c*x^9 + 12144*a^2*b^3*c*x^7 + 11432*a^3*b^2*c*x^5 + 4910*a^4*b*c*x^3 + 315*a^5*c*x)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b^2*x^2 + a*b)]","A",0
238,1,87,0,0.637506," ","integrate(x*(c*(b*x^2+a)^3)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{4} c x^{8} + 4 \, a b^{3} c x^{6} + 6 \, a^{2} b^{2} c x^{4} + 4 \, a^{3} b c x^{2} + a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{11 \, b}"," ",0,"1/11*(b^4*c*x^8 + 4*a*b^3*c*x^6 + 6*a^2*b^2*c*x^4 + 4*a^3*b*c*x^2 + a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)/b","B",0
239,1,402,0,0.617686," ","integrate((c*(b*x^2+a)^3)^(3/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{5} b c x^{2} + a^{6} c\right)} \sqrt{\frac{c}{b}} \log\left(-\frac{2 \, b^{2} c x^{4} + 3 \, a b c x^{2} + a^{2} c + 2 \, \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} b x \sqrt{\frac{c}{b}}}{b x^{2} + a}\right) + 2 \, {\left(128 \, b^{4} c x^{9} + 656 \, a b^{3} c x^{7} + 1368 \, a^{2} b^{2} c x^{5} + 1490 \, a^{3} b c x^{3} + 965 \, a^{4} c x\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{2560 \, {\left(b x^{2} + a\right)}}, -\frac{315 \, {\left(a^{5} b c x^{2} + a^{6} c\right)} \sqrt{-\frac{c}{b}} \arctan\left(\frac{\sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} b x \sqrt{-\frac{c}{b}}}{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}\right) - {\left(128 \, b^{4} c x^{9} + 656 \, a b^{3} c x^{7} + 1368 \, a^{2} b^{2} c x^{5} + 1490 \, a^{3} b c x^{3} + 965 \, a^{4} c x\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{1280 \, {\left(b x^{2} + a\right)}}\right]"," ",0,"[1/2560*(315*(a^5*b*c*x^2 + a^6*c)*sqrt(c/b)*log(-(2*b^2*c*x^4 + 3*a*b*c*x^2 + a^2*c + 2*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*b*x*sqrt(c/b))/(b*x^2 + a)) + 2*(128*b^4*c*x^9 + 656*a*b^3*c*x^7 + 1368*a^2*b^2*c*x^5 + 1490*a^3*b*c*x^3 + 965*a^4*c*x)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^2 + a), -1/1280*(315*(a^5*b*c*x^2 + a^6*c)*sqrt(-c/b)*arctan(sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*b*x*sqrt(-c/b)/(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)) - (128*b^4*c*x^9 + 656*a*b^3*c*x^7 + 1368*a^2*b^2*c*x^5 + 1490*a^3*b*c*x^3 + 965*a^4*c*x)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^2 + a)]","A",0
240,1,391,0,0.710742," ","integrate((c*(b*x^2+a)^3)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{4} b c x^{2} + a^{5} c\right)} \sqrt{a c} \log\left(-\frac{b^{2} c x^{4} + 3 \, a b c x^{2} + 2 \, a^{2} c - 2 \, \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} \sqrt{a c}}{b x^{4} + a x^{2}}\right) + 2 \, {\left(35 \, b^{4} c x^{8} + 185 \, a b^{3} c x^{6} + 408 \, a^{2} b^{2} c x^{4} + 506 \, a^{3} b c x^{2} + 563 \, a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{630 \, {\left(b x^{2} + a\right)}}, \frac{315 \, {\left(a^{4} b c x^{2} + a^{5} c\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} \sqrt{-a c}}{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}\right) + {\left(35 \, b^{4} c x^{8} + 185 \, a b^{3} c x^{6} + 408 \, a^{2} b^{2} c x^{4} + 506 \, a^{3} b c x^{2} + 563 \, a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{315 \, {\left(b x^{2} + a\right)}}\right]"," ",0,"[1/630*(315*(a^4*b*c*x^2 + a^5*c)*sqrt(a*c)*log(-(b^2*c*x^4 + 3*a*b*c*x^2 + 2*a^2*c - 2*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*sqrt(a*c))/(b*x^4 + a*x^2)) + 2*(35*b^4*c*x^8 + 185*a*b^3*c*x^6 + 408*a^2*b^2*c*x^4 + 506*a^3*b*c*x^2 + 563*a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^2 + a), 1/315*(315*(a^4*b*c*x^2 + a^5*c)*sqrt(-a*c)*arctan(sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*sqrt(-a*c)/(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)) + (35*b^4*c*x^8 + 185*a*b^3*c*x^6 + 408*a^2*b^2*c*x^4 + 506*a^3*b*c*x^2 + 563*a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^2 + a)]","A",0
241,1,396,0,0.730957," ","integrate((c*(b*x^2+a)^3)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{4} b c x^{3} + a^{5} c x\right)} \sqrt{b c} \log\left(-\frac{2 \, b^{2} c x^{4} + 3 \, a b c x^{2} + a^{2} c + 2 \, \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} \sqrt{b c} x}{b x^{2} + a}\right) + 2 \, {\left(16 \, b^{4} c x^{8} + 88 \, a b^{3} c x^{6} + 210 \, a^{2} b^{2} c x^{4} + 325 \, a^{3} b c x^{2} - 128 \, a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{256 \, {\left(b x^{3} + a x\right)}}, -\frac{315 \, {\left(a^{4} b c x^{3} + a^{5} c x\right)} \sqrt{-b c} \arctan\left(\frac{\sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} \sqrt{-b c} x}{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}\right) - {\left(16 \, b^{4} c x^{8} + 88 \, a b^{3} c x^{6} + 210 \, a^{2} b^{2} c x^{4} + 325 \, a^{3} b c x^{2} - 128 \, a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{128 \, {\left(b x^{3} + a x\right)}}\right]"," ",0,"[1/256*(315*(a^4*b*c*x^3 + a^5*c*x)*sqrt(b*c)*log(-(2*b^2*c*x^4 + 3*a*b*c*x^2 + a^2*c + 2*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*sqrt(b*c)*x)/(b*x^2 + a)) + 2*(16*b^4*c*x^8 + 88*a*b^3*c*x^6 + 210*a^2*b^2*c*x^4 + 325*a^3*b*c*x^2 - 128*a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^3 + a*x), -1/128*(315*(a^4*b*c*x^3 + a^5*c*x)*sqrt(-b*c)*arctan(sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*sqrt(-b*c)*x/(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)) - (16*b^4*c*x^8 + 88*a*b^3*c*x^6 + 210*a^2*b^2*c*x^4 + 325*a^3*b*c*x^2 - 128*a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^3 + a*x)]","A",0
242,1,411,0,0.812005," ","integrate((c*(b*x^2+a)^3)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{3} b^{2} c x^{4} + a^{4} b c x^{2}\right)} \sqrt{a c} \log\left(-\frac{b^{2} c x^{4} + 3 \, a b c x^{2} + 2 \, a^{2} c - 2 \, \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} \sqrt{a c}}{b x^{4} + a x^{2}}\right) + 2 \, {\left(10 \, b^{4} c x^{8} + 58 \, a b^{3} c x^{6} + 156 \, a^{2} b^{2} c x^{4} + 388 \, a^{3} b c x^{2} - 35 \, a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{140 \, {\left(b x^{4} + a x^{2}\right)}}, \frac{315 \, {\left(a^{3} b^{2} c x^{4} + a^{4} b c x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c} \sqrt{-a c}}{b^{2} c x^{4} + 2 \, a b c x^{2} + a^{2} c}\right) + {\left(10 \, b^{4} c x^{8} + 58 \, a b^{3} c x^{6} + 156 \, a^{2} b^{2} c x^{4} + 388 \, a^{3} b c x^{2} - 35 \, a^{4} c\right)} \sqrt{b^{3} c x^{6} + 3 \, a b^{2} c x^{4} + 3 \, a^{2} b c x^{2} + a^{3} c}}{70 \, {\left(b x^{4} + a x^{2}\right)}}\right]"," ",0,"[1/140*(315*(a^3*b^2*c*x^4 + a^4*b*c*x^2)*sqrt(a*c)*log(-(b^2*c*x^4 + 3*a*b*c*x^2 + 2*a^2*c - 2*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*sqrt(a*c))/(b*x^4 + a*x^2)) + 2*(10*b^4*c*x^8 + 58*a*b^3*c*x^6 + 156*a^2*b^2*c*x^4 + 388*a^3*b*c*x^2 - 35*a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^4 + a*x^2), 1/70*(315*(a^3*b^2*c*x^4 + a^4*b*c*x^2)*sqrt(-a*c)*arctan(sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c)*sqrt(-a*c)/(b^2*c*x^4 + 2*a*b*c*x^2 + a^2*c)) + (10*b^4*c*x^8 + 58*a*b^3*c*x^6 + 156*a^2*b^2*c*x^4 + 388*a^3*b*c*x^2 - 35*a^4*c)*sqrt(b^3*c*x^6 + 3*a*b^2*c*x^4 + 3*a^2*b*c*x^2 + a^3*c))/(b*x^4 + a*x^2)]","A",0
243,1,141,0,0.640040," ","integrate(x^2*(c/(b*x^2+a))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, c x \sqrt{\frac{c}{b x^{2} + a}} - c \sqrt{\frac{c}{b}} \log\left(-2 \, b c x^{2} - a c - 2 \, {\left(b^{2} x^{3} + a b x\right)} \sqrt{\frac{c}{b x^{2} + a}} \sqrt{\frac{c}{b}}\right)}{2 \, b}, -\frac{c x \sqrt{\frac{c}{b x^{2} + a}} + c \sqrt{-\frac{c}{b}} \arctan\left(\frac{b x \sqrt{\frac{c}{b x^{2} + a}} \sqrt{-\frac{c}{b}}}{c}\right)}{b}\right]"," ",0,"[-1/2*(2*c*x*sqrt(c/(b*x^2 + a)) - c*sqrt(c/b)*log(-2*b*c*x^2 - a*c - 2*(b^2*x^3 + a*b*x)*sqrt(c/(b*x^2 + a))*sqrt(c/b)))/b, -(c*x*sqrt(c/(b*x^2 + a)) + c*sqrt(-c/b)*arctan(b*x*sqrt(c/(b*x^2 + a))*sqrt(-c/b)/c))/b]","A",0
244,1,19,0,0.897133," ","integrate(x*(c/(b*x^2+a))^(3/2),x, algorithm=""fricas"")","-\frac{c \sqrt{\frac{c}{b x^{2} + a}}}{b}"," ",0,"-c*sqrt(c/(b*x^2 + a))/b","A",0
245,1,19,0,0.497366," ","integrate((c/(b*x^2+a))^(3/2),x, algorithm=""fricas"")","\frac{c x \sqrt{\frac{c}{b x^{2} + a}}}{a}"," ",0,"c*x*sqrt(c/(b*x^2 + a))/a","A",0
246,1,138,0,0.684361," ","integrate((c/(b*x^2+a))^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{c \sqrt{\frac{c}{a}} \log\left(-\frac{b c x^{2} + 2 \, a c - 2 \, {\left(a b x^{2} + a^{2}\right)} \sqrt{\frac{c}{b x^{2} + a}} \sqrt{\frac{c}{a}}}{x^{2}}\right) + 2 \, c \sqrt{\frac{c}{b x^{2} + a}}}{2 \, a}, \frac{c \sqrt{-\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{b x^{2} + a}} \sqrt{-\frac{c}{a}}}{c}\right) + c \sqrt{\frac{c}{b x^{2} + a}}}{a}\right]"," ",0,"[1/2*(c*sqrt(c/a)*log(-(b*c*x^2 + 2*a*c - 2*(a*b*x^2 + a^2)*sqrt(c/(b*x^2 + a))*sqrt(c/a))/x^2) + 2*c*sqrt(c/(b*x^2 + a)))/a, (c*sqrt(-c/a)*arctan(a*sqrt(c/(b*x^2 + a))*sqrt(-c/a)/c) + c*sqrt(c/(b*x^2 + a)))/a]","A",0
247,1,32,0,0.427458," ","integrate((c/(b*x^2+a))^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, b c x^{2} + a c\right)} \sqrt{\frac{c}{b x^{2} + a}}}{a^{2} x}"," ",0,"-(2*b*c*x^2 + a*c)*sqrt(c/(b*x^2 + a))/(a^2*x)","A",0
248,1,175,0,0.698332," ","integrate((c/(b*x^2+a))^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, b c x^{2} \sqrt{\frac{c}{a}} \log\left(-\frac{b c x^{2} + 2 \, a c + 2 \, {\left(a b x^{2} + a^{2}\right)} \sqrt{\frac{c}{b x^{2} + a}} \sqrt{\frac{c}{a}}}{x^{2}}\right) - 2 \, {\left(3 \, b c x^{2} + a c\right)} \sqrt{\frac{c}{b x^{2} + a}}}{4 \, a^{2} x^{2}}, -\frac{3 \, b c x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{b x^{2} + a}} \sqrt{-\frac{c}{a}}}{c}\right) + {\left(3 \, b c x^{2} + a c\right)} \sqrt{\frac{c}{b x^{2} + a}}}{2 \, a^{2} x^{2}}\right]"," ",0,"[1/4*(3*b*c*x^2*sqrt(c/a)*log(-(b*c*x^2 + 2*a*c + 2*(a*b*x^2 + a^2)*sqrt(c/(b*x^2 + a))*sqrt(c/a))/x^2) - 2*(3*b*c*x^2 + a*c)*sqrt(c/(b*x^2 + a)))/(a^2*x^2), -1/2*(3*b*c*x^2*sqrt(-c/a)*arctan(a*sqrt(c/(b*x^2 + a))*sqrt(-c/a)/c) + (3*b*c*x^2 + a*c)*sqrt(c/(b*x^2 + a)))/(a^2*x^2)]","A",0
249,1,75,0,0.921452," ","integrate(x^7*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(385 \, b^{4} c x^{8} + 77 \, a b^{3} c x^{6} - 84 \, a^{2} b^{2} c x^{4} + 96 \, a^{3} b c x^{2} - 128 \, a^{4} c\right)} \sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c}}{7315 \, b^{4}}"," ",0,"2/7315*(385*b^4*c*x^8 + 77*a*b^3*c*x^6 - 84*a^2*b^2*c*x^4 + 96*a^3*b*c*x^2 - 128*a^4*c)*sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)/b^4","A",0
250,1,63,0,0.717188," ","integrate(x^5*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, b^{3} c x^{6} + 21 \, a b^{2} c x^{4} - 24 \, a^{2} b c x^{2} + 32 \, a^{3} c\right)} \sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c}}{1155 \, b^{3}}"," ",0,"2/1155*(77*b^3*c*x^6 + 21*a*b^2*c*x^4 - 24*a^2*b*c*x^2 + 32*a^3*c)*sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)/b^3","A",0
251,1,51,0,0.650542," ","integrate(x^3*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{2} c x^{4} + 3 \, a b c x^{2} - 4 \, a^{2} c\right)} \sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c}}{77 \, b^{2}}"," ",0,"2/77*(7*b^2*c*x^4 + 3*a*b*c*x^2 - 4*a^2*c)*sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)/b^2","A",0
252,1,37,0,1.077925," ","integrate(x*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b c x^{2} + a c\right)} \sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c}}{7 \, b}"," ",0,"2/7*(b*c*x^2 + a*c)*sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)/b","A",0
253,-1,0,0,0.000000," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,0,0,0,0.897328," ","integrate(x^2*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c} c x^{2}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)*c*x^2, x)","F",0
256,0,0,0,1.200061," ","integrate((c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c} c, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)*c, x)","F",0
257,0,0,0,0.884137," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{\sqrt{b x^{2} + a} c} c}{x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(sqrt(b*x^2 + a)*c)*c/x^2, x)","F",0
258,-2,0,0,0.000000," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x^4,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Shouldn't happen","F(-2)",0
259,1,80,0,0.733633," ","integrate(((b-x)*(-a+x))^(1/2),x, algorithm=""fricas"")","-\frac{1}{8} \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \arctan\left(-\frac{\sqrt{-a b + {\left(a + b\right)} x - x^{2}} {\left(a + b - 2 \, x\right)}}{2 \, {\left(a b - {\left(a + b\right)} x + x^{2}\right)}}\right) - \frac{1}{4} \, \sqrt{-a b + {\left(a + b\right)} x - x^{2}} {\left(a + b - 2 \, x\right)}"," ",0,"-1/8*(a^2 - 2*a*b + b^2)*arctan(-1/2*sqrt(-a*b + (a + b)*x - x^2)*(a + b - 2*x)/(a*b - (a + b)*x + x^2)) - 1/4*sqrt(-a*b + (a + b)*x - x^2)*(a + b - 2*x)","A",0
260,0,0,0,0.879424," ","integrate(((-x^2+1)*(x^2+3))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} - 2 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(-x^4 - 2*x^2 + 3), x)","F",0
261,1,43,0,0.891403," ","integrate(1/((b-x)*(-a+x))^(1/2),x, algorithm=""fricas"")","-\arctan\left(-\frac{\sqrt{-a b + {\left(a + b\right)} x - x^{2}} {\left(a + b - 2 \, x\right)}}{2 \, {\left(a b - {\left(a + b\right)} x + x^{2}\right)}}\right)"," ",0,"-arctan(-1/2*sqrt(-a*b + (a + b)*x - x^2)*(a + b - 2*x)/(a*b - (a + b)*x + x^2))","A",0
262,0,0,0,0.925347," ","integrate(1/((-x^2+1)*(x^2+3))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} - 2 \, x^{2} + 3}}{x^{4} + 2 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-x^4 - 2*x^2 + 3)/(x^4 + 2*x^2 - 3), x)","F",0
263,1,541,0,0.955838," ","integrate(x^5*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{\frac{e}{b d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d + a b c d^{2} + {\left(3 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{b d}}\right) - 4 \, {\left(8 \, b^{2} d^{3} x^{6} + 15 \, b^{2} c^{3} - 4 \, a b c^{2} d - 3 \, a^{2} c d^{2} - 2 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{4} + {\left(5 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{192 \, b^{2} d^{3}}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-\frac{e}{b d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{b d}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) + 2 \, {\left(8 \, b^{2} d^{3} x^{6} + 15 \, b^{2} c^{3} - 4 \, a b c^{2} d - 3 \, a^{2} c d^{2} - 2 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{4} + {\left(5 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{96 \, b^{2} d^{3}}\right]"," ",0,"[-1/192*(3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*sqrt(e/(b*d))*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b^2*d^3*x^4 + b^2*c^2*d + a*b*c*d^2 + (3*b^2*c*d^2 + a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(b*d))) - 4*(8*b^2*d^3*x^6 + 15*b^2*c^3 - 4*a*b*c^2*d - 3*a^2*c*d^2 - 2*(b^2*c*d^2 - a*b*d^3)*x^4 + (5*b^2*c^2*d - 2*a*b*c*d^2 - 3*a^2*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^2*d^3), 1/96*(3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*sqrt(-e/(b*d))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(b*d))/(b*e*x^2 + a*e)) + 2*(8*b^2*d^3*x^6 + 15*b^2*c^3 - 4*a*b*c^2*d - 3*a^2*c*d^2 - 2*(b^2*c*d^2 - a*b*d^3)*x^4 + (5*b^2*c^2*d - 2*a*b*c*d^2 - 3*a^2*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^2*d^3)]","A",0
264,1,407,0,0.898072," ","integrate(x^3*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{\frac{e}{b d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e - 4 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d + a b c d^{2} + {\left(3 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{b d}}\right) - 4 \, {\left(2 \, b d^{2} x^{4} - 3 \, b c^{2} + a c d - {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, b d^{2}}, -\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{-\frac{e}{b d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{b d}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) - 2 \, {\left(2 \, b d^{2} x^{4} - 3 \, b c^{2} + a c d - {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, b d^{2}}\right]"," ",0,"[-1/32*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(e/(b*d))*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e - 4*(2*b^2*d^3*x^4 + b^2*c^2*d + a*b*c*d^2 + (3*b^2*c*d^2 + a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(b*d))) - 4*(2*b*d^2*x^4 - 3*b*c^2 + a*c*d - (b*c*d - a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b*d^2), -1/16*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(-e/(b*d))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(b*d))/(b*e*x^2 + a*e)) - 2*(2*b*d^2*x^4 - 3*b*c^2 + a*c*d - (b*c*d - a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b*d^2)]","A",0
265,1,313,0,0.683754," ","integrate(x*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c - a d\right)} \sqrt{\frac{e}{b d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d + a b c d^{2} + {\left(3 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{b d}}\right) - 4 \, {\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, d}, \frac{{\left(b c - a d\right)} \sqrt{-\frac{e}{b d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{b d}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) + 2 \, {\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, d}\right]"," ",0,"[-1/8*((b*c - a*d)*sqrt(e/(b*d))*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b^2*d^3*x^4 + b^2*c^2*d + a*b*c*d^2 + (3*b^2*c*d^2 + a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(b*d))) - 4*(d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/d, 1/4*((b*c - a*d)*sqrt(-e/(b*d))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(b*d))/(b*e*x^2 + a*e)) + 2*(d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/d]","A",0
266,1,865,0,1.341927," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{\frac{b e}{d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{3} x^{4} + b c^{2} d + a c d^{2} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) + \frac{1}{4} \, \sqrt{\frac{a e}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left({\left(b c^{2} d + a c d^{2}\right)} x^{4} + 2 \, a c^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}\right)} \sqrt{\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right), -\frac{1}{2} \, \sqrt{-\frac{b e}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} e x^{2} + a b e\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{a e}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left({\left(b c^{2} d + a c d^{2}\right)} x^{4} + 2 \, a c^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}\right)} \sqrt{\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right), \frac{1}{2} \, \sqrt{-\frac{a e}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{-\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b e x^{2} + a^{2} e\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{b e}{d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{3} x^{4} + b c^{2} d + a c d^{2} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right), \frac{1}{2} \, \sqrt{-\frac{a e}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{-\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b e x^{2} + a^{2} e\right)}}\right) - \frac{1}{2} \, \sqrt{-\frac{b e}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} e x^{2} + a b e\right)}}\right)\right]"," ",0,"[1/4*sqrt(b*e/d)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^3*x^4 + b*c^2*d + a*c*d^2 + (3*b*c*d^2 + a*d^3)*x^2)*sqrt(b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) + 1/4*sqrt(a*e/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*((b*c^2*d + a*c*d^2)*x^4 + 2*a*c^3 + (b*c^3 + 3*a*c^2*d)*x^2)*sqrt(a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4), -1/2*sqrt(-b*e/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e*x^2 + a*b*e)) + 1/4*sqrt(a*e/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*((b*c^2*d + a*c*d^2)*x^4 + 2*a*c^3 + (b*c^3 + 3*a*c^2*d)*x^2)*sqrt(a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4), 1/2*sqrt(-a*e/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(-a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*e*x^2 + a^2*e)) + 1/4*sqrt(b*e/d)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^3*x^4 + b*c^2*d + a*c*d^2 + (3*b*c*d^2 + a*d^3)*x^2)*sqrt(b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))), 1/2*sqrt(-a*e/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(-a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*e*x^2 + a^2*e)) - 1/2*sqrt(-b*e/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e*x^2 + a*b*e))]","A",0
267,1,333,0,1.200219," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b c - a d\right)} x^{2} \sqrt{\frac{e}{a c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} + 4 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d + a^{2} c d^{2}\right)} x^{4} + {\left(a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{a c}}}{x^{4}}\right) + 4 \, {\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, c x^{2}}, \frac{{\left(b c - a d\right)} x^{2} \sqrt{-\frac{e}{a c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{a c}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) - 2 \, {\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, c x^{2}}\right]"," ",0,"[-1/8*((b*c - a*d)*x^2*sqrt(e/(a*c))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 + 4*(2*a^2*c^3 + (a*b*c^2*d + a^2*c*d^2)*x^4 + (a*b*c^3 + 3*a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(a*c)))/x^4) + 4*(d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c*x^2), 1/4*((b*c - a*d)*x^2*sqrt(-e/(a*c))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(a*c))/(b*e*x^2 + a*e)) - 2*(d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c*x^2)]","A",0
268,1,427,0,2.320480," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} x^{4} \sqrt{\frac{e}{a c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d + a^{2} c d^{2}\right)} x^{4} + {\left(a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{a c}}}{x^{4}}\right) + 4 \, {\left({\left(b c d - 3 \, a d^{2}\right)} x^{4} + 2 \, a c^{2} + {\left(b c^{2} - a c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, a c^{2} x^{4}}, -\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} x^{4} \sqrt{-\frac{e}{a c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{a c}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) + 2 \, {\left({\left(b c d - 3 \, a d^{2}\right)} x^{4} + 2 \, a c^{2} + {\left(b c^{2} - a c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, a c^{2} x^{4}}\right]"," ",0,"[-1/32*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*x^4*sqrt(e/(a*c))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*(2*a^2*c^3 + (a*b*c^2*d + a^2*c*d^2)*x^4 + (a*b*c^3 + 3*a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(a*c)))/x^4) + 4*((b*c*d - 3*a*d^2)*x^4 + 2*a*c^2 + (b*c^2 - a*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*c^2*x^4), -1/16*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*x^4*sqrt(-e/(a*c))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(a*c))/(b*e*x^2 + a*e)) + 2*((b*c*d - 3*a*d^2)*x^4 + 2*a*c^2 + (b*c^2 - a*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*c^2*x^4)]","A",0
269,1,561,0,6.168968," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} x^{6} \sqrt{\frac{e}{a c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} + 4 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d + a^{2} c d^{2}\right)} x^{4} + {\left(a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{a c}}}{x^{4}}\right) - 4 \, {\left({\left(3 \, b^{2} c^{2} d + 4 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} x^{6} - 8 \, a^{2} c^{3} + {\left(3 \, b^{2} c^{3} + 2 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} x^{4} - 2 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{192 \, a^{2} c^{3} x^{6}}, \frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} x^{6} \sqrt{-\frac{e}{a c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{a c}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) + 2 \, {\left({\left(3 \, b^{2} c^{2} d + 4 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} x^{6} - 8 \, a^{2} c^{3} + {\left(3 \, b^{2} c^{3} + 2 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} x^{4} - 2 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{96 \, a^{2} c^{3} x^{6}}\right]"," ",0,"[-1/192*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*x^6*sqrt(e/(a*c))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 + 4*(2*a^2*c^3 + (a*b*c^2*d + a^2*c*d^2)*x^4 + (a*b*c^3 + 3*a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(a*c)))/x^4) - 4*((3*b^2*c^2*d + 4*a*b*c*d^2 - 15*a^2*d^3)*x^6 - 8*a^2*c^3 + (3*b^2*c^3 + 2*a*b*c^2*d - 5*a^2*c*d^2)*x^4 - 2*(a*b*c^3 - a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^2*c^3*x^6), 1/96*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*x^6*sqrt(-e/(a*c))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(a*c))/(b*e*x^2 + a*e)) + 2*((3*b^2*c^2*d + 4*a*b*c*d^2 - 15*a^2*d^3)*x^6 - 8*a^2*c^3 + (3*b^2*c^3 + 2*a*b*c^2*d - 5*a^2*c*d^2)*x^4 - 2*(a*b*c^3 - a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^2*c^3*x^6)]","A",0
270,0,0,0,0.809320," ","integrate(x^4*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}, x\right)"," ",0,"integral(x^4*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)), x)","F",0
271,0,0,0,0.954277," ","integrate(x^2*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}, x\right)"," ",0,"integral(x^2*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)), x)","F",0
272,0,0,0,0.778465," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt((b*e*x^2 + a*e)/(d*x^2 + c)), x)","F",0
273,0,0,0,0.919114," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{2}}, x\right)"," ",0,"integral(sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/x^2, x)","F",0
274,0,0,0,0.933338," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}, x\right)"," ",0,"integral(sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/x^4, x)","F",0
275,0,0,0,0.933927," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{6}}, x\right)"," ",0,"integral(sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/x^6, x)","F",0
276,1,553,0,3.455919," ","integrate(x^5*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{3} c^{3} - 45 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e \sqrt{\frac{e}{b d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e - 4 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d + a b c d^{2} + {\left(3 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{b d}}\right) + 4 \, {\left(8 \, b^{2} d^{3} e x^{6} - 14 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e x^{4} + {\left(35 \, b^{2} c^{2} d - 38 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} e x^{2} + {\left(105 \, b^{2} c^{3} - 100 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{192 \, b d^{4}}, \frac{3 \, {\left(35 \, b^{3} c^{3} - 45 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e \sqrt{-\frac{e}{b d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{b d}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) + 2 \, {\left(8 \, b^{2} d^{3} e x^{6} - 14 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e x^{4} + {\left(35 \, b^{2} c^{2} d - 38 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} e x^{2} + {\left(105 \, b^{2} c^{3} - 100 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{96 \, b d^{4}}\right]"," ",0,"[1/192*(3*(35*b^3*c^3 - 45*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e*sqrt(e/(b*d))*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e - 4*(2*b^2*d^3*x^4 + b^2*c^2*d + a*b*c*d^2 + (3*b^2*c*d^2 + a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(b*d))) + 4*(8*b^2*d^3*e*x^6 - 14*(b^2*c*d^2 - a*b*d^3)*e*x^4 + (35*b^2*c^2*d - 38*a*b*c*d^2 + 3*a^2*d^3)*e*x^2 + (105*b^2*c^3 - 100*a*b*c^2*d + 3*a^2*c*d^2)*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b*d^4), 1/96*(3*(35*b^3*c^3 - 45*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e*sqrt(-e/(b*d))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(b*d))/(b*e*x^2 + a*e)) + 2*(8*b^2*d^3*e*x^6 - 14*(b^2*c*d^2 - a*b*d^3)*e*x^4 + (35*b^2*c^2*d - 38*a*b*c*d^2 + 3*a^2*d^3)*e*x^2 + (105*b^2*c^3 - 100*a*b*c^2*d + 3*a^2*c*d^2)*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b*d^4)]","A",0
277,1,417,0,1.932940," ","integrate(x^3*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2}\right)} e \sqrt{\frac{e}{b d}} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d + a b c d^{2} + {\left(3 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{b d}}\right) + 4 \, {\left(2 \, b d^{2} e x^{4} - 5 \, {\left(b c d - a d^{2}\right)} e x^{2} - {\left(15 \, b c^{2} - 13 \, a c d\right)} e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, d^{3}}, -\frac{3 \, {\left(5 \, b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2}\right)} e \sqrt{-\frac{e}{b d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{b d}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) - 2 \, {\left(2 \, b d^{2} e x^{4} - 5 \, {\left(b c d - a d^{2}\right)} e x^{2} - {\left(15 \, b c^{2} - 13 \, a c d\right)} e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, d^{3}}\right]"," ",0,"[1/32*(3*(5*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*e*sqrt(e/(b*d))*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b^2*d^3*x^4 + b^2*c^2*d + a*b*c*d^2 + (3*b^2*c*d^2 + a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(b*d))) + 4*(2*b*d^2*e*x^4 - 5*(b*c*d - a*d^2)*e*x^2 - (15*b*c^2 - 13*a*c*d)*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/d^3, -1/16*(3*(5*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*e*sqrt(-e/(b*d))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(b*d))/(b*e*x^2 + a*e)) - 2*(2*b*d^2*e*x^4 - 5*(b*c*d - a*d^2)*e*x^2 - (15*b*c^2 - 13*a*c*d)*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/d^3]","A",0
278,1,328,0,1.327814," ","integrate(x*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} \sqrt{\frac{b e}{d}} e \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{3} x^{4} + b c^{2} d + a c d^{2} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) - 4 \, {\left(b d e x^{2} + {\left(3 \, b c - 2 \, a d\right)} e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, d^{2}}, \frac{3 \, {\left(b c - a d\right)} \sqrt{-\frac{b e}{d}} e \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} e x^{2} + a b e\right)}}\right) + 2 \, {\left(b d e x^{2} + {\left(3 \, b c - 2 \, a d\right)} e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, d^{2}}\right]"," ",0,"[-1/8*(3*(b*c - a*d)*sqrt(b*e/d)*e*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^3*x^4 + b*c^2*d + a*c*d^2 + (3*b*c*d^2 + a*d^3)*x^2)*sqrt(b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) - 4*(b*d*e*x^2 + (3*b*c - 2*a*d)*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/d^2, 1/4*(3*(b*c - a*d)*sqrt(-b*e/d)*e*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e*x^2 + a*b*e)) + 2*(b*d*e*x^2 + (3*b*c - 2*a*d)*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/d^2]","A",0
279,1,1049,0,2.462603," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{b c \sqrt{\frac{b e}{d}} e \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{3} x^{4} + b c^{2} d + a c d^{2} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) + a d \sqrt{\frac{a e}{c}} e \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left({\left(b c^{2} d + a c d^{2}\right)} x^{4} + 2 \, a c^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}\right)} \sqrt{\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(b c - a d\right)} e \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, c d}, -\frac{2 \, b c \sqrt{-\frac{b e}{d}} e \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} e x^{2} + a b e\right)}}\right) - a d \sqrt{\frac{a e}{c}} e \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left({\left(b c^{2} d + a c d^{2}\right)} x^{4} + 2 \, a c^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}\right)} \sqrt{\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right) + 4 \, {\left(b c - a d\right)} e \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, c d}, \frac{2 \, a d \sqrt{-\frac{a e}{c}} e \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{-\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b e x^{2} + a^{2} e\right)}}\right) + b c \sqrt{\frac{b e}{d}} e \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{3} x^{4} + b c^{2} d + a c d^{2} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) - 4 \, {\left(b c - a d\right)} e \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, c d}, \frac{a d \sqrt{-\frac{a e}{c}} e \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{-\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b e x^{2} + a^{2} e\right)}}\right) - b c \sqrt{-\frac{b e}{d}} e \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-\frac{b e}{d}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} e x^{2} + a b e\right)}}\right) - 2 \, {\left(b c - a d\right)} e \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, c d}\right]"," ",0,"[1/4*(b*c*sqrt(b*e/d)*e*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^3*x^4 + b*c^2*d + a*c*d^2 + (3*b*c*d^2 + a*d^3)*x^2)*sqrt(b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) + a*d*sqrt(a*e/c)*e*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*((b*c^2*d + a*c*d^2)*x^4 + 2*a*c^3 + (b*c^3 + 3*a*c^2*d)*x^2)*sqrt(a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4) - 4*(b*c - a*d)*e*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c*d), -1/4*(2*b*c*sqrt(-b*e/d)*e*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e*x^2 + a*b*e)) - a*d*sqrt(a*e/c)*e*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*((b*c^2*d + a*c*d^2)*x^4 + 2*a*c^3 + (b*c^3 + 3*a*c^2*d)*x^2)*sqrt(a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4) + 4*(b*c - a*d)*e*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c*d), 1/4*(2*a*d*sqrt(-a*e/c)*e*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(-a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*e*x^2 + a^2*e)) + b*c*sqrt(b*e/d)*e*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^3*x^4 + b*c^2*d + a*c*d^2 + (3*b*c*d^2 + a*d^3)*x^2)*sqrt(b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) - 4*(b*c - a*d)*e*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c*d), 1/2*(a*d*sqrt(-a*e/c)*e*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(-a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*e*x^2 + a^2*e)) - b*c*sqrt(-b*e/d)*e*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*e/d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e*x^2 + a*b*e)) - 2*(b*c - a*d)*e*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c*d)]","A",0
280,1,350,0,2.571904," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} \sqrt{\frac{a e}{c}} e x^{2} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} + 4 \, {\left({\left(b c^{2} d + a c d^{2}\right)} x^{4} + 2 \, a c^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}\right)} \sqrt{\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left({\left(2 \, b c - 3 \, a d\right)} e x^{2} - a c e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, c^{2} x^{2}}, \frac{3 \, {\left(b c - a d\right)} \sqrt{-\frac{a e}{c}} e x^{2} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{-\frac{a e}{c}} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b e x^{2} + a^{2} e\right)}}\right) + 2 \, {\left({\left(2 \, b c - 3 \, a d\right)} e x^{2} - a c e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, c^{2} x^{2}}\right]"," ",0,"[-1/8*(3*(b*c - a*d)*sqrt(a*e/c)*e*x^2*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 + 4*((b*c^2*d + a*c*d^2)*x^4 + 2*a*c^3 + (b*c^3 + 3*a*c^2*d)*x^2)*sqrt(a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4) - 4*((2*b*c - 3*a*d)*e*x^2 - a*c*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c^2*x^2), 1/4*(3*(b*c - a*d)*sqrt(-a*e/c)*e*x^2*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(-a*e/c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*e*x^2 + a^2*e)) + 2*((2*b*c - 3*a*d)*e*x^2 - a*c*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c^2*x^2)]","A",0
281,1,435,0,7.435156," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 6 \, a b c d + 5 \, a^{2} d^{2}\right)} e x^{4} \sqrt{\frac{e}{a c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d + a^{2} c d^{2}\right)} x^{4} + {\left(a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{a c}}}{x^{4}}\right) - 4 \, {\left({\left(13 \, b c d - 15 \, a d^{2}\right)} e x^{4} + 2 \, a c^{2} e + 5 \, {\left(b c^{2} - a c d\right)} e x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, c^{3} x^{4}}, \frac{3 \, {\left(b^{2} c^{2} - 6 \, a b c d + 5 \, a^{2} d^{2}\right)} e x^{4} \sqrt{-\frac{e}{a c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{a c}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) - 2 \, {\left({\left(13 \, b c d - 15 \, a d^{2}\right)} e x^{4} + 2 \, a c^{2} e + 5 \, {\left(b c^{2} - a c d\right)} e x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, c^{3} x^{4}}\right]"," ",0,"[1/32*(3*(b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*e*x^4*sqrt(e/(a*c))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*(2*a^2*c^3 + (a*b*c^2*d + a^2*c*d^2)*x^4 + (a*b*c^3 + 3*a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(a*c)))/x^4) - 4*((13*b*c*d - 15*a*d^2)*e*x^4 + 2*a*c^2*e + 5*(b*c^2 - a*c*d)*e*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c^3*x^4), 1/16*(3*(b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*e*x^4*sqrt(-e/(a*c))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(a*c))/(b*e*x^2 + a*e)) - 2*((13*b*c*d - 15*a*d^2)*e*x^4 + 2*a*c^2*e + 5*(b*c^2 - a*c*d)*e*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(c^3*x^4)]","A",0
282,1,573,0,20.909560," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} + 35 \, a^{3} d^{3}\right)} e x^{6} \sqrt{\frac{e}{a c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} + 4 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d + a^{2} c d^{2}\right)} x^{4} + {\left(a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{e}{a c}}}{x^{4}}\right) - 4 \, {\left({\left(3 \, b^{2} c^{2} d - 100 \, a b c d^{2} + 105 \, a^{2} d^{3}\right)} e x^{6} + 8 \, a^{2} c^{3} e + {\left(3 \, b^{2} c^{3} - 38 \, a b c^{2} d + 35 \, a^{2} c d^{2}\right)} e x^{4} + 14 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} e x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{192 \, a c^{4} x^{6}}, -\frac{3 \, {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} + 35 \, a^{3} d^{3}\right)} e x^{6} \sqrt{-\frac{e}{a c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{e}{a c}}}{2 \, {\left(b e x^{2} + a e\right)}}\right) + 2 \, {\left({\left(3 \, b^{2} c^{2} d - 100 \, a b c d^{2} + 105 \, a^{2} d^{3}\right)} e x^{6} + 8 \, a^{2} c^{3} e + {\left(3 \, b^{2} c^{3} - 38 \, a b c^{2} d + 35 \, a^{2} c d^{2}\right)} e x^{4} + 14 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} e x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{96 \, a c^{4} x^{6}}\right]"," ",0,"[1/192*(3*(b^3*c^3 + 9*a*b^2*c^2*d - 45*a^2*b*c*d^2 + 35*a^3*d^3)*e*x^6*sqrt(e/(a*c))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 + 4*(2*a^2*c^3 + (a*b*c^2*d + a^2*c*d^2)*x^4 + (a*b*c^3 + 3*a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(e/(a*c)))/x^4) - 4*((3*b^2*c^2*d - 100*a*b*c*d^2 + 105*a^2*d^3)*e*x^6 + 8*a^2*c^3*e + (3*b^2*c^3 - 38*a*b*c^2*d + 35*a^2*c*d^2)*e*x^4 + 14*(a*b*c^3 - a^2*c^2*d)*e*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*c^4*x^6), -1/96*(3*(b^3*c^3 + 9*a*b^2*c^2*d - 45*a^2*b*c*d^2 + 35*a^3*d^3)*e*x^6*sqrt(-e/(a*c))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-e/(a*c))/(b*e*x^2 + a*e)) + 2*((3*b^2*c^2*d - 100*a*b*c*d^2 + 105*a^2*d^3)*e*x^6 + 8*a^2*c^3*e + (3*b^2*c^3 - 38*a*b*c^2*d + 35*a^2*c*d^2)*e*x^4 + 14*(a*b*c^3 - a^2*c^2*d)*e*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*c^4*x^6)]","A",0
283,0,0,0,0.571744," ","integrate(x^4*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e x^{6} + a e x^{4}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{d x^{2} + c}, x\right)"," ",0,"integral((b*e*x^6 + a*e*x^4)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(d*x^2 + c), x)","F",0
284,0,0,0,0.495041," ","integrate(x^2*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e x^{4} + a e x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{d x^{2} + c}, x\right)"," ",0,"integral((b*e*x^4 + a*e*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(d*x^2 + c), x)","F",0
285,0,0,0,0.604935," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e x^{2} + a e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{d x^{2} + c}, x\right)"," ",0,"integral((b*e*x^2 + a*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(d*x^2 + c), x)","F",0
286,0,0,0,0.675401," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e x^{2} + a e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{d x^{4} + c x^{2}}, x\right)"," ",0,"integral((b*e*x^2 + a*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(d*x^4 + c*x^2), x)","F",0
287,0,0,0,0.683253," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e x^{2} + a e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{d x^{6} + c x^{4}}, x\right)"," ",0,"integral((b*e*x^2 + a*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(d*x^6 + c*x^4), x)","F",0
288,0,0,0,0.774582," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e x^{2} + a e\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{d x^{8} + c x^{6}}, x\right)"," ",0,"integral((b*e*x^2 + a*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(d*x^8 + c*x^6), x)","F",0
289,1,55,0,0.724754," ","integrate(x*((-x^2+1)/(x^2+1))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} + 1\right)} \sqrt{-\frac{x^{2} - 1}{x^{2} + 1}} - \arctan\left(\frac{{\left(x^{2} + 1\right)} \sqrt{-\frac{x^{2} - 1}{x^{2} + 1}} - 1}{x^{2}}\right)"," ",0,"1/2*(x^2 + 1)*sqrt(-(x^2 - 1)/(x^2 + 1)) - arctan(((x^2 + 1)*sqrt(-(x^2 - 1)/(x^2 + 1)) - 1)/x^2)","A",0
290,1,77,0,0.658883," ","integrate(x*((-7*x^2+5)/(5*x^2+7))^(1/2),x, algorithm=""fricas"")","\frac{1}{10} \, {\left(5 \, x^{2} + 7\right)} \sqrt{-\frac{7 \, x^{2} - 5}{5 \, x^{2} + 7}} - \frac{37}{350} \, \sqrt{35} \arctan\left(\frac{\sqrt{35} {\left(35 \, x^{2} + 12\right)} \sqrt{-\frac{7 \, x^{2} - 5}{5 \, x^{2} + 7}}}{35 \, {\left(7 \, x^{2} - 5\right)}}\right)"," ",0,"1/10*(5*x^2 + 7)*sqrt(-(7*x^2 - 5)/(5*x^2 + 7)) - 37/350*sqrt(35)*arctan(1/35*sqrt(35)*(35*x^2 + 12)*sqrt(-(7*x^2 - 5)/(5*x^2 + 7))/(7*x^2 - 5))","A",0
291,1,55,0,0.746343," ","integrate(x^2*((-x^3+1)/(x^3+1))^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{3} + 1\right)} \sqrt{-\frac{x^{3} - 1}{x^{3} + 1}} - \frac{2}{3} \, \arctan\left(\frac{{\left(x^{3} + 1\right)} \sqrt{-\frac{x^{3} - 1}{x^{3} + 1}} - 1}{x^{3}}\right)"," ",0,"1/3*(x^3 + 1)*sqrt(-(x^3 - 1)/(x^3 + 1)) - 2/3*arctan(((x^3 + 1)*sqrt(-(x^3 - 1)/(x^3 + 1)) - 1)/x^3)","A",0
292,1,65,0,0.784270," ","integrate(x^8*((-x^3+1)/(x^3+1))^(1/2),x, algorithm=""fricas"")","\frac{1}{18} \, {\left(2 \, x^{9} - x^{6} + x^{3} + 4\right)} \sqrt{-\frac{x^{3} - 1}{x^{3} + 1}} - \frac{1}{3} \, \arctan\left(\frac{{\left(x^{3} + 1\right)} \sqrt{-\frac{x^{3} - 1}{x^{3} + 1}} - 1}{x^{3}}\right)"," ",0,"1/18*(2*x^9 - x^6 + x^3 + 4)*sqrt(-(x^3 - 1)/(x^3 + 1)) - 1/3*arctan(((x^3 + 1)*sqrt(-(x^3 - 1)/(x^3 + 1)) - 1)/x^3)","A",0
293,1,82,0,0.805293," ","integrate(x^9*((-7*x^5+5)/(5*x^5+7))^(1/2),x, algorithm=""fricas"")","\frac{1}{1750} \, {\left(175 \, x^{10} - 185 \, x^{5} - 602\right)} \sqrt{-\frac{7 \, x^{5} - 5}{5 \, x^{5} + 7}} + \frac{2257}{61250} \, \sqrt{35} \arctan\left(\frac{\sqrt{35} {\left(35 \, x^{5} + 12\right)} \sqrt{-\frac{7 \, x^{5} - 5}{5 \, x^{5} + 7}}}{35 \, {\left(7 \, x^{5} - 5\right)}}\right)"," ",0,"1/1750*(175*x^10 - 185*x^5 - 602)*sqrt(-(7*x^5 - 5)/(5*x^5 + 7)) + 2257/61250*sqrt(35)*arctan(1/35*sqrt(35)*(35*x^5 + 12)*sqrt(-(7*x^5 - 5)/(5*x^5 + 7))/(7*x^5 - 5))","A",0
294,1,32,0,0.551583," ","integrate((x^2/(x^2-1))^(1/2)/(x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x^{2} - 1\right)} \sqrt{\frac{x^{2}}{x^{2} - 1}}}{2 \, x}\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 - 1)*sqrt(x^2/(x^2 - 1))/x)","A",0
295,1,42,0,0.635609," ","integrate((x^2/(-1+a+(1+a)*x^2))^(1/2)/(x^2+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left({\left(a + 1\right)} x^{2} + a - 3\right)} \sqrt{\frac{x^{2}}{{\left(a + 1\right)} x^{2} + a - 1}}}{4 \, x}\right)"," ",0,"1/4*sqrt(2)*arctan(1/4*sqrt(2)*((a + 1)*x^2 + a - 3)*sqrt(x^2/((a + 1)*x^2 + a - 1))/x)","A",0
296,1,545,0,0.640470," ","integrate(x^5/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{b d e} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e - 4 \, {\left(2 \, b d^{2} x^{4} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) - 4 \, {\left(8 \, b^{3} d^{4} x^{6} - 3 \, b^{3} c^{3} d - 4 \, a b^{2} c^{2} d^{2} + 15 \, a^{2} b c d^{3} + 10 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{4} - {\left(b^{3} c^{2} d^{2} + 14 \, a b^{2} c d^{3} - 15 \, a^{2} b d^{4}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{192 \, b^{4} d^{3} e}, -\frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-b d e} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} d e x^{2} + a b d e\right)}}\right) - 2 \, {\left(8 \, b^{3} d^{4} x^{6} - 3 \, b^{3} c^{3} d - 4 \, a b^{2} c^{2} d^{2} + 15 \, a^{2} b c d^{3} + 10 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{4} - {\left(b^{3} c^{2} d^{2} + 14 \, a b^{2} c d^{3} - 15 \, a^{2} b d^{4}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{96 \, b^{4} d^{3} e}\right]"," ",0,"[-1/192*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(b*d*e)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e - 4*(2*b*d^2*x^4 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x^2)*sqrt(b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) - 4*(8*b^3*d^4*x^6 - 3*b^3*c^3*d - 4*a*b^2*c^2*d^2 + 15*a^2*b*c*d^3 + 10*(b^3*c*d^3 - a*b^2*d^4)*x^4 - (b^3*c^2*d^2 + 14*a*b^2*c*d^3 - 15*a^2*b*d^4)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^4*d^3*e), -1/96*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-b*d*e)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*d*e*x^2 + a*b*d*e)) - 2*(8*b^3*d^4*x^6 - 3*b^3*c^3*d - 4*a*b^2*c^2*d^2 + 15*a^2*b*c*d^3 + 10*(b^3*c*d^3 - a*b^2*d^4)*x^4 - (b^3*c^2*d^2 + 14*a*b^2*c*d^3 - 15*a^2*b*d^4)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^4*d^3*e)]","A",0
297,1,413,0,0.782430," ","integrate(x^3/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{b d e} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{2} x^{4} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) - 4 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d - 3 \, a b c d^{2} + 3 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, b^{3} d^{2} e}, \frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-b d e} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} d e x^{2} + a b d e\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{3} x^{4} + b^{2} c^{2} d - 3 \, a b c d^{2} + 3 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, b^{3} d^{2} e}\right]"," ",0,"[-1/32*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(b*d*e)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^2*x^4 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x^2)*sqrt(b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) - 4*(2*b^2*d^3*x^4 + b^2*c^2*d - 3*a*b*c*d^2 + 3*(b^2*c*d^2 - a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^3*d^2*e), 1/16*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(-b*d*e)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*d*e*x^2 + a*b*d*e)) + 2*(2*b^2*d^3*x^4 + b^2*c^2*d - 3*a*b*c*d^2 + 3*(b^2*c*d^2 - a*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^3*d^2*e)]","A",0
298,1,313,0,0.663448," ","integrate(x/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b d e} {\left(b c - a d\right)} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e - 4 \, {\left(2 \, b d^{2} x^{4} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) - 4 \, {\left(b d^{2} x^{2} + b c d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, b^{2} d e}, -\frac{\sqrt{-b d e} {\left(b c - a d\right)} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} d e x^{2} + a b d e\right)}}\right) - 2 \, {\left(b d^{2} x^{2} + b c d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, b^{2} d e}\right]"," ",0,"[-1/8*(sqrt(b*d*e)*(b*c - a*d)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e - 4*(2*b*d^2*x^4 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x^2)*sqrt(b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) - 4*(b*d^2*x^2 + b*c*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^2*d*e), -1/4*(sqrt(-b*d*e)*(b*c - a*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*d*e*x^2 + a*b*d*e)) - 2*(b*d^2*x^2 + b*c*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^2*d*e)]","A",0
299,1,881,0,0.985696," ","integrate(1/x/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{\frac{d}{b e}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + a b c d + {\left(3 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{d}{b e}}\right) + \frac{1}{4} \, \sqrt{\frac{c}{a e}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} + {\left(a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{c}{a e}}}{x^{4}}\right), -\frac{1}{2} \, \sqrt{-\frac{d}{b e}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{d}{b e}}}{2 \, {\left(b d x^{2} + a d\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{c}{a e}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} + {\left(a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{c}{a e}}}{x^{4}}\right), \frac{1}{2} \, \sqrt{-\frac{c}{a e}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{c}{a e}}}{2 \, {\left(b c x^{2} + a c\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{d}{b e}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + a b c d + {\left(3 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{d}{b e}}\right), \frac{1}{2} \, \sqrt{-\frac{c}{a e}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{c}{a e}}}{2 \, {\left(b c x^{2} + a c\right)}}\right) - \frac{1}{2} \, \sqrt{-\frac{d}{b e}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{d}{b e}}}{2 \, {\left(b d x^{2} + a d\right)}}\right)\right]"," ",0,"[1/4*sqrt(d/(b*e))*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b^2*d^2*x^4 + b^2*c^2 + a*b*c*d + (3*b^2*c*d + a*b*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(d/(b*e))) + 1/4*sqrt(c/(a*e))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 + (a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(c/(a*e)))/x^4), -1/2*sqrt(-d/(b*e))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-d/(b*e))/(b*d*x^2 + a*d)) + 1/4*sqrt(c/(a*e))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 + (a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(c/(a*e)))/x^4), 1/2*sqrt(-c/(a*e))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-c/(a*e))/(b*c*x^2 + a*c)) + 1/4*sqrt(d/(b*e))*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b^2*d^2*x^4 + b^2*c^2 + a*b*c*d + (3*b^2*c*d + a*b*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(d/(b*e))), 1/2*sqrt(-c/(a*e))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-c/(a*e))/(b*c*x^2 + a*c)) - 1/2*sqrt(-d/(b*e))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-d/(b*e))/(b*d*x^2 + a*d))]","A",0
300,1,333,0,1.027894," ","integrate(1/x^3/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a c e} {\left(b c - a d\right)} x^{2} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left({\left(b c d + a d^{2}\right)} x^{4} + 2 \, a c^{2} + {\left(b c^{2} + 3 \, a c d\right)} x^{2}\right)} \sqrt{a c e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right) + 4 \, {\left(a c d x^{2} + a c^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, a^{2} c e x^{2}}, -\frac{\sqrt{-a c e} {\left(b c - a d\right)} x^{2} \arctan\left(\frac{\sqrt{-a c e} {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b c e x^{2} + a^{2} c e\right)}}\right) + 2 \, {\left(a c d x^{2} + a c^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, a^{2} c e x^{2}}\right]"," ",0,"[-1/8*(sqrt(a*c*e)*(b*c - a*d)*x^2*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*((b*c*d + a*d^2)*x^4 + 2*a*c^2 + (b*c^2 + 3*a*c*d)*x^2)*sqrt(a*c*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4) + 4*(a*c*d*x^2 + a*c^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^2*c*e*x^2), -1/4*(sqrt(-a*c*e)*(b*c - a*d)*x^2*arctan(1/2*sqrt(-a*c*e)*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*c*e*x^2 + a^2*c*e)) + 2*(a*c*d*x^2 + a*c^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^2*c*e*x^2)]","A",0
301,1,443,0,2.244514," ","integrate(1/x^5/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{a c e} x^{4} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} + 4 \, {\left({\left(b c d + a d^{2}\right)} x^{4} + 2 \, a c^{2} + {\left(b c^{2} + 3 \, a c d\right)} x^{2}\right)} \sqrt{a c e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right) + 4 \, {\left(2 \, a^{2} c^{3} - {\left(3 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{4} - 3 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, a^{3} c^{2} e x^{4}}, \frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{-a c e} x^{4} \arctan\left(\frac{\sqrt{-a c e} {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b c e x^{2} + a^{2} c e\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{3} - {\left(3 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{4} - 3 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, a^{3} c^{2} e x^{4}}\right]"," ",0,"[-1/32*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(a*c*e)*x^4*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 + 4*((b*c*d + a*d^2)*x^4 + 2*a*c^2 + (b*c^2 + 3*a*c*d)*x^2)*sqrt(a*c*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4) + 4*(2*a^2*c^3 - (3*a*b*c^2*d - a^2*c*d^2)*x^4 - 3*(a*b*c^3 - a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^3*c^2*e*x^4), 1/16*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(-a*c*e)*x^4*arctan(1/2*sqrt(-a*c*e)*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*c*e*x^2 + a^2*c*e)) - 2*(2*a^2*c^3 - (3*a*b*c^2*d - a^2*c*d^2)*x^4 - 3*(a*b*c^3 - a^2*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^3*c^2*e*x^4)]","A",0
302,0,0,0,0.551134," ","integrate(x^4/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{6} + c x^{4}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b e x^{2} + a e}, x\right)"," ",0,"integral((d*x^6 + c*x^4)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b*e*x^2 + a*e), x)","F",0
303,0,0,0,0.632300," ","integrate(x^2/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{4} + c x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b e x^{2} + a e}, x\right)"," ",0,"integral((d*x^4 + c*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b*e*x^2 + a*e), x)","F",0
304,0,0,0,0.835762," ","integrate(1/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b e x^{2} + a e}, x\right)"," ",0,"integral((d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b*e*x^2 + a*e), x)","F",0
305,0,0,0,1.145729," ","integrate(1/x^2/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b e x^{4} + a e x^{2}}, x\right)"," ",0,"integral((d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b*e*x^4 + a*e*x^2), x)","F",0
306,0,0,0,0.667419," ","integrate(1/x^4/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b e x^{6} + a e x^{4}}, x\right)"," ",0,"integral((d*x^2 + c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b*e*x^6 + a*e*x^4), x)","F",0
307,1,781,0,2.846486," ","integrate(x^5/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} c^{3} + 9 \, a^{2} b^{2} c^{2} d - 45 \, a^{3} b c d^{2} + 35 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 9 \, a b^{3} c^{2} d - 45 \, a^{2} b^{2} c d^{2} + 35 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{b d e} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e - 4 \, {\left(2 \, b d^{2} x^{4} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) + 4 \, {\left(8 \, b^{4} d^{4} x^{8} + 3 \, a b^{3} c^{3} d - 100 \, a^{2} b^{2} c^{2} d^{2} + 105 \, a^{3} b c d^{3} + 2 \, {\left(11 \, b^{4} c d^{3} - 7 \, a b^{3} d^{4}\right)} x^{6} + {\left(17 \, b^{4} c^{2} d^{2} - 52 \, a b^{3} c d^{3} + 35 \, a^{2} b^{2} d^{4}\right)} x^{4} + {\left(3 \, b^{4} c^{3} d - 35 \, a b^{3} c^{2} d^{2} - 65 \, a^{2} b^{2} c d^{3} + 105 \, a^{3} b d^{4}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{192 \, {\left(b^{6} d^{2} e^{2} x^{2} + a b^{5} d^{2} e^{2}\right)}}, \frac{3 \, {\left(a b^{3} c^{3} + 9 \, a^{2} b^{2} c^{2} d - 45 \, a^{3} b c d^{2} + 35 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 9 \, a b^{3} c^{2} d - 45 \, a^{2} b^{2} c d^{2} + 35 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-b d e} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} d e x^{2} + a b d e\right)}}\right) + 2 \, {\left(8 \, b^{4} d^{4} x^{8} + 3 \, a b^{3} c^{3} d - 100 \, a^{2} b^{2} c^{2} d^{2} + 105 \, a^{3} b c d^{3} + 2 \, {\left(11 \, b^{4} c d^{3} - 7 \, a b^{3} d^{4}\right)} x^{6} + {\left(17 \, b^{4} c^{2} d^{2} - 52 \, a b^{3} c d^{3} + 35 \, a^{2} b^{2} d^{4}\right)} x^{4} + {\left(3 \, b^{4} c^{3} d - 35 \, a b^{3} c^{2} d^{2} - 65 \, a^{2} b^{2} c d^{3} + 105 \, a^{3} b d^{4}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{96 \, {\left(b^{6} d^{2} e^{2} x^{2} + a b^{5} d^{2} e^{2}\right)}}\right]"," ",0,"[1/192*(3*(a*b^3*c^3 + 9*a^2*b^2*c^2*d - 45*a^3*b*c*d^2 + 35*a^4*d^3 + (b^4*c^3 + 9*a*b^3*c^2*d - 45*a^2*b^2*c*d^2 + 35*a^3*b*d^3)*x^2)*sqrt(b*d*e)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e - 4*(2*b*d^2*x^4 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x^2)*sqrt(b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) + 4*(8*b^4*d^4*x^8 + 3*a*b^3*c^3*d - 100*a^2*b^2*c^2*d^2 + 105*a^3*b*c*d^3 + 2*(11*b^4*c*d^3 - 7*a*b^3*d^4)*x^6 + (17*b^4*c^2*d^2 - 52*a*b^3*c*d^3 + 35*a^2*b^2*d^4)*x^4 + (3*b^4*c^3*d - 35*a*b^3*c^2*d^2 - 65*a^2*b^2*c*d^3 + 105*a^3*b*d^4)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^6*d^2*e^2*x^2 + a*b^5*d^2*e^2), 1/96*(3*(a*b^3*c^3 + 9*a^2*b^2*c^2*d - 45*a^3*b*c*d^2 + 35*a^4*d^3 + (b^4*c^3 + 9*a*b^3*c^2*d - 45*a^2*b^2*c*d^2 + 35*a^3*b*d^3)*x^2)*sqrt(-b*d*e)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*d*e*x^2 + a*b*d*e)) + 2*(8*b^4*d^4*x^8 + 3*a*b^3*c^3*d - 100*a^2*b^2*c^2*d^2 + 105*a^3*b*c*d^3 + 2*(11*b^4*c*d^3 - 7*a*b^3*d^4)*x^6 + (17*b^4*c^2*d^2 - 52*a*b^3*c*d^3 + 35*a^2*b^2*d^4)*x^4 + (3*b^4*c^3*d - 35*a*b^3*c^2*d^2 - 65*a^2*b^2*c*d^3 + 105*a^3*b*d^4)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^6*d^2*e^2*x^2 + a*b^5*d^2*e^2)]","A",0
308,1,585,0,1.935743," ","integrate(x^3/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{2} c^{2} - 6 \, a^{2} b c d + 5 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 6 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{b d e} \log\left(8 \, b^{2} d^{2} e x^{4} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} e x^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e + 4 \, {\left(2 \, b d^{2} x^{4} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x^{2}\right)} \sqrt{b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}\right) + 4 \, {\left(2 \, b^{3} d^{3} x^{6} + 13 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} + {\left(7 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x^{4} + {\left(5 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} - 15 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, {\left(b^{5} d e^{2} x^{2} + a b^{4} d e^{2}\right)}}, -\frac{3 \, {\left(a b^{2} c^{2} - 6 \, a^{2} b c d + 5 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 6 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-b d e} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{-b d e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(b^{2} d e x^{2} + a b d e\right)}}\right) - 2 \, {\left(2 \, b^{3} d^{3} x^{6} + 13 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} + {\left(7 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x^{4} + {\left(5 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} - 15 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, {\left(b^{5} d e^{2} x^{2} + a b^{4} d e^{2}\right)}}\right]"," ",0,"[1/32*(3*(a*b^2*c^2 - 6*a^2*b*c*d + 5*a^3*d^2 + (b^3*c^2 - 6*a*b^2*c*d + 5*a^2*b*d^2)*x^2)*sqrt(b*d*e)*log(8*b^2*d^2*e*x^4 + 8*(b^2*c*d + a*b*d^2)*e*x^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e + 4*(2*b*d^2*x^4 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x^2)*sqrt(b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))) + 4*(2*b^3*d^3*x^6 + 13*a*b^2*c^2*d - 15*a^2*b*c*d^2 + (7*b^3*c*d^2 - 5*a*b^2*d^3)*x^4 + (5*b^3*c^2*d + 8*a*b^2*c*d^2 - 15*a^2*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^5*d*e^2*x^2 + a*b^4*d*e^2), -1/16*(3*(a*b^2*c^2 - 6*a^2*b*c*d + 5*a^3*d^2 + (b^3*c^2 - 6*a*b^2*c*d + 5*a^2*b*d^2)*x^2)*sqrt(-b*d*e)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(-b*d*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*d*e*x^2 + a*b*d*e)) - 2*(2*b^3*d^3*x^6 + 13*a*b^2*c^2*d - 15*a^2*b*c*d^2 + (7*b^3*c*d^2 - 5*a*b^2*d^3)*x^4 + (5*b^3*c^2*d + 8*a*b^2*c*d^2 - 15*a^2*b*d^3)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^5*d*e^2*x^2 + a*b^4*d*e^2)]","A",0
309,1,443,0,1.010962," ","integrate(x/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{2} c - a b d\right)} e x^{2} + {\left(a b c - a^{2} d\right)} e\right)} \sqrt{\frac{d}{b e}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + a b c d + {\left(3 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{d}{b e}}\right) - 4 \, {\left(b d^{2} x^{4} - 2 \, b c^{2} + 3 \, a c d - {\left(b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, {\left(b^{3} e^{2} x^{2} + a b^{2} e^{2}\right)}}, -\frac{3 \, {\left({\left(b^{2} c - a b d\right)} e x^{2} + {\left(a b c - a^{2} d\right)} e\right)} \sqrt{-\frac{d}{b e}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{d}{b e}}}{2 \, {\left(b d x^{2} + a d\right)}}\right) - 2 \, {\left(b d^{2} x^{4} - 2 \, b c^{2} + 3 \, a c d - {\left(b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, {\left(b^{3} e^{2} x^{2} + a b^{2} e^{2}\right)}}\right]"," ",0,"[-1/8*(3*((b^2*c - a*b*d)*e*x^2 + (a*b*c - a^2*d)*e)*sqrt(d/(b*e))*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 - 4*(2*b^2*d^2*x^4 + b^2*c^2 + a*b*c*d + (3*b^2*c*d + a*b*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(d/(b*e))) - 4*(b*d^2*x^4 - 2*b*c^2 + 3*a*c*d - (b*c*d - 3*a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^3*e^2*x^2 + a*b^2*e^2), -1/4*(3*((b^2*c - a*b*d)*e*x^2 + (a*b*c - a^2*d)*e)*sqrt(-d/(b*e))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-d/(b*e))/(b*d*x^2 + a*d)) - 2*(b*d^2*x^4 - 2*b*c^2 + 3*a*c*d - (b*c*d - 3*a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(b^3*e^2*x^2 + a*b^2*e^2)]","A",0
310,1,1293,0,2.147337," ","integrate(1/x/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b d e x^{2} + a^{2} d e\right)} \sqrt{\frac{d}{b e}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + a b c d + {\left(3 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{d}{b e}}\right) + {\left(b^{2} c e x^{2} + a b c e\right)} \sqrt{\frac{c}{a e}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} + {\left(a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{c}{a e}}}{x^{4}}\right) + 4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, {\left(a b^{2} e^{2} x^{2} + a^{2} b e^{2}\right)}}, -\frac{2 \, {\left(a b d e x^{2} + a^{2} d e\right)} \sqrt{-\frac{d}{b e}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{d}{b e}}}{2 \, {\left(b d x^{2} + a d\right)}}\right) - {\left(b^{2} c e x^{2} + a b c e\right)} \sqrt{\frac{c}{a e}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} + {\left(a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{c}{a e}}}{x^{4}}\right) - 4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, {\left(a b^{2} e^{2} x^{2} + a^{2} b e^{2}\right)}}, \frac{2 \, {\left(b^{2} c e x^{2} + a b c e\right)} \sqrt{-\frac{c}{a e}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{c}{a e}}}{2 \, {\left(b c x^{2} + a c\right)}}\right) + {\left(a b d e x^{2} + a^{2} d e\right)} \sqrt{\frac{d}{b e}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + a b c d + {\left(3 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{d}{b e}}\right) + 4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, {\left(a b^{2} e^{2} x^{2} + a^{2} b e^{2}\right)}}, \frac{{\left(b^{2} c e x^{2} + a b c e\right)} \sqrt{-\frac{c}{a e}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{c}{a e}}}{2 \, {\left(b c x^{2} + a c\right)}}\right) - {\left(a b d e x^{2} + a^{2} d e\right)} \sqrt{-\frac{d}{b e}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{d}{b e}}}{2 \, {\left(b d x^{2} + a d\right)}}\right) + 2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b^{2} e^{2} x^{2} + a^{2} b e^{2}\right)}}\right]"," ",0,"[1/4*((a*b*d*e*x^2 + a^2*d*e)*sqrt(d/(b*e))*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b^2*d^2*x^4 + b^2*c^2 + a*b*c*d + (3*b^2*c*d + a*b*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(d/(b*e))) + (b^2*c*e*x^2 + a*b*c*e)*sqrt(c/(a*e))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 + (a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(c/(a*e)))/x^4) + 4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*b^2*e^2*x^2 + a^2*b*e^2), -1/4*(2*(a*b*d*e*x^2 + a^2*d*e)*sqrt(-d/(b*e))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-d/(b*e))/(b*d*x^2 + a*d)) - (b^2*c*e*x^2 + a*b*c*e)*sqrt(c/(a*e))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 + (a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(c/(a*e)))/x^4) - 4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*b^2*e^2*x^2 + a^2*b*e^2), 1/4*(2*(b^2*c*e*x^2 + a*b*c*e)*sqrt(-c/(a*e))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-c/(a*e))/(b*c*x^2 + a*c)) + (a*b*d*e*x^2 + a^2*d*e)*sqrt(d/(b*e))*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b^2*d^2*x^4 + b^2*c^2 + a*b*c*d + (3*b^2*c*d + a*b*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(d/(b*e))) + 4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*b^2*e^2*x^2 + a^2*b*e^2), 1/2*((b^2*c*e*x^2 + a*b*c*e)*sqrt(-c/(a*e))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-c/(a*e))/(b*c*x^2 + a*c)) - (a*b*d*e*x^2 + a^2*d*e)*sqrt(-d/(b*e))*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-d/(b*e))/(b*d*x^2 + a*d)) + 2*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a*b^2*e^2*x^2 + a^2*b*e^2)]","B",0
311,1,469,0,3.107356," ","integrate(1/x^3/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{2} c - a b d\right)} e x^{4} + {\left(a b c - a^{2} d\right)} e x^{2}\right)} \sqrt{\frac{c}{a e}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} + {\left(a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{\frac{c}{a e}}}{x^{4}}\right) + 4 \, {\left({\left(3 \, b c d - 2 \, a d^{2}\right)} x^{4} + a c^{2} + {\left(3 \, b c^{2} - a c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{8 \, {\left(a^{2} b e^{2} x^{4} + a^{3} e^{2} x^{2}\right)}}, -\frac{3 \, {\left({\left(b^{2} c - a b d\right)} e x^{4} + {\left(a b c - a^{2} d\right)} e x^{2}\right)} \sqrt{-\frac{c}{a e}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}} \sqrt{-\frac{c}{a e}}}{2 \, {\left(b c x^{2} + a c\right)}}\right) + 2 \, {\left({\left(3 \, b c d - 2 \, a d^{2}\right)} x^{4} + a c^{2} + {\left(3 \, b c^{2} - a c d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{4 \, {\left(a^{2} b e^{2} x^{4} + a^{3} e^{2} x^{2}\right)}}\right]"," ",0,"[-1/8*(3*((b^2*c - a*b*d)*e*x^4 + (a*b*c - a^2*d)*e*x^2)*sqrt(c/(a*e))*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 + (a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(c/(a*e)))/x^4) + 4*((3*b*c*d - 2*a*d^2)*x^4 + a*c^2 + (3*b*c^2 - a*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^2*b*e^2*x^4 + a^3*e^2*x^2), -1/4*(3*((b^2*c - a*b*d)*e*x^4 + (a*b*c - a^2*d)*e*x^2)*sqrt(-c/(a*e))*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))*sqrt(-c/(a*e))/(b*c*x^2 + a*c)) + 2*((3*b*c*d - 2*a*d^2)*x^4 + a*c^2 + (3*b*c^2 - a*c*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^2*b*e^2*x^4 + a^3*e^2*x^2)]","A",0
312,1,613,0,10.114289," ","integrate(1/x^5/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, b^{3} c^{2} - 6 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{6} + {\left(5 \, a b^{2} c^{2} - 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{4}\right)} \sqrt{a c e} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e x^{4} + 8 \, a^{2} c^{2} e + 8 \, {\left(a b c^{2} + a^{2} c d\right)} e x^{2} - 4 \, {\left({\left(b c d + a d^{2}\right)} x^{4} + 2 \, a c^{2} + {\left(b c^{2} + 3 \, a c d\right)} x^{2}\right)} \sqrt{a c e} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{x^{4}}\right) + 4 \, {\left({\left(15 \, a b^{2} c^{2} d - 13 \, a^{2} b c d^{2}\right)} x^{6} - 2 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d - 5 \, a^{3} c d^{2}\right)} x^{4} + {\left(5 \, a^{2} b c^{3} - 7 \, a^{3} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{32 \, {\left(a^{4} b c e^{2} x^{6} + a^{5} c e^{2} x^{4}\right)}}, \frac{3 \, {\left({\left(5 \, b^{3} c^{2} - 6 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{6} + {\left(5 \, a b^{2} c^{2} - 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{4}\right)} \sqrt{-a c e} \arctan\left(\frac{\sqrt{-a c e} {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{2 \, {\left(a b c e x^{2} + a^{2} c e\right)}}\right) + 2 \, {\left({\left(15 \, a b^{2} c^{2} d - 13 \, a^{2} b c d^{2}\right)} x^{6} - 2 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d - 5 \, a^{3} c d^{2}\right)} x^{4} + {\left(5 \, a^{2} b c^{3} - 7 \, a^{3} c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{16 \, {\left(a^{4} b c e^{2} x^{6} + a^{5} c e^{2} x^{4}\right)}}\right]"," ",0,"[1/32*(3*((5*b^3*c^2 - 6*a*b^2*c*d + a^2*b*d^2)*x^6 + (5*a*b^2*c^2 - 6*a^2*b*c*d + a^3*d^2)*x^4)*sqrt(a*c*e)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e*x^4 + 8*a^2*c^2*e + 8*(a*b*c^2 + a^2*c*d)*e*x^2 - 4*((b*c*d + a*d^2)*x^4 + 2*a*c^2 + (b*c^2 + 3*a*c*d)*x^2)*sqrt(a*c*e)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/x^4) + 4*((15*a*b^2*c^2*d - 13*a^2*b*c*d^2)*x^6 - 2*a^3*c^3 + (15*a*b^2*c^3 - 8*a^2*b*c^2*d - 5*a^3*c*d^2)*x^4 + (5*a^2*b*c^3 - 7*a^3*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^4*b*c*e^2*x^6 + a^5*c*e^2*x^4), 1/16*(3*((5*b^3*c^2 - 6*a*b^2*c*d + a^2*b*d^2)*x^6 + (5*a*b^2*c^2 - 6*a^2*b*c*d + a^3*d^2)*x^4)*sqrt(-a*c*e)*arctan(1/2*sqrt(-a*c*e)*((b*c + a*d)*x^2 + 2*a*c)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(a*b*c*e*x^2 + a^2*c*e)) + 2*((15*a*b^2*c^2*d - 13*a^2*b*c*d^2)*x^6 - 2*a^3*c^3 + (15*a*b^2*c^3 - 8*a^2*b*c^2*d - 5*a^3*c*d^2)*x^4 + (5*a^2*b*c^3 - 7*a^3*c^2*d)*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c)))/(a^4*b*c*e^2*x^6 + a^5*c*e^2*x^4)]","A",0
313,0,0,0,0.601514," ","integrate(x^4/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{8} + 2 \, c d x^{6} + c^{2} x^{4}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b^{2} e^{2} x^{4} + 2 \, a b e^{2} x^{2} + a^{2} e^{2}}, x\right)"," ",0,"integral((d^2*x^8 + 2*c*d*x^6 + c^2*x^4)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e^2*x^4 + 2*a*b*e^2*x^2 + a^2*e^2), x)","F",0
314,0,0,0,0.665844," ","integrate(x^2/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{6} + 2 \, c d x^{4} + c^{2} x^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b^{2} e^{2} x^{4} + 2 \, a b e^{2} x^{2} + a^{2} e^{2}}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^4 + c^2*x^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e^2*x^4 + 2*a*b*e^2*x^2 + a^2*e^2), x)","F",0
315,0,0,0,0.803612," ","integrate(1/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b^{2} e^{2} x^{4} + 2 \, a b e^{2} x^{2} + a^{2} e^{2}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e^2*x^4 + 2*a*b*e^2*x^2 + a^2*e^2), x)","F",0
316,0,0,0,0.640407," ","integrate(1/x^2/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b^{2} e^{2} x^{6} + 2 \, a b e^{2} x^{4} + a^{2} e^{2} x^{2}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e^2*x^6 + 2*a*b*e^2*x^4 + a^2*e^2*x^2), x)","F",0
317,0,0,0,0.671866," ","integrate(1/x^4/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} \sqrt{\frac{b e x^{2} + a e}{d x^{2} + c}}}{b^{2} e^{2} x^{8} + 2 \, a b e^{2} x^{6} + a^{2} e^{2} x^{4}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*sqrt((b*e*x^2 + a*e)/(d*x^2 + c))/(b^2*e^2*x^8 + 2*a*b*e^2*x^6 + a^2*e^2*x^4), x)","F",0
318,1,423,0,0.968657," ","integrate(x^5*(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a^{2} b c^{2} + 4 \, a b^{2} c + b^{3}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(8 \, a^{3} d^{3} x^{6} + 2 \, a^{2} b d^{2} x^{4} + 8 \, a^{3} c^{3} - 10 \, a^{2} b c^{2} - 3 \, a b^{2} c - {\left(8 \, a^{2} b c + 3 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{192 \, a^{3} d^{3}}, -\frac{3 \, {\left(8 \, a^{2} b c^{2} + 4 \, a b^{2} c + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - 2 \, {\left(8 \, a^{3} d^{3} x^{6} + 2 \, a^{2} b d^{2} x^{4} + 8 \, a^{3} c^{3} - 10 \, a^{2} b c^{2} - 3 \, a b^{2} c - {\left(8 \, a^{2} b c + 3 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{96 \, a^{3} d^{3}}\right]"," ",0,"[1/192*(3*(8*a^2*b*c^2 + 4*a*b^2*c + b^3)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(8*a^3*d^3*x^6 + 2*a^2*b*d^2*x^4 + 8*a^3*c^3 - 10*a^2*b*c^2 - 3*a*b^2*c - (8*a^2*b*c + 3*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^3*d^3), -1/96*(3*(8*a^2*b*c^2 + 4*a*b^2*c + b^3)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - 2*(8*a^3*d^3*x^6 + 2*a^2*b*d^2*x^4 + 8*a^3*c^3 - 10*a^2*b*c^2 - 3*a*b^2*c - (8*a^2*b*c + 3*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^3*d^3)]","A",0
319,1,325,0,0.733369," ","integrate(x^3*(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a b c + b^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} - 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(2 \, a^{2} d^{2} x^{4} + a b d x^{2} - 2 \, a^{2} c^{2} + a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, a^{2} d^{2}}, \frac{{\left(4 \, a b c + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + 2 \, {\left(2 \, a^{2} d^{2} x^{4} + a b d x^{2} - 2 \, a^{2} c^{2} + a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, a^{2} d^{2}}\right]"," ",0,"[1/32*((4*a*b*c + b^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 - 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(2*a^2*d^2*x^4 + a*b*d*x^2 - 2*a^2*c^2 + a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^2*d^2), 1/16*((4*a*b*c + b^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 2*(2*a^2*d^2*x^4 + a*b*d*x^2 - 2*a^2*c^2 + a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^2*d^2)]","A",0
320,1,267,0,0.755715," ","integrate(x*(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(a d x^{2} + a c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, a d}, -\frac{\sqrt{-a} b \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - 2 \, {\left(a d x^{2} + a c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, a d}\right]"," ",0,"[1/8*(sqrt(a)*b*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(a*d*x^2 + a*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a*d), -1/4*(sqrt(-a)*b*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - 2*(a*d*x^2 + a*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a*d)]","A",0
321,1,927,0,0.917267," ","integrate((a+b/(d*x^2+c))^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + \frac{1}{4} \, \sqrt{\frac{a c + b}{c}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c^{2} + b c\right)} d^{2} x^{4} + 2 \, a c^{4} + 2 \, b c^{3} + {\left(4 \, a c^{3} + 3 \, b c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{a c + b}{c}}}{x^{4}}\right), -\frac{1}{2} \, \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{a c + b}{c}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c^{2} + b c\right)} d^{2} x^{4} + 2 \, a c^{4} + 2 \, b c^{3} + {\left(4 \, a c^{3} + 3 \, b c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{a c + b}{c}}}{x^{4}}\right), \frac{1}{2} \, \sqrt{-\frac{a c + b}{c}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{a c + b}{c}}}{2 \, {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)}}\right) + \frac{1}{4} \, \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right), -\frac{1}{2} \, \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + \frac{1}{2} \, \sqrt{-\frac{a c + b}{c}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{a c + b}{c}}}{2 \, {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)}}\right)\right]"," ",0,"[1/4*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 1/4*sqrt((a*c + b)/c)*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c^2 + b*c)*d^2*x^4 + 2*a*c^4 + 2*b*c^3 + (4*a*c^3 + 3*b*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt((a*c + b)/c))/x^4), -1/2*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 1/4*sqrt((a*c + b)/c)*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c^2 + b*c)*d^2*x^4 + 2*a*c^4 + 2*b*c^3 + (4*a*c^3 + 3*b*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt((a*c + b)/c))/x^4), 1/2*sqrt(-(a*c + b)/c)*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-(a*c + b)/c)/(a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)) + 1/4*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))), -1/2*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 1/2*sqrt(-(a*c + b)/c)*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-(a*c + b)/c)/(a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2))]","B",0
322,1,433,0,0.642944," ","integrate((a+b/(d*x^2+c))^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{a c^{2} + b c} b d x^{2} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} + 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(a c^{3} + {\left(a c^{2} + b c\right)} d x^{2} + b c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, {\left(a c^{3} + b c^{2}\right)} x^{2}}, -\frac{\sqrt{-a c^{2} - b c} b d x^{2} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) + 2 \, {\left(a c^{3} + {\left(a c^{2} + b c\right)} d x^{2} + b c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left(a c^{3} + b c^{2}\right)} x^{2}}\right]"," ",0,"[1/8*(sqrt(a*c^2 + b*c)*b*d*x^2*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 + 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(a*c^3 + (a*c^2 + b*c)*d*x^2 + b*c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a*c^3 + b*c^2)*x^2), -1/4*(sqrt(-a*c^2 - b*c)*b*d*x^2*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) + 2*(a*c^3 + (a*c^2 + b*c)*d*x^2 + b*c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a*c^3 + b*c^2)*x^2)]","B",0
323,1,577,0,0.930714," ","integrate((a+b/(d*x^2+c))^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a b c + 3 \, b^{2}\right)} \sqrt{a c^{2} + b c} d^{2} x^{4} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(2 \, a^{2} c^{5} - {\left(2 \, a^{2} c^{3} + 5 \, a b c^{2} + 3 \, b^{2} c\right)} d^{2} x^{4} + 4 \, a b c^{4} + 2 \, b^{2} c^{3} - {\left(a b c^{3} + b^{2} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, {\left(a^{2} c^{5} + 2 \, a b c^{4} + b^{2} c^{3}\right)} x^{4}}, \frac{{\left(4 \, a b c + 3 \, b^{2}\right)} \sqrt{-a c^{2} - b c} d^{2} x^{4} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{5} - {\left(2 \, a^{2} c^{3} + 5 \, a b c^{2} + 3 \, b^{2} c\right)} d^{2} x^{4} + 4 \, a b c^{4} + 2 \, b^{2} c^{3} - {\left(a b c^{3} + b^{2} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, {\left(a^{2} c^{5} + 2 \, a b c^{4} + b^{2} c^{3}\right)} x^{4}}\right]"," ",0,"[1/32*((4*a*b*c + 3*b^2)*sqrt(a*c^2 + b*c)*d^2*x^4*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(2*a^2*c^5 - (2*a^2*c^3 + 5*a*b*c^2 + 3*b^2*c)*d^2*x^4 + 4*a*b*c^4 + 2*b^2*c^3 - (a*b*c^3 + b^2*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^2*c^5 + 2*a*b*c^4 + b^2*c^3)*x^4), 1/16*((4*a*b*c + 3*b^2)*sqrt(-a*c^2 - b*c)*d^2*x^4*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) - 2*(2*a^2*c^5 - (2*a^2*c^3 + 5*a*b*c^2 + 3*b^2*c)*d^2*x^4 + 4*a*b*c^4 + 2*b^2*c^3 - (a*b*c^3 + b^2*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^2*c^5 + 2*a*b*c^4 + b^2*c^3)*x^4)]","A",0
324,1,755,0,1.528959," ","integrate((a+b/(d*x^2+c))^(1/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a^{2} b c^{2} + 12 \, a b^{2} c + 5 \, b^{3}\right)} \sqrt{a c^{2} + b c} d^{3} x^{6} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} + 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(8 \, a^{3} c^{7} + {\left(8 \, a^{3} c^{4} + 34 \, a^{2} b c^{3} + 41 \, a b^{2} c^{2} + 15 \, b^{3} c\right)} d^{3} x^{6} + 24 \, a^{2} b c^{6} + 24 \, a b^{2} c^{5} + 8 \, b^{3} c^{4} + {\left(8 \, a^{2} b c^{4} + 13 \, a b^{2} c^{3} + 5 \, b^{3} c^{2}\right)} d^{2} x^{4} - 2 \, {\left(a^{2} b c^{5} + 2 \, a b^{2} c^{4} + b^{3} c^{3}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{192 \, {\left(a^{3} c^{7} + 3 \, a^{2} b c^{6} + 3 \, a b^{2} c^{5} + b^{3} c^{4}\right)} x^{6}}, -\frac{3 \, {\left(8 \, a^{2} b c^{2} + 12 \, a b^{2} c + 5 \, b^{3}\right)} \sqrt{-a c^{2} - b c} d^{3} x^{6} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{7} + {\left(8 \, a^{3} c^{4} + 34 \, a^{2} b c^{3} + 41 \, a b^{2} c^{2} + 15 \, b^{3} c\right)} d^{3} x^{6} + 24 \, a^{2} b c^{6} + 24 \, a b^{2} c^{5} + 8 \, b^{3} c^{4} + {\left(8 \, a^{2} b c^{4} + 13 \, a b^{2} c^{3} + 5 \, b^{3} c^{2}\right)} d^{2} x^{4} - 2 \, {\left(a^{2} b c^{5} + 2 \, a b^{2} c^{4} + b^{3} c^{3}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{96 \, {\left(a^{3} c^{7} + 3 \, a^{2} b c^{6} + 3 \, a b^{2} c^{5} + b^{3} c^{4}\right)} x^{6}}\right]"," ",0,"[1/192*(3*(8*a^2*b*c^2 + 12*a*b^2*c + 5*b^3)*sqrt(a*c^2 + b*c)*d^3*x^6*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 + 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(8*a^3*c^7 + (8*a^3*c^4 + 34*a^2*b*c^3 + 41*a*b^2*c^2 + 15*b^3*c)*d^3*x^6 + 24*a^2*b*c^6 + 24*a*b^2*c^5 + 8*b^3*c^4 + (8*a^2*b*c^4 + 13*a*b^2*c^3 + 5*b^3*c^2)*d^2*x^4 - 2*(a^2*b*c^5 + 2*a*b^2*c^4 + b^3*c^3)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^3*c^7 + 3*a^2*b*c^6 + 3*a*b^2*c^5 + b^3*c^4)*x^6), -1/96*(3*(8*a^2*b*c^2 + 12*a*b^2*c + 5*b^3)*sqrt(-a*c^2 - b*c)*d^3*x^6*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) + 2*(8*a^3*c^7 + (8*a^3*c^4 + 34*a^2*b*c^3 + 41*a*b^2*c^2 + 15*b^3*c)*d^3*x^6 + 24*a^2*b*c^6 + 24*a*b^2*c^5 + 8*b^3*c^4 + (8*a^2*b*c^4 + 13*a*b^2*c^3 + 5*b^3*c^2)*d^2*x^4 - 2*(a^2*b*c^5 + 2*a*b^2*c^4 + b^3*c^3)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^3*c^7 + 3*a^2*b*c^6 + 3*a*b^2*c^5 + b^3*c^4)*x^6)]","A",0
325,0,0,0,0.719931," ","integrate(x^4*(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}, x\right)"," ",0,"integral(x^4*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)), x)","F",0
326,0,0,0,0.616899," ","integrate(x^2*(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}, x\right)"," ",0,"integral(x^2*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)), x)","F",0
327,0,0,0,0.677920," ","integrate((a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)), x)","F",0
328,0,0,0,0.728074," ","integrate((a+b/(d*x^2+c))^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{2}}, x\right)"," ",0,"integral(sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/x^2, x)","F",0
329,0,0,0,0.668045," ","integrate((a+b/(d*x^2+c))^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}, x\right)"," ",0,"integral(sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/x^4, x)","F",0
330,0,0,0,0.731025," ","integrate((a+b/(d*x^2+c))^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{6}}, x\right)"," ",0,"integral(sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/x^6, x)","F",0
331,1,427,0,0.853015," ","integrate(x^5*(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(24 \, a^{2} b c^{2} - 12 \, a b^{2} c - b^{3}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(8 \, a^{3} d^{3} x^{6} + 14 \, a^{2} b d^{2} x^{4} + 8 \, a^{3} c^{3} - 94 \, a^{2} b c^{2} + 3 \, a b^{2} c - {\left(32 \, a^{2} b c - 3 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{192 \, a^{2} d^{3}}, -\frac{3 \, {\left(24 \, a^{2} b c^{2} - 12 \, a b^{2} c - b^{3}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - 2 \, {\left(8 \, a^{3} d^{3} x^{6} + 14 \, a^{2} b d^{2} x^{4} + 8 \, a^{3} c^{3} - 94 \, a^{2} b c^{2} + 3 \, a b^{2} c - {\left(32 \, a^{2} b c - 3 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{96 \, a^{2} d^{3}}\right]"," ",0,"[1/192*(3*(24*a^2*b*c^2 - 12*a*b^2*c - b^3)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(8*a^3*d^3*x^6 + 14*a^2*b*d^2*x^4 + 8*a^3*c^3 - 94*a^2*b*c^2 + 3*a*b^2*c - (32*a^2*b*c - 3*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^2*d^3), -1/96*(3*(24*a^2*b*c^2 - 12*a*b^2*c - b^3)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - 2*(8*a^3*d^3*x^6 + 14*a^2*b*d^2*x^4 + 8*a^3*c^3 - 94*a^2*b*c^2 + 3*a*b^2*c - (32*a^2*b*c - 3*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^2*d^3)]","A",0
332,1,335,0,0.793870," ","integrate(x^3*(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a b c - b^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} - 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(2 \, a^{2} d^{2} x^{4} + 5 \, a b d x^{2} - 2 \, a^{2} c^{2} + 13 \, a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, a d^{2}}, \frac{3 \, {\left(4 \, a b c - b^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + 2 \, {\left(2 \, a^{2} d^{2} x^{4} + 5 \, a b d x^{2} - 2 \, a^{2} c^{2} + 13 \, a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, a d^{2}}\right]"," ",0,"[1/32*(3*(4*a*b*c - b^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 - 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(2*a^2*d^2*x^4 + 5*a*b*d*x^2 - 2*a^2*c^2 + 13*a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a*d^2), 1/16*(3*(4*a*b*c - b^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 2*(2*a^2*d^2*x^4 + 5*a*b*d*x^2 - 2*a^2*c^2 + 13*a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a*d^2)]","A",0
333,1,269,0,0.613841," ","integrate(x*(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(a d x^{2} + a c - 2 \, b\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, d}, -\frac{3 \, \sqrt{-a} b \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - 2 \, {\left(a d x^{2} + a c - 2 \, b\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, d}\right]"," ",0,"[1/8*(3*sqrt(a)*b*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(a*d*x^2 + a*c - 2*b)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/d, -1/4*(3*sqrt(-a)*b*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - 2*(a*d*x^2 + a*c - 2*b)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/d]","A",0
334,1,1073,0,1.023100," ","integrate((a+b/(d*x^2+c))^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{a^{\frac{3}{2}} c \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + {\left(a c + b\right)} \sqrt{\frac{a c + b}{c}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c^{2} + b c\right)} d^{2} x^{4} + 2 \, a c^{4} + 2 \, b c^{3} + {\left(4 \, a c^{3} + 3 \, b c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{a c + b}{c}}}{x^{4}}\right) + 4 \, b \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, c}, -\frac{2 \, \sqrt{-a} a c \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - {\left(a c + b\right)} \sqrt{\frac{a c + b}{c}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c^{2} + b c\right)} d^{2} x^{4} + 2 \, a c^{4} + 2 \, b c^{3} + {\left(4 \, a c^{3} + 3 \, b c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{a c + b}{c}}}{x^{4}}\right) - 4 \, b \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, c}, \frac{a^{\frac{3}{2}} c \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 2 \, {\left(a c + b\right)} \sqrt{-\frac{a c + b}{c}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{a c + b}{c}}}{2 \, {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)}}\right) + 4 \, b \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, c}, -\frac{\sqrt{-a} a c \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - {\left(a c + b\right)} \sqrt{-\frac{a c + b}{c}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{a c + b}{c}}}{2 \, {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)}}\right) - 2 \, b \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, c}\right]"," ",0,"[1/4*(a^(3/2)*c*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + (a*c + b)*sqrt((a*c + b)/c)*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c^2 + b*c)*d^2*x^4 + 2*a*c^4 + 2*b*c^3 + (4*a*c^3 + 3*b*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt((a*c + b)/c))/x^4) + 4*b*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/c, -1/4*(2*sqrt(-a)*a*c*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - (a*c + b)*sqrt((a*c + b)/c)*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c^2 + b*c)*d^2*x^4 + 2*a*c^4 + 2*b*c^3 + (4*a*c^3 + 3*b*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt((a*c + b)/c))/x^4) - 4*b*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/c, 1/4*(a^(3/2)*c*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 2*(a*c + b)*sqrt(-(a*c + b)/c)*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-(a*c + b)/c)/(a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)) + 4*b*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/c, -1/2*(sqrt(-a)*a*c*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - (a*c + b)*sqrt(-(a*c + b)/c)*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-(a*c + b)/c)/(a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)) - 2*b*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/c]","A",0
335,1,404,0,0.882139," ","integrate((a+b/(d*x^2+c))^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, b d x^{2} \sqrt{\frac{a c + b}{c}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} + 4 \, {\left({\left(2 \, a c^{2} + b c\right)} d^{2} x^{4} + 2 \, a c^{4} + 2 \, b c^{3} + {\left(4 \, a c^{3} + 3 \, b c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{a c + b}{c}}}{x^{4}}\right) - 4 \, {\left({\left(a c + 3 \, b\right)} d x^{2} + a c^{2} + b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, c^{2} x^{2}}, -\frac{3 \, b d x^{2} \sqrt{-\frac{a c + b}{c}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{a c + b}{c}}}{2 \, {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)}}\right) + 2 \, {\left({\left(a c + 3 \, b\right)} d x^{2} + a c^{2} + b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, c^{2} x^{2}}\right]"," ",0,"[1/8*(3*b*d*x^2*sqrt((a*c + b)/c)*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 + 4*((2*a*c^2 + b*c)*d^2*x^4 + 2*a*c^4 + 2*b*c^3 + (4*a*c^3 + 3*b*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt((a*c + b)/c))/x^4) - 4*((a*c + 3*b)*d*x^2 + a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(c^2*x^2), -1/4*(3*b*d*x^2*sqrt(-(a*c + b)/c)*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-(a*c + b)/c)/(a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)) + 2*((a*c + 3*b)*d*x^2 + a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(c^2*x^2)]","A",0
336,1,557,0,1.701580," ","integrate((a+b/(d*x^2+c))^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a b c + 5 \, b^{2}\right)} \sqrt{a c^{2} + b c} d^{2} x^{4} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(2 \, a^{2} c^{5} - {\left(2 \, a^{2} c^{3} + 17 \, a b c^{2} + 15 \, b^{2} c\right)} d^{2} x^{4} + 4 \, a b c^{4} + 2 \, b^{2} c^{3} - 5 \, {\left(a b c^{3} + b^{2} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, {\left(a c^{5} + b c^{4}\right)} x^{4}}, \frac{3 \, {\left(4 \, a b c + 5 \, b^{2}\right)} \sqrt{-a c^{2} - b c} d^{2} x^{4} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{5} - {\left(2 \, a^{2} c^{3} + 17 \, a b c^{2} + 15 \, b^{2} c\right)} d^{2} x^{4} + 4 \, a b c^{4} + 2 \, b^{2} c^{3} - 5 \, {\left(a b c^{3} + b^{2} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, {\left(a c^{5} + b c^{4}\right)} x^{4}}\right]"," ",0,"[1/32*(3*(4*a*b*c + 5*b^2)*sqrt(a*c^2 + b*c)*d^2*x^4*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(2*a^2*c^5 - (2*a^2*c^3 + 17*a*b*c^2 + 15*b^2*c)*d^2*x^4 + 4*a*b*c^4 + 2*b^2*c^3 - 5*(a*b*c^3 + b^2*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a*c^5 + b*c^4)*x^4), 1/16*(3*(4*a*b*c + 5*b^2)*sqrt(-a*c^2 - b*c)*d^2*x^4*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) - 2*(2*a^2*c^5 - (2*a^2*c^3 + 17*a*b*c^2 + 15*b^2*c)*d^2*x^4 + 4*a*b*c^4 + 2*b^2*c^3 - 5*(a*b*c^3 + b^2*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a*c^5 + b*c^4)*x^4)]","A",0
337,1,733,0,2.312189," ","integrate((a+b/(d*x^2+c))^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(24 \, a^{2} b c^{2} + 60 \, a b^{2} c + 35 \, b^{3}\right)} \sqrt{a c^{2} + b c} d^{3} x^{6} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} + 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(8 \, a^{3} c^{7} + {\left(8 \, a^{3} c^{4} + 118 \, a^{2} b c^{3} + 215 \, a b^{2} c^{2} + 105 \, b^{3} c\right)} d^{3} x^{6} + 24 \, a^{2} b c^{6} + 24 \, a b^{2} c^{5} + 8 \, b^{3} c^{4} + {\left(32 \, a^{2} b c^{4} + 67 \, a b^{2} c^{3} + 35 \, b^{3} c^{2}\right)} d^{2} x^{4} - 14 \, {\left(a^{2} b c^{5} + 2 \, a b^{2} c^{4} + b^{3} c^{3}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{192 \, {\left(a^{2} c^{7} + 2 \, a b c^{6} + b^{2} c^{5}\right)} x^{6}}, -\frac{3 \, {\left(24 \, a^{2} b c^{2} + 60 \, a b^{2} c + 35 \, b^{3}\right)} \sqrt{-a c^{2} - b c} d^{3} x^{6} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{7} + {\left(8 \, a^{3} c^{4} + 118 \, a^{2} b c^{3} + 215 \, a b^{2} c^{2} + 105 \, b^{3} c\right)} d^{3} x^{6} + 24 \, a^{2} b c^{6} + 24 \, a b^{2} c^{5} + 8 \, b^{3} c^{4} + {\left(32 \, a^{2} b c^{4} + 67 \, a b^{2} c^{3} + 35 \, b^{3} c^{2}\right)} d^{2} x^{4} - 14 \, {\left(a^{2} b c^{5} + 2 \, a b^{2} c^{4} + b^{3} c^{3}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{96 \, {\left(a^{2} c^{7} + 2 \, a b c^{6} + b^{2} c^{5}\right)} x^{6}}\right]"," ",0,"[1/192*(3*(24*a^2*b*c^2 + 60*a*b^2*c + 35*b^3)*sqrt(a*c^2 + b*c)*d^3*x^6*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 + 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(8*a^3*c^7 + (8*a^3*c^4 + 118*a^2*b*c^3 + 215*a*b^2*c^2 + 105*b^3*c)*d^3*x^6 + 24*a^2*b*c^6 + 24*a*b^2*c^5 + 8*b^3*c^4 + (32*a^2*b*c^4 + 67*a*b^2*c^3 + 35*b^3*c^2)*d^2*x^4 - 14*(a^2*b*c^5 + 2*a*b^2*c^4 + b^3*c^3)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^2*c^7 + 2*a*b*c^6 + b^2*c^5)*x^6), -1/96*(3*(24*a^2*b*c^2 + 60*a*b^2*c + 35*b^3)*sqrt(-a*c^2 - b*c)*d^3*x^6*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) + 2*(8*a^3*c^7 + (8*a^3*c^4 + 118*a^2*b*c^3 + 215*a*b^2*c^2 + 105*b^3*c)*d^3*x^6 + 24*a^2*b*c^6 + 24*a*b^2*c^5 + 8*b^3*c^4 + (32*a^2*b*c^4 + 67*a*b^2*c^3 + 35*b^3*c^2)*d^2*x^4 - 14*(a^2*b*c^5 + 2*a*b^2*c^4 + b^3*c^3)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^2*c^7 + 2*a*b*c^6 + b^2*c^5)*x^6)]","A",0
338,0,0,0,0.721990," ","integrate(x^4*(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a d x^{6} + {\left(a c + b\right)} x^{4}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{d x^{2} + c}, x\right)"," ",0,"integral((a*d*x^6 + (a*c + b)*x^4)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(d*x^2 + c), x)","F",0
339,0,0,0,0.888864," ","integrate(x^2*(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a d x^{4} + {\left(a c + b\right)} x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{d x^{2} + c}, x\right)"," ",0,"integral((a*d*x^4 + (a*c + b)*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(d*x^2 + c), x)","F",0
340,0,0,0,0.552988," ","integrate((a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a d x^{2} + a c + b\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{d x^{2} + c}, x\right)"," ",0,"integral((a*d*x^2 + a*c + b)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(d*x^2 + c), x)","F",0
341,0,0,0,0.682060," ","integrate((a+b/(d*x^2+c))^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a d x^{2} + a c + b\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{d x^{4} + c x^{2}}, x\right)"," ",0,"integral((a*d*x^2 + a*c + b)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(d*x^4 + c*x^2), x)","F",0
342,0,0,0,0.540431," ","integrate((a+b/(d*x^2+c))^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a d x^{2} + a c + b\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{d x^{6} + c x^{4}}, x\right)"," ",0,"integral((a*d*x^2 + a*c + b)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(d*x^6 + c*x^4), x)","F",0
343,0,0,0,0.494744," ","integrate((a+b/(d*x^2+c))^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a d x^{2} + a c + b\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{d x^{8} + c x^{6}}, x\right)"," ",0,"integral((a*d*x^2 + a*c + b)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(d*x^8 + c*x^6), x)","F",0
344,1,425,0,0.772420," ","integrate(x^5/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a^{2} b c^{2} + 12 \, a b^{2} c + 5 \, b^{3}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} - 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(8 \, a^{3} d^{3} x^{6} - 10 \, a^{2} b d^{2} x^{4} + 8 \, a^{3} c^{3} + 26 \, a^{2} b c^{2} + 15 \, a b^{2} c + {\left(16 \, a^{2} b c + 15 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{192 \, a^{4} d^{3}}, \frac{3 \, {\left(8 \, a^{2} b c^{2} + 12 \, a b^{2} c + 5 \, b^{3}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + 2 \, {\left(8 \, a^{3} d^{3} x^{6} - 10 \, a^{2} b d^{2} x^{4} + 8 \, a^{3} c^{3} + 26 \, a^{2} b c^{2} + 15 \, a b^{2} c + {\left(16 \, a^{2} b c + 15 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{96 \, a^{4} d^{3}}\right]"," ",0,"[1/192*(3*(8*a^2*b*c^2 + 12*a*b^2*c + 5*b^3)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 - 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(8*a^3*d^3*x^6 - 10*a^2*b*d^2*x^4 + 8*a^3*c^3 + 26*a^2*b*c^2 + 15*a*b^2*c + (16*a^2*b*c + 15*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*d^3), 1/96*(3*(8*a^2*b*c^2 + 12*a*b^2*c + 5*b^3)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 2*(8*a^3*d^3*x^6 - 10*a^2*b*d^2*x^4 + 8*a^3*c^3 + 26*a^2*b*c^2 + 15*a*b^2*c + (16*a^2*b*c + 15*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*d^3)]","A",0
345,1,333,0,0.535160," ","integrate(x^3/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a b c + 3 \, b^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(2 \, a^{2} d^{2} x^{4} - 3 \, a b d x^{2} - 2 \, a^{2} c^{2} - 3 \, a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, a^{3} d^{2}}, -\frac{{\left(4 \, a b c + 3 \, b^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - 2 \, {\left(2 \, a^{2} d^{2} x^{4} - 3 \, a b d x^{2} - 2 \, a^{2} c^{2} - 3 \, a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, a^{3} d^{2}}\right]"," ",0,"[1/32*((4*a*b*c + 3*b^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(2*a^2*d^2*x^4 - 3*a*b*d*x^2 - 2*a^2*c^2 - 3*a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^3*d^2), -1/16*((4*a*b*c + 3*b^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - 2*(2*a^2*d^2*x^4 - 3*a*b*d*x^2 - 2*a^2*c^2 - 3*a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^3*d^2)]","A",0
346,1,267,0,0.742030," ","integrate(x/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} - 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(a d x^{2} + a c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, a^{2} d}, \frac{\sqrt{-a} b \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + 2 \, {\left(a d x^{2} + a c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, a^{2} d}\right]"," ",0,"[1/8*(sqrt(a)*b*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 - 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(a*d*x^2 + a*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^2*d), 1/4*(sqrt(-a)*b*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 2*(a*d*x^2 + a*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^2*d)]","A",0
347,1,972,0,0.769564," ","integrate(1/x/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{\frac{c}{a c + b}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a^{2} c^{2} + 3 \, a b c + b^{2}\right)} d^{2} x^{4} + 2 \, a^{2} c^{4} + 4 \, a b c^{3} + 2 \, b^{2} c^{2} + {\left(4 \, a^{2} c^{3} + 7 \, a b c^{2} + 3 \, b^{2} c\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{c}{a c + b}}}{x^{4}}\right) + \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right)}{4 \, a}, \frac{a \sqrt{\frac{c}{a c + b}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a^{2} c^{2} + 3 \, a b c + b^{2}\right)} d^{2} x^{4} + 2 \, a^{2} c^{4} + 4 \, a b c^{3} + 2 \, b^{2} c^{2} + {\left(4 \, a^{2} c^{3} + 7 \, a b c^{2} + 3 \, b^{2} c\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{c}{a c + b}}}{x^{4}}\right) - 2 \, \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right)}{4 \, a}, \frac{2 \, a \sqrt{-\frac{c}{a c + b}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{c}{a c + b}}}{2 \, {\left(a c d x^{2} + a c^{2} + b c\right)}}\right) + \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right)}{4 \, a}, \frac{a \sqrt{-\frac{c}{a c + b}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{c}{a c + b}}}{2 \, {\left(a c d x^{2} + a c^{2} + b c\right)}}\right) - \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*(a*sqrt(c/(a*c + b))*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a^2*c^2 + 3*a*b*c + b^2)*d^2*x^4 + 2*a^2*c^4 + 4*a*b*c^3 + 2*b^2*c^2 + (4*a^2*c^3 + 7*a*b*c^2 + 3*b^2*c)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(c/(a*c + b)))/x^4) + sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))))/a, 1/4*(a*sqrt(c/(a*c + b))*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a^2*c^2 + 3*a*b*c + b^2)*d^2*x^4 + 2*a^2*c^4 + 4*a*b*c^3 + 2*b^2*c^2 + (4*a^2*c^3 + 7*a*b*c^2 + 3*b^2*c)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(c/(a*c + b)))/x^4) - 2*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)))/a, 1/4*(2*a*sqrt(-c/(a*c + b))*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-c/(a*c + b))/(a*c*d*x^2 + a*c^2 + b*c)) + sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))))/a, 1/2*(a*sqrt(-c/(a*c + b))*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-c/(a*c + b))/(a*c*d*x^2 + a*c^2 + b*c)) - sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)))/a]","B",0
348,1,451,0,0.890481," ","integrate(1/x^3/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c^{2} + b c} b d x^{2} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(a c^{3} + {\left(a c^{2} + b c\right)} d x^{2} + b c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + b^{2} c\right)} x^{2}}, \frac{\sqrt{-a c^{2} - b c} b d x^{2} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) - 2 \, {\left(a c^{3} + {\left(a c^{2} + b c\right)} d x^{2} + b c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + b^{2} c\right)} x^{2}}\right]"," ",0,"[1/8*(sqrt(a*c^2 + b*c)*b*d*x^2*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(a*c^3 + (a*c^2 + b*c)*d*x^2 + b*c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^2*c^3 + 2*a*b*c^2 + b^2*c)*x^2), 1/4*(sqrt(-a*c^2 - b*c)*b*d*x^2*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) - 2*(a*c^3 + (a*c^2 + b*c)*d*x^2 + b*c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^2*c^3 + 2*a*b*c^2 + b^2*c)*x^2)]","B",0
349,1,593,0,1.021971," ","integrate(1/x^5/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a b c + b^{2}\right)} \sqrt{a c^{2} + b c} d^{2} x^{4} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} + 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) - 4 \, {\left(2 \, a^{2} c^{5} - {\left(2 \, a^{2} c^{3} + a b c^{2} - b^{2} c\right)} d^{2} x^{4} + 4 \, a b c^{4} + 2 \, b^{2} c^{3} + 3 \, {\left(a b c^{3} + b^{2} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, {\left(a^{3} c^{5} + 3 \, a^{2} b c^{4} + 3 \, a b^{2} c^{3} + b^{3} c^{2}\right)} x^{4}}, -\frac{{\left(4 \, a b c + b^{2}\right)} \sqrt{-a c^{2} - b c} d^{2} x^{4} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{5} - {\left(2 \, a^{2} c^{3} + a b c^{2} - b^{2} c\right)} d^{2} x^{4} + 4 \, a b c^{4} + 2 \, b^{2} c^{3} + 3 \, {\left(a b c^{3} + b^{2} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, {\left(a^{3} c^{5} + 3 \, a^{2} b c^{4} + 3 \, a b^{2} c^{3} + b^{3} c^{2}\right)} x^{4}}\right]"," ",0,"[1/32*((4*a*b*c + b^2)*sqrt(a*c^2 + b*c)*d^2*x^4*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 + 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) - 4*(2*a^2*c^5 - (2*a^2*c^3 + a*b*c^2 - b^2*c)*d^2*x^4 + 4*a*b*c^4 + 2*b^2*c^3 + 3*(a*b*c^3 + b^2*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^3*c^5 + 3*a^2*b*c^4 + 3*a*b^2*c^3 + b^3*c^2)*x^4), -1/16*((4*a*b*c + b^2)*sqrt(-a*c^2 - b*c)*d^2*x^4*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) + 2*(2*a^2*c^5 - (2*a^2*c^3 + a*b*c^2 - b^2*c)*d^2*x^4 + 4*a*b*c^4 + 2*b^2*c^3 + 3*(a*b*c^3 + b^2*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^3*c^5 + 3*a^2*b*c^4 + 3*a*b^2*c^3 + b^3*c^2)*x^4)]","A",0
350,0,0,0,0.681605," ","integrate(x^4/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{6} + c x^{4}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a d x^{2} + a c + b}, x\right)"," ",0,"integral((d*x^6 + c*x^4)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a*d*x^2 + a*c + b), x)","F",0
351,0,0,0,0.686203," ","integrate(x^2/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{4} + c x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a d x^{2} + a c + b}, x\right)"," ",0,"integral((d*x^4 + c*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a*d*x^2 + a*c + b), x)","F",0
352,0,0,0,0.555422," ","integrate(1/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a d x^{2} + a c + b}, x\right)"," ",0,"integral((d*x^2 + c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a*d*x^2 + a*c + b), x)","F",0
353,0,0,0,0.669851," ","integrate(1/x^2/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a d x^{4} + {\left(a c + b\right)} x^{2}}, x\right)"," ",0,"integral((d*x^2 + c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a*d*x^4 + (a*c + b)*x^2), x)","F",0
354,0,0,0,0.566711," ","integrate(1/x^4/(a+b/(d*x^2+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a d x^{6} + {\left(a c + b\right)} x^{4}}, x\right)"," ",0,"integral((d*x^2 + c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a*d*x^6 + (a*c + b)*x^4), x)","F",0
355,1,675,0,0.842352," ","integrate(x^5/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(24 \, a^{3} b c^{3} + 84 \, a^{2} b^{2} c^{2} + 95 \, a b^{3} c + 35 \, b^{4} + {\left(24 \, a^{3} b c^{2} + 60 \, a^{2} b^{2} c + 35 \, a b^{3}\right)} d x^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} - 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(8 \, a^{4} d^{4} x^{8} + 2 \, {\left(4 \, a^{4} c - 7 \, a^{3} b\right)} d^{3} x^{6} + 8 \, a^{4} c^{4} + 118 \, a^{3} b c^{3} + {\left(18 \, a^{3} b c + 35 \, a^{2} b^{2}\right)} d^{2} x^{4} + 215 \, a^{2} b^{2} c^{2} + 105 \, a b^{3} c + {\left(8 \, a^{4} c^{3} + 150 \, a^{3} b c^{2} + 250 \, a^{2} b^{2} c + 105 \, a b^{3}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{192 \, {\left(a^{6} d^{4} x^{2} + {\left(a^{6} c + a^{5} b\right)} d^{3}\right)}}, \frac{3 \, {\left(24 \, a^{3} b c^{3} + 84 \, a^{2} b^{2} c^{2} + 95 \, a b^{3} c + 35 \, b^{4} + {\left(24 \, a^{3} b c^{2} + 60 \, a^{2} b^{2} c + 35 \, a b^{3}\right)} d x^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + 2 \, {\left(8 \, a^{4} d^{4} x^{8} + 2 \, {\left(4 \, a^{4} c - 7 \, a^{3} b\right)} d^{3} x^{6} + 8 \, a^{4} c^{4} + 118 \, a^{3} b c^{3} + {\left(18 \, a^{3} b c + 35 \, a^{2} b^{2}\right)} d^{2} x^{4} + 215 \, a^{2} b^{2} c^{2} + 105 \, a b^{3} c + {\left(8 \, a^{4} c^{3} + 150 \, a^{3} b c^{2} + 250 \, a^{2} b^{2} c + 105 \, a b^{3}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{96 \, {\left(a^{6} d^{4} x^{2} + {\left(a^{6} c + a^{5} b\right)} d^{3}\right)}}\right]"," ",0,"[1/192*(3*(24*a^3*b*c^3 + 84*a^2*b^2*c^2 + 95*a*b^3*c + 35*b^4 + (24*a^3*b*c^2 + 60*a^2*b^2*c + 35*a*b^3)*d*x^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 - 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(8*a^4*d^4*x^8 + 2*(4*a^4*c - 7*a^3*b)*d^3*x^6 + 8*a^4*c^4 + 118*a^3*b*c^3 + (18*a^3*b*c + 35*a^2*b^2)*d^2*x^4 + 215*a^2*b^2*c^2 + 105*a*b^3*c + (8*a^4*c^3 + 150*a^3*b*c^2 + 250*a^2*b^2*c + 105*a*b^3)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^6*d^4*x^2 + (a^6*c + a^5*b)*d^3), 1/96*(3*(24*a^3*b*c^3 + 84*a^2*b^2*c^2 + 95*a*b^3*c + 35*b^4 + (24*a^3*b*c^2 + 60*a^2*b^2*c + 35*a*b^3)*d*x^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 2*(8*a^4*d^4*x^8 + 2*(4*a^4*c - 7*a^3*b)*d^3*x^6 + 8*a^4*c^4 + 118*a^3*b*c^3 + (18*a^3*b*c + 35*a^2*b^2)*d^2*x^4 + 215*a^2*b^2*c^2 + 105*a*b^3*c + (8*a^4*c^3 + 150*a^3*b*c^2 + 250*a^2*b^2*c + 105*a*b^3)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^6*d^4*x^2 + (a^6*c + a^5*b)*d^3)]","A",0
356,1,541,0,0.842095," ","integrate(x^3/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a^{2} b c^{2} + 9 \, a b^{2} c + {\left(4 \, a^{2} b c + 5 \, a b^{2}\right)} d x^{2} + 5 \, b^{3}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(2 \, a^{3} d^{3} x^{6} + {\left(2 \, a^{3} c - 5 \, a^{2} b\right)} d^{2} x^{4} - 2 \, a^{3} c^{3} - 17 \, a^{2} b c^{2} - 15 \, a b^{2} c - {\left(2 \, a^{3} c^{2} + 22 \, a^{2} b c + 15 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, {\left(a^{5} d^{3} x^{2} + {\left(a^{5} c + a^{4} b\right)} d^{2}\right)}}, -\frac{3 \, {\left(4 \, a^{2} b c^{2} + 9 \, a b^{2} c + {\left(4 \, a^{2} b c + 5 \, a b^{2}\right)} d x^{2} + 5 \, b^{3}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - 2 \, {\left(2 \, a^{3} d^{3} x^{6} + {\left(2 \, a^{3} c - 5 \, a^{2} b\right)} d^{2} x^{4} - 2 \, a^{3} c^{3} - 17 \, a^{2} b c^{2} - 15 \, a b^{2} c - {\left(2 \, a^{3} c^{2} + 22 \, a^{2} b c + 15 \, a b^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, {\left(a^{5} d^{3} x^{2} + {\left(a^{5} c + a^{4} b\right)} d^{2}\right)}}\right]"," ",0,"[1/32*(3*(4*a^2*b*c^2 + 9*a*b^2*c + (4*a^2*b*c + 5*a*b^2)*d*x^2 + 5*b^3)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(2*a^3*d^3*x^6 + (2*a^3*c - 5*a^2*b)*d^2*x^4 - 2*a^3*c^3 - 17*a^2*b*c^2 - 15*a*b^2*c - (2*a^3*c^2 + 22*a^2*b*c + 15*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^5*d^3*x^2 + (a^5*c + a^4*b)*d^2), -1/16*(3*(4*a^2*b*c^2 + 9*a*b^2*c + (4*a^2*b*c + 5*a*b^2)*d*x^2 + 5*b^3)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - 2*(2*a^3*d^3*x^6 + (2*a^3*c - 5*a^2*b)*d^2*x^4 - 2*a^3*c^3 - 17*a^2*b*c^2 - 15*a*b^2*c - (2*a^3*c^2 + 22*a^2*b*c + 15*a*b^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^5*d^3*x^2 + (a^5*c + a^4*b)*d^2)]","A",0
357,1,395,0,0.891803," ","integrate(x/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b d x^{2} + a b c + b^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} - 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + 4 \, {\left(a^{2} d^{2} x^{4} + a^{2} c^{2} + {\left(2 \, a^{2} c + 3 \, a b\right)} d x^{2} + 3 \, a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, {\left(a^{4} d^{2} x^{2} + {\left(a^{4} c + a^{3} b\right)} d\right)}}, \frac{3 \, {\left(a b d x^{2} + a b c + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) + 2 \, {\left(a^{2} d^{2} x^{4} + a^{2} c^{2} + {\left(2 \, a^{2} c + 3 \, a b\right)} d x^{2} + 3 \, a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left(a^{4} d^{2} x^{2} + {\left(a^{4} c + a^{3} b\right)} d\right)}}\right]"," ",0,"[1/8*(3*(a*b*d*x^2 + a*b*c + b^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 - 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + 4*(a^2*d^2*x^4 + a^2*c^2 + (2*a^2*c + 3*a*b)*d*x^2 + 3*a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*d^2*x^2 + (a^4*c + a^3*b)*d), 1/4*(3*(a*b*d*x^2 + a*b*c + b^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) + 2*(a^2*d^2*x^4 + a^2*c^2 + (2*a^2*c + 3*a*b)*d*x^2 + 3*a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*d^2*x^2 + (a^4*c + a^3*b)*d)]","B",0
358,1,1477,0,1.016118," ","integrate(1/x/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) + {\left(a^{3} c d x^{2} + a^{3} c^{2} + a^{2} b c\right)} \sqrt{\frac{c}{a c + b}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a^{2} c^{2} + 3 \, a b c + b^{2}\right)} d^{2} x^{4} + 2 \, a^{2} c^{4} + 4 \, a b c^{3} + 2 \, b^{2} c^{2} + {\left(4 \, a^{2} c^{3} + 7 \, a b c^{2} + 3 \, b^{2} c\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{c}{a c + b}}}{x^{4}}\right) - 4 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left(a^{4} c^{2} + 2 \, a^{3} b c + a^{2} b^{2} + {\left(a^{4} c + a^{3} b\right)} d x^{2}\right)}}, -\frac{2 \, {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - {\left(a^{3} c d x^{2} + a^{3} c^{2} + a^{2} b c\right)} \sqrt{\frac{c}{a c + b}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a^{2} c^{2} + 3 \, a b c + b^{2}\right)} d^{2} x^{4} + 2 \, a^{2} c^{4} + 4 \, a b c^{3} + 2 \, b^{2} c^{2} + {\left(4 \, a^{2} c^{3} + 7 \, a b c^{2} + 3 \, b^{2} c\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{c}{a c + b}}}{x^{4}}\right) + 4 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left(a^{4} c^{2} + 2 \, a^{3} b c + a^{2} b^{2} + {\left(a^{4} c + a^{3} b\right)} d x^{2}\right)}}, \frac{2 \, {\left(a^{3} c d x^{2} + a^{3} c^{2} + a^{2} b c\right)} \sqrt{-\frac{c}{a c + b}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{c}{a c + b}}}{2 \, {\left(a c d x^{2} + a c^{2} + b c\right)}}\right) + {\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)} \sqrt{a} \log\left(8 \, a^{2} d^{2} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(2 \, a^{2} c + a b\right)} d x^{2} + 8 \, a b c + b^{2} + 4 \, {\left(2 \, a d^{2} x^{4} + {\left(4 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + b c\right)} \sqrt{a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}\right) - 4 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left(a^{4} c^{2} + 2 \, a^{3} b c + a^{2} b^{2} + {\left(a^{4} c + a^{3} b\right)} d x^{2}\right)}}, -\frac{{\left(a^{2} c^{2} + {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a d x^{2} + 2 \, a c + b\right)} \sqrt{-a} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} d x^{2} + a^{2} c + a b\right)}}\right) - {\left(a^{3} c d x^{2} + a^{3} c^{2} + a^{2} b c\right)} \sqrt{-\frac{c}{a c + b}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{c}{a c + b}}}{2 \, {\left(a c d x^{2} + a c^{2} + b c\right)}}\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{4} c^{2} + 2 \, a^{3} b c + a^{2} b^{2} + {\left(a^{4} c + a^{3} b\right)} d x^{2}\right)}}\right]"," ",0,"[1/4*((a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) + (a^3*c*d*x^2 + a^3*c^2 + a^2*b*c)*sqrt(c/(a*c + b))*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a^2*c^2 + 3*a*b*c + b^2)*d^2*x^4 + 2*a^2*c^4 + 4*a*b*c^3 + 2*b^2*c^2 + (4*a^2*c^3 + 7*a*b*c^2 + 3*b^2*c)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(c/(a*c + b)))/x^4) - 4*(a*b*d*x^2 + a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*c^2 + 2*a^3*b*c + a^2*b^2 + (a^4*c + a^3*b)*d*x^2), -1/4*(2*(a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - (a^3*c*d*x^2 + a^3*c^2 + a^2*b*c)*sqrt(c/(a*c + b))*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a^2*c^2 + 3*a*b*c + b^2)*d^2*x^4 + 2*a^2*c^4 + 4*a*b*c^3 + 2*b^2*c^2 + (4*a^2*c^3 + 7*a*b*c^2 + 3*b^2*c)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(c/(a*c + b)))/x^4) + 4*(a*b*d*x^2 + a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*c^2 + 2*a^3*b*c + a^2*b^2 + (a^4*c + a^3*b)*d*x^2), 1/4*(2*(a^3*c*d*x^2 + a^3*c^2 + a^2*b*c)*sqrt(-c/(a*c + b))*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-c/(a*c + b))/(a*c*d*x^2 + a*c^2 + b*c)) + (a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)*sqrt(a)*log(8*a^2*d^2*x^4 + 8*a^2*c^2 + 8*(2*a^2*c + a*b)*d*x^2 + 8*a*b*c + b^2 + 4*(2*a*d^2*x^4 + (4*a*c + b)*d*x^2 + 2*a*c^2 + b*c)*sqrt(a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))) - 4*(a*b*d*x^2 + a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*c^2 + 2*a^3*b*c + a^2*b^2 + (a^4*c + a^3*b)*d*x^2), -1/2*((a^2*c^2 + (a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2)*sqrt(-a)*arctan(1/2*(2*a*d*x^2 + 2*a*c + b)*sqrt(-a)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d*x^2 + a^2*c + a*b)) - (a^3*c*d*x^2 + a^3*c^2 + a^2*b*c)*sqrt(-c/(a*c + b))*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-c/(a*c + b))/(a*c*d*x^2 + a*c^2 + b*c)) + 2*(a*b*d*x^2 + a*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/(a^4*c^2 + 2*a^3*b*c + a^2*b^2 + (a^4*c + a^3*b)*d*x^2)]","B",0
359,1,599,0,0.773746," ","integrate(1/x^3/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b d^{2} x^{4} + {\left(a b c + b^{2}\right)} d x^{2}\right)} \sqrt{\frac{c}{a c + b}} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} - 4 \, {\left({\left(2 \, a^{2} c^{2} + 3 \, a b c + b^{2}\right)} d^{2} x^{4} + 2 \, a^{2} c^{4} + 4 \, a b c^{3} + 2 \, b^{2} c^{2} + {\left(4 \, a^{2} c^{3} + 7 \, a b c^{2} + 3 \, b^{2} c\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{\frac{c}{a c + b}}}{x^{4}}\right) - 4 \, {\left({\left(a c - 2 \, b\right)} d^{2} x^{4} + a c^{3} + {\left(2 \, a c^{2} - b c\right)} d x^{2} + b c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{8 \, {\left({\left(a^{3} c^{2} + 2 \, a^{2} b c + a b^{2}\right)} d x^{4} + {\left(a^{3} c^{3} + 3 \, a^{2} b c^{2} + 3 \, a b^{2} c + b^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left(a b d^{2} x^{4} + {\left(a b c + b^{2}\right)} d x^{2}\right)} \sqrt{-\frac{c}{a c + b}} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}} \sqrt{-\frac{c}{a c + b}}}{2 \, {\left(a c d x^{2} + a c^{2} + b c\right)}}\right) - 2 \, {\left({\left(a c - 2 \, b\right)} d^{2} x^{4} + a c^{3} + {\left(2 \, a c^{2} - b c\right)} d x^{2} + b c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{4 \, {\left({\left(a^{3} c^{2} + 2 \, a^{2} b c + a b^{2}\right)} d x^{4} + {\left(a^{3} c^{3} + 3 \, a^{2} b c^{2} + 3 \, a b^{2} c + b^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*(a*b*d^2*x^4 + (a*b*c + b^2)*d*x^2)*sqrt(c/(a*c + b))*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 - 4*((2*a^2*c^2 + 3*a*b*c + b^2)*d^2*x^4 + 2*a^2*c^4 + 4*a*b*c^3 + 2*b^2*c^2 + (4*a^2*c^3 + 7*a*b*c^2 + 3*b^2*c)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(c/(a*c + b)))/x^4) - 4*((a*c - 2*b)*d^2*x^4 + a*c^3 + (2*a*c^2 - b*c)*d*x^2 + b*c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^3*c^2 + 2*a^2*b*c + a*b^2)*d*x^4 + (a^3*c^3 + 3*a^2*b*c^2 + 3*a*b^2*c + b^3)*x^2), 1/4*(3*(a*b*d^2*x^4 + (a*b*c + b^2)*d*x^2)*sqrt(-c/(a*c + b))*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))*sqrt(-c/(a*c + b))/(a*c*d*x^2 + a*c^2 + b*c)) - 2*((a*c - 2*b)*d^2*x^4 + a*c^3 + (2*a*c^2 - b*c)*d*x^2 + b*c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^3*c^2 + 2*a^2*b*c + a*b^2)*d*x^4 + (a^3*c^3 + 3*a^2*b*c^2 + 3*a*b^2*c + b^3)*x^2)]","A",0
360,1,961,0,1.427676," ","integrate(1/x^5/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(4 \, a^{2} b c - a b^{2}\right)} d^{3} x^{6} + {\left(4 \, a^{2} b c^{2} + 3 \, a b^{2} c - b^{3}\right)} d^{2} x^{4}\right)} \sqrt{a c^{2} + b c} \log\left(\frac{{\left(8 \, a^{2} c^{2} + 8 \, a b c + b^{2}\right)} d^{2} x^{4} + 8 \, a^{2} c^{4} + 16 \, a b c^{3} + 8 \, b^{2} c^{2} + 8 \, {\left(2 \, a^{2} c^{3} + 3 \, a b c^{2} + b^{2} c\right)} d x^{2} + 4 \, {\left({\left(2 \, a c + b\right)} d^{2} x^{4} + 2 \, a c^{3} + {\left(4 \, a c^{2} + 3 \, b c\right)} d x^{2} + 2 \, b c^{2}\right)} \sqrt{a c^{2} + b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{x^{4}}\right) + 4 \, {\left({\left(2 \, a^{3} c^{3} - 11 \, a^{2} b c^{2} - 13 \, a b^{2} c\right)} d^{3} x^{6} - 2 \, a^{3} c^{6} - 6 \, a^{2} b c^{5} - 6 \, a b^{2} c^{4} + {\left(2 \, a^{3} c^{4} - 16 \, a^{2} b c^{3} - 23 \, a b^{2} c^{2} - 5 \, b^{3} c\right)} d^{2} x^{4} - 2 \, b^{3} c^{3} - {\left(2 \, a^{3} c^{5} + 11 \, a^{2} b c^{4} + 16 \, a b^{2} c^{3} + 7 \, b^{3} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{32 \, {\left({\left(a^{5} c^{5} + 4 \, a^{4} b c^{4} + 6 \, a^{3} b^{2} c^{3} + 4 \, a^{2} b^{3} c^{2} + a b^{4} c\right)} d x^{6} + {\left(a^{5} c^{6} + 5 \, a^{4} b c^{5} + 10 \, a^{3} b^{2} c^{4} + 10 \, a^{2} b^{3} c^{3} + 5 \, a b^{4} c^{2} + b^{5} c\right)} x^{4}\right)}}, -\frac{3 \, {\left({\left(4 \, a^{2} b c - a b^{2}\right)} d^{3} x^{6} + {\left(4 \, a^{2} b c^{2} + 3 \, a b^{2} c - b^{3}\right)} d^{2} x^{4}\right)} \sqrt{-a c^{2} - b c} \arctan\left(\frac{{\left({\left(2 \, a c + b\right)} d x^{2} + 2 \, a c^{2} + 2 \, b c\right)} \sqrt{-a c^{2} - b c} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{2 \, {\left(a^{2} c^{3} + 2 \, a b c^{2} + {\left(a^{2} c^{2} + a b c\right)} d x^{2} + b^{2} c\right)}}\right) - 2 \, {\left({\left(2 \, a^{3} c^{3} - 11 \, a^{2} b c^{2} - 13 \, a b^{2} c\right)} d^{3} x^{6} - 2 \, a^{3} c^{6} - 6 \, a^{2} b c^{5} - 6 \, a b^{2} c^{4} + {\left(2 \, a^{3} c^{4} - 16 \, a^{2} b c^{3} - 23 \, a b^{2} c^{2} - 5 \, b^{3} c\right)} d^{2} x^{4} - 2 \, b^{3} c^{3} - {\left(2 \, a^{3} c^{5} + 11 \, a^{2} b c^{4} + 16 \, a b^{2} c^{3} + 7 \, b^{3} c^{2}\right)} d x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{16 \, {\left({\left(a^{5} c^{5} + 4 \, a^{4} b c^{4} + 6 \, a^{3} b^{2} c^{3} + 4 \, a^{2} b^{3} c^{2} + a b^{4} c\right)} d x^{6} + {\left(a^{5} c^{6} + 5 \, a^{4} b c^{5} + 10 \, a^{3} b^{2} c^{4} + 10 \, a^{2} b^{3} c^{3} + 5 \, a b^{4} c^{2} + b^{5} c\right)} x^{4}\right)}}\right]"," ",0,"[1/32*(3*((4*a^2*b*c - a*b^2)*d^3*x^6 + (4*a^2*b*c^2 + 3*a*b^2*c - b^3)*d^2*x^4)*sqrt(a*c^2 + b*c)*log(((8*a^2*c^2 + 8*a*b*c + b^2)*d^2*x^4 + 8*a^2*c^4 + 16*a*b*c^3 + 8*b^2*c^2 + 8*(2*a^2*c^3 + 3*a*b*c^2 + b^2*c)*d*x^2 + 4*((2*a*c + b)*d^2*x^4 + 2*a*c^3 + (4*a*c^2 + 3*b*c)*d*x^2 + 2*b*c^2)*sqrt(a*c^2 + b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/x^4) + 4*((2*a^3*c^3 - 11*a^2*b*c^2 - 13*a*b^2*c)*d^3*x^6 - 2*a^3*c^6 - 6*a^2*b*c^5 - 6*a*b^2*c^4 + (2*a^3*c^4 - 16*a^2*b*c^3 - 23*a*b^2*c^2 - 5*b^3*c)*d^2*x^4 - 2*b^3*c^3 - (2*a^3*c^5 + 11*a^2*b*c^4 + 16*a*b^2*c^3 + 7*b^3*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^5*c^5 + 4*a^4*b*c^4 + 6*a^3*b^2*c^3 + 4*a^2*b^3*c^2 + a*b^4*c)*d*x^6 + (a^5*c^6 + 5*a^4*b*c^5 + 10*a^3*b^2*c^4 + 10*a^2*b^3*c^3 + 5*a*b^4*c^2 + b^5*c)*x^4), -1/16*(3*((4*a^2*b*c - a*b^2)*d^3*x^6 + (4*a^2*b*c^2 + 3*a*b^2*c - b^3)*d^2*x^4)*sqrt(-a*c^2 - b*c)*arctan(1/2*((2*a*c + b)*d*x^2 + 2*a*c^2 + 2*b*c)*sqrt(-a*c^2 - b*c)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*c^3 + 2*a*b*c^2 + (a^2*c^2 + a*b*c)*d*x^2 + b^2*c)) - 2*((2*a^3*c^3 - 11*a^2*b*c^2 - 13*a*b^2*c)*d^3*x^6 - 2*a^3*c^6 - 6*a^2*b*c^5 - 6*a*b^2*c^4 + (2*a^3*c^4 - 16*a^2*b*c^3 - 23*a*b^2*c^2 - 5*b^3*c)*d^2*x^4 - 2*b^3*c^3 - (2*a^3*c^5 + 11*a^2*b*c^4 + 16*a*b^2*c^3 + 7*b^3*c^2)*d*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c)))/((a^5*c^5 + 4*a^4*b*c^4 + 6*a^3*b^2*c^3 + 4*a^2*b^3*c^2 + a*b^4*c)*d*x^6 + (a^5*c^6 + 5*a^4*b*c^5 + 10*a^3*b^2*c^4 + 10*a^2*b^3*c^3 + 5*a*b^4*c^2 + b^5*c)*x^4)]","B",0
361,0,0,0,0.726644," ","integrate(x^4/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{8} + 2 \, c d x^{6} + c^{2} x^{4}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a^{2} d^{2} x^{4} + a^{2} c^{2} + 2 \, {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}}, x\right)"," ",0,"integral((d^2*x^8 + 2*c*d*x^6 + c^2*x^4)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d^2*x^4 + a^2*c^2 + 2*(a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2), x)","F",0
362,0,0,0,0.592406," ","integrate(x^2/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{6} + 2 \, c d x^{4} + c^{2} x^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a^{2} d^{2} x^{4} + a^{2} c^{2} + 2 \, {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}}, x\right)"," ",0,"integral((d^2*x^6 + 2*c*d*x^4 + c^2*x^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d^2*x^4 + a^2*c^2 + 2*(a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2), x)","F",0
363,0,0,0,0.635654," ","integrate(1/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a^{2} d^{2} x^{4} + a^{2} c^{2} + 2 \, {\left(a^{2} c + a b\right)} d x^{2} + 2 \, a b c + b^{2}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d^2*x^4 + a^2*c^2 + 2*(a^2*c + a*b)*d*x^2 + 2*a*b*c + b^2), x)","F",0
364,0,0,0,0.615516," ","integrate(1/x^2/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a^{2} d^{2} x^{6} + 2 \, {\left(a^{2} c + a b\right)} d x^{4} + {\left(a^{2} c^{2} + 2 \, a b c + b^{2}\right)} x^{2}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d^2*x^6 + 2*(a^2*c + a*b)*d*x^4 + (a^2*c^2 + 2*a*b*c + b^2)*x^2), x)","F",0
365,0,0,0,0.643702," ","integrate(1/x^4/(a+b/(d*x^2+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} \sqrt{\frac{a d x^{2} + a c + b}{d x^{2} + c}}}{a^{2} d^{2} x^{8} + 2 \, {\left(a^{2} c + a b\right)} d x^{6} + {\left(a^{2} c^{2} + 2 \, a b c + b^{2}\right)} x^{4}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*sqrt((a*d*x^2 + a*c + b)/(d*x^2 + c))/(a^2*d^2*x^8 + 2*(a^2*c + a*b)*d*x^6 + (a^2*c^2 + 2*a*b*c + b^2)*x^4), x)","F",0
366,1,169,0,0.803368," ","integrate((a*x^23)^(1/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} x^{9} \log\left(-\frac{8 \, a x^{19} + 8 \, a x^{14} + a x^{9} + 4 \, \sqrt{a x^{23}} {\left(2 \, x^{5} + 1\right)} \sqrt{x^{5} + 1} \sqrt{a}}{x^{9}}\right) + 4 \, \sqrt{a x^{23}} {\left(2 \, x^{5} - 3\right)} \sqrt{x^{5} + 1}}{80 \, x^{9}}, -\frac{3 \, \sqrt{-a} x^{9} \arctan\left(\frac{\sqrt{a x^{23}} {\left(2 \, x^{5} + 1\right)} \sqrt{x^{5} + 1} \sqrt{-a}}{2 \, {\left(a x^{19} + a x^{14}\right)}}\right) - 2 \, \sqrt{a x^{23}} {\left(2 \, x^{5} - 3\right)} \sqrt{x^{5} + 1}}{40 \, x^{9}}\right]"," ",0,"[1/80*(3*sqrt(a)*x^9*log(-(8*a*x^19 + 8*a*x^14 + a*x^9 + 4*sqrt(a*x^23)*(2*x^5 + 1)*sqrt(x^5 + 1)*sqrt(a))/x^9) + 4*sqrt(a*x^23)*(2*x^5 - 3)*sqrt(x^5 + 1))/x^9, -1/40*(3*sqrt(-a)*x^9*arctan(1/2*sqrt(a*x^23)*(2*x^5 + 1)*sqrt(x^5 + 1)*sqrt(-a)/(a*x^19 + a*x^14)) - 2*sqrt(a*x^23)*(2*x^5 - 3)*sqrt(x^5 + 1))/x^9]","A",0
367,1,153,0,1.085905," ","integrate((a*x^13)^(1/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} x^{4} \log\left(-\frac{8 \, a x^{14} + 8 \, a x^{9} + a x^{4} - 4 \, \sqrt{a x^{13}} {\left(2 \, x^{5} + 1\right)} \sqrt{x^{5} + 1} \sqrt{a}}{x^{4}}\right) + 4 \, \sqrt{a x^{13}} \sqrt{x^{5} + 1}}{20 \, x^{4}}, \frac{\sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{a x^{13}} {\left(2 \, x^{5} + 1\right)} \sqrt{x^{5} + 1} \sqrt{-a}}{2 \, {\left(a x^{14} + a x^{9}\right)}}\right) + 2 \, \sqrt{a x^{13}} \sqrt{x^{5} + 1}}{10 \, x^{4}}\right]"," ",0,"[1/20*(sqrt(a)*x^4*log(-(8*a*x^14 + 8*a*x^9 + a*x^4 - 4*sqrt(a*x^13)*(2*x^5 + 1)*sqrt(x^5 + 1)*sqrt(a))/x^4) + 4*sqrt(a*x^13)*sqrt(x^5 + 1))/x^4, 1/10*(sqrt(-a)*x^4*arctan(1/2*sqrt(a*x^13)*(2*x^5 + 1)*sqrt(x^5 + 1)*sqrt(-a)/(a*x^14 + a*x^9)) + 2*sqrt(a*x^13)*sqrt(x^5 + 1))/x^4]","B",0
368,1,98,0,0.827690," ","integrate((a*x^3)^(1/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{10} \, \sqrt{a} \log\left(-8 \, a x^{10} - 8 \, a x^{5} - 4 \, {\left(2 \, x^{6} + x\right)} \sqrt{x^{5} + 1} \sqrt{a x^{3}} \sqrt{a} - a\right), -\frac{1}{5} \, \sqrt{-a} \arctan\left(\frac{{\left(2 \, x^{5} + 1\right)} \sqrt{x^{5} + 1} \sqrt{a x^{3}} \sqrt{-a}}{2 \, {\left(a x^{9} + a x^{4}\right)}}\right)\right]"," ",0,"[1/10*sqrt(a)*log(-8*a*x^10 - 8*a*x^5 - 4*(2*x^6 + x)*sqrt(x^5 + 1)*sqrt(a*x^3)*sqrt(a) - a), -1/5*sqrt(-a)*arctan(1/2*(2*x^5 + 1)*sqrt(x^5 + 1)*sqrt(a*x^3)*sqrt(-a)/(a*x^9 + a*x^4))]","B",0
369,1,17,0,0.600862," ","integrate((a/x^7)^(1/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{5} \, \sqrt{x^{5} + 1} x \sqrt{\frac{a}{x^{7}}}"," ",0,"-2/5*sqrt(x^5 + 1)*x*sqrt(a/x^7)","A",0
370,1,25,0,0.522622," ","integrate((a/x^17)^(1/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(2 \, x^{6} - x\right)} \sqrt{x^{5} + 1} \sqrt{\frac{a}{x^{17}}}"," ",0,"2/15*(2*x^6 - x)*sqrt(x^5 + 1)*sqrt(a/x^17)","A",0
371,1,29,0,0.726081," ","integrate((a*x^6)^(1/2)/x/(-x^4+1),x, algorithm=""fricas"")","-\frac{\sqrt{a x^{6}} {\left(2 \, \arctan\left(x\right) - \log\left(\frac{x + 1}{x - 1}\right)\right)}}{4 \, x^{3}}"," ",0,"-1/4*sqrt(a*x^6)*(2*arctan(x) - log((x + 1)/(x - 1)))/x^3","A",0
372,1,29,0,0.551965," ","integrate((a*x^6)^(1/2)/(-x^5+x),x, algorithm=""fricas"")","-\frac{\sqrt{a x^{6}} {\left(2 \, \arctan\left(x\right) - \log\left(\frac{x + 1}{x - 1}\right)\right)}}{4 \, x^{3}}"," ",0,"-1/4*sqrt(a*x^6)*(2*arctan(x) - log((x + 1)/(x - 1)))/x^3","A",0
373,1,41,0,0.655572," ","integrate((a*x^6)^(3/2)/x/(-x^4+1),x, algorithm=""fricas"")","-\frac{\sqrt{a x^{6}} {\left(4 \, a x^{5} + 20 \, a x - 10 \, a \arctan\left(x\right) - 5 \, a \log\left(\frac{x + 1}{x - 1}\right)\right)}}{20 \, x^{3}}"," ",0,"-1/20*sqrt(a*x^6)*(4*a*x^5 + 20*a*x - 10*a*arctan(x) - 5*a*log((x + 1)/(x - 1)))/x^3","A",0
374,1,256,0,0.651804," ","integrate(1/(-x^4+1)-(a*x^6)^(1/2)/x/(-x^4+1),x, algorithm=""fricas"")","\left[\frac{x^{3} \sqrt{-\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}} \log\left(\frac{{\left(a - 1\right)} x^{4} - {\left(a - 1\right)} x^{2} - 2 \, {\left(x^{3} - \sqrt{a x^{6}}\right)} \sqrt{-\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}}}{x^{4} + x^{2}}\right) + x^{3} \log\left(x + 1\right) - x^{3} \log\left(x - 1\right) - \sqrt{a x^{6}} {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)}}{4 \, x^{3}}, \frac{2 \, x^{3} \sqrt{\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}} \arctan\left(-\frac{{\left(x^{3} - \sqrt{a x^{6}}\right)} \sqrt{\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}}}{{\left(a - 1\right)} x^{2}}\right) + x^{3} \log\left(x + 1\right) - x^{3} \log\left(x - 1\right) - \sqrt{a x^{6}} {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)}}{4 \, x^{3}}\right]"," ",0,"[1/4*(x^3*sqrt(-((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3)*log(((a - 1)*x^4 - (a - 1)*x^2 - 2*(x^3 - sqrt(a*x^6))*sqrt(-((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3))/(x^4 + x^2)) + x^3*log(x + 1) - x^3*log(x - 1) - sqrt(a*x^6)*(log(x + 1) - log(x - 1)))/x^3, 1/4*(2*x^3*sqrt(((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3)*arctan(-(x^3 - sqrt(a*x^6))*sqrt(((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3)/((a - 1)*x^2)) + x^3*log(x + 1) - x^3*log(x - 1) - sqrt(a*x^6)*(log(x + 1) - log(x - 1)))/x^3]","B",0
375,1,256,0,0.671403," ","integrate(1/(-x^4+1)-(a*x^6)^(1/2)/(-x^5+x),x, algorithm=""fricas"")","\left[\frac{x^{3} \sqrt{-\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}} \log\left(\frac{{\left(a - 1\right)} x^{4} - {\left(a - 1\right)} x^{2} - 2 \, {\left(x^{3} - \sqrt{a x^{6}}\right)} \sqrt{-\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}}}{x^{4} + x^{2}}\right) + x^{3} \log\left(x + 1\right) - x^{3} \log\left(x - 1\right) - \sqrt{a x^{6}} {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)}}{4 \, x^{3}}, \frac{2 \, x^{3} \sqrt{\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}} \arctan\left(-\frac{{\left(x^{3} - \sqrt{a x^{6}}\right)} \sqrt{\frac{{\left(a + 1\right)} x^{3} + 2 \, \sqrt{a x^{6}}}{x^{3}}}}{{\left(a - 1\right)} x^{2}}\right) + x^{3} \log\left(x + 1\right) - x^{3} \log\left(x - 1\right) - \sqrt{a x^{6}} {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)}}{4 \, x^{3}}\right]"," ",0,"[1/4*(x^3*sqrt(-((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3)*log(((a - 1)*x^4 - (a - 1)*x^2 - 2*(x^3 - sqrt(a*x^6))*sqrt(-((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3))/(x^4 + x^2)) + x^3*log(x + 1) - x^3*log(x - 1) - sqrt(a*x^6)*(log(x + 1) - log(x - 1)))/x^3, 1/4*(2*x^3*sqrt(((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3)*arctan(-(x^3 - sqrt(a*x^6))*sqrt(((a + 1)*x^3 + 2*sqrt(a*x^6))/x^3)/((a - 1)*x^2)) + x^3*log(x + 1) - x^3*log(x - 1) - sqrt(a*x^6)*(log(x + 1) - log(x - 1)))/x^3]","B",0
376,1,127,0,0.698524," ","integrate((a*x^3)^(1/2)/(-x^3+x),x, algorithm=""fricas"")","\left[-\sqrt{a} \arctan\left(\frac{\sqrt{a x^{3}}}{\sqrt{a} x}\right) + \frac{1}{2} \, \sqrt{a} \log\left(\frac{a x^{2} + a x + 2 \, \sqrt{a x^{3}} \sqrt{a}}{x^{2} - x}\right), -\sqrt{-a} \arctan\left(\frac{\sqrt{a x^{3}} \sqrt{-a}}{a x}\right) + \frac{1}{2} \, \sqrt{-a} \log\left(\frac{a x^{2} - a x - 2 \, \sqrt{a x^{3}} \sqrt{-a}}{x^{2} + x}\right)\right]"," ",0,"[-sqrt(a)*arctan(sqrt(a*x^3)/(sqrt(a)*x)) + 1/2*sqrt(a)*log((a*x^2 + a*x + 2*sqrt(a*x^3)*sqrt(a))/(x^2 - x)), -sqrt(-a)*arctan(sqrt(a*x^3)*sqrt(-a)/(a*x)) + 1/2*sqrt(-a)*log((a*x^2 - a*x - 2*sqrt(a*x^3)*sqrt(-a))/(x^2 + x))]","A",0
377,1,42,0,0.546827," ","integrate((a*x^4)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a x^{4}} \sqrt{x^{2} + 1} x + \sqrt{a x^{4}} \log\left(-x + \sqrt{x^{2} + 1}\right)}{2 \, x^{2}}"," ",0,"1/2*(sqrt(a*x^4)*sqrt(x^2 + 1)*x + sqrt(a*x^4)*log(-x + sqrt(x^2 + 1)))/x^2","A",0
378,0,0,0,0.612654," ","integrate((a*x^3)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a x^{3}}}{\sqrt{x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(a*x^3)/sqrt(x^2 + 1), x)","F",0
379,1,18,0,0.516119," ","integrate((a*x^2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a x^{2}} \sqrt{x^{2} + 1}}{x}"," ",0,"sqrt(a*x^2)*sqrt(x^2 + 1)/x","A",0
380,0,0,0,0.736426," ","integrate((a*x)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a x}}{\sqrt{x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(a*x)/sqrt(x^2 + 1), x)","F",0
381,0,0,0,0.658698," ","integrate((a/x)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a}{x}}}{\sqrt{x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(a/x)/sqrt(x^2 + 1), x)","F",0
382,1,76,0,0.716412," ","integrate((a/x^2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\left[x \sqrt{\frac{a}{x^{2}}} \log\left(\frac{\sqrt{x^{2} + 1} - 1}{x}\right), 2 \, \sqrt{-a} \arctan\left(-\frac{\sqrt{-a} x^{2} \sqrt{\frac{a}{x^{2}}} - \sqrt{x^{2} + 1} \sqrt{-a} x \sqrt{\frac{a}{x^{2}}}}{a}\right)\right]"," ",0,"[x*sqrt(a/x^2)*log((sqrt(x^2 + 1) - 1)/x), 2*sqrt(-a)*arctan(-(sqrt(-a)*x^2*sqrt(a/x^2) - sqrt(x^2 + 1)*sqrt(-a)*x*sqrt(a/x^2))/a)]","A",0
383,0,0,0,0.705870," ","integrate((a/x^3)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a}{x^{3}}}}{\sqrt{x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(a/x^3)/sqrt(x^2 + 1), x)","F",0
384,1,30,0,0.494036," ","integrate((a/x^4)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","-x^{2} \sqrt{\frac{a}{x^{4}}} - \sqrt{x^{2} + 1} x \sqrt{\frac{a}{x^{4}}}"," ",0,"-x^2*sqrt(a/x^4) - sqrt(x^2 + 1)*x*sqrt(a/x^4)","A",0
385,1,19,0,0.578951," ","integrate((a*x^4)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a x^{4}} \sqrt{x^{3} + 1}}{3 \, x^{2}}"," ",0,"2/3*sqrt(a*x^4)*sqrt(x^3 + 1)/x^2","A",0
386,0,0,0,0.774847," ","integrate((a*x^3)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a x^{3}}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(sqrt(a*x^3)/sqrt(x^3 + 1), x)","F",0
387,0,0,0,0.590861," ","integrate((a*x^2)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a x^{2}}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(sqrt(a*x^2)/sqrt(x^3 + 1), x)","F",0
388,1,85,0,0.768699," ","integrate((a*x)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{6} \, \sqrt{a} \log\left(-8 \, a x^{6} - 8 \, a x^{3} - 4 \, {\left(2 \, x^{4} + x\right)} \sqrt{x^{3} + 1} \sqrt{a x} \sqrt{a} - a\right), -\frac{1}{3} \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{x^{3} + 1} \sqrt{a x} \sqrt{-a} x}{2 \, a x^{3} + a}\right)\right]"," ",0,"[1/6*sqrt(a)*log(-8*a*x^6 - 8*a*x^3 - 4*(2*x^4 + x)*sqrt(x^3 + 1)*sqrt(a*x)*sqrt(a) - a), -1/3*sqrt(-a)*arctan(2*sqrt(x^3 + 1)*sqrt(a*x)*sqrt(-a)*x/(2*a*x^3 + a))]","B",0
389,0,0,0,0.772049," ","integrate((a/x)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a}{x}}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(sqrt(a/x)/sqrt(x^3 + 1), x)","F",0
390,1,68,0,0.789620," ","integrate((a/x^2)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{3} \, x \sqrt{\frac{a}{x^{2}}} \log\left(\frac{x^{3} - 2 \, \sqrt{x^{3} + 1} + 2}{x^{3}}\right), \frac{2}{3} \, \sqrt{-a} \arctan\left(\frac{\sqrt{x^{3} + 1} \sqrt{-a} x \sqrt{\frac{a}{x^{2}}}}{a x^{3} + a}\right)\right]"," ",0,"[1/3*x*sqrt(a/x^2)*log((x^3 - 2*sqrt(x^3 + 1) + 2)/x^3), 2/3*sqrt(-a)*arctan(sqrt(x^3 + 1)*sqrt(-a)*x*sqrt(a/x^2)/(a*x^3 + a))]","A",0
391,0,0,0,0.794690," ","integrate((a/x^3)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a}{x^{3}}}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(sqrt(a/x^3)/sqrt(x^3 + 1), x)","F",0
392,0,0,0,0.617312," ","integrate((a/x^4)^(1/2)/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a}{x^{4}}}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(sqrt(a/x^4)/sqrt(x^3 + 1), x)","F",0
393,-2,0,0,0.000000," ","integrate((a*x^(2*n))^(1/2)/(1+x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
394,-2,0,0,0.000000," ","integrate((a*x^n)^(1/2)/(1+x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
395,-2,0,0,0.000000," ","integrate((a*x^(1/2*n))^(1/2)/(1+x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
396,-2,0,0,0.000000," ","integrate((a*x^(2*n))^(1/2)/(1+x^n)^(1/2)+2*(a*x^(2*n))^(1/2)/(2+n)/(x^n)/(1+x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
397,0,0,0,1.057075," ","integrate((a*x)^(1/2)/(e*x+d)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a x} \sqrt{e x + d} \sqrt{f x + e}}{e f x^{2} + d e + {\left(e^{2} + d f\right)} x}, x\right)"," ",0,"integral(sqrt(a*x)*sqrt(e*x + d)*sqrt(f*x + e)/(e*f*x^2 + d*e + (e^2 + d*f)*x), x)","F",0
398,1,20,0,0.664249," ","integrate((a*x^m)^r,x, algorithm=""fricas"")","\frac{x e^{\left(m r \log\left(x\right) + r \log\left(a\right)\right)}}{m r + 1}"," ",0,"x*e^(m*r*log(x) + r*log(a))/(m*r + 1)","A",0
399,1,32,0,0.645227," ","integrate((a*x^m)^r*(b*x^n)^s,x, algorithm=""fricas"")","\frac{x e^{\left(m r \log\left(x\right) + n s \log\left(x\right) + r \log\left(a\right) + s \log\left(b\right)\right)}}{m r + n s + 1}"," ",0,"x*e^(m*r*log(x) + n*s*log(x) + r*log(a) + s*log(b))/(m*r + n*s + 1)","A",0
400,1,44,0,0.521678," ","integrate((a*x^m)^r*(b*x^n)^s*(c*x^p)^t,x, algorithm=""fricas"")","\frac{x e^{\left(m r \log\left(x\right) + n s \log\left(x\right) + p t \log\left(x\right) + r \log\left(a\right) + s \log\left(b\right) + t \log\left(c\right)\right)}}{m r + n s + p t + 1}"," ",0,"x*e^(m*r*log(x) + n*s*log(x) + p*t*log(x) + r*log(a) + s*log(b) + t*log(c))/(m*r + n*s + p*t + 1)","A",0
401,1,94,0,0.582194," ","integrate(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(15 \, b^{3} x^{3} + 3 \, a b^{2} x^{2} - 4 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a} - {\left(15 \, b^{3} x^{3} + 3 \, b^{2} c x^{2} - 4 \, b c^{2} x + 8 \, c^{3}\right)} \sqrt{b x + c}\right)}}{105 \, {\left(a b^{3} - b^{3} c\right)}}"," ",0,"2/105*((15*b^3*x^3 + 3*a*b^2*x^2 - 4*a^2*b*x + 8*a^3)*sqrt(b*x + a) - (15*b^3*x^3 + 3*b^2*c*x^2 - 4*b*c^2*x + 8*c^3)*sqrt(b*x + c))/(a*b^3 - b^3*c)","A",0
402,1,70,0,0.535513," ","integrate(x/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(3 \, b^{2} x^{2} + a b x - 2 \, a^{2}\right)} \sqrt{b x + a} - {\left(3 \, b^{2} x^{2} + b c x - 2 \, c^{2}\right)} \sqrt{b x + c}\right)}}{15 \, {\left(a b^{2} - b^{2} c\right)}}"," ",0,"2/15*((3*b^2*x^2 + a*b*x - 2*a^2)*sqrt(b*x + a) - (3*b^2*x^2 + b*c*x - 2*c^2)*sqrt(b*x + c))/(a*b^2 - b^2*c)","A",0
403,1,29,0,0.712695," ","integrate(1/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - {\left(b x + c\right)}^{\frac{3}{2}}\right)}}{3 \, {\left(a b - b c\right)}}"," ",0,"2/3*((b*x + a)^(3/2) - (b*x + c)^(3/2))/(a*b - b*c)","A",0
404,1,318,0,0.607231," ","integrate(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + \sqrt{c} \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, \sqrt{b x + a} + 2 \, \sqrt{b x + c}}{a - c}, -\frac{2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, \sqrt{b x + a} + 2 \, \sqrt{b x + c}}{a - c}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{c} \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, \sqrt{b x + a} - 2 \, \sqrt{b x + c}}{a - c}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{-c} \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + \sqrt{b x + a} - \sqrt{b x + c}\right)}}{a - c}\right]"," ",0,"[-(sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + sqrt(c)*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) - 2*sqrt(b*x + a) + 2*sqrt(b*x + c))/(a - c), -(2*sqrt(-c)*arctan(sqrt(b*x + c)*sqrt(-c)/c) + sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*sqrt(b*x + a) + 2*sqrt(b*x + c))/(a - c), (2*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(c)*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) + 2*sqrt(b*x + a) - 2*sqrt(b*x + c))/(a - c), 2*(sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(-c)*arctan(sqrt(b*x + c)*sqrt(-c)/c) + sqrt(b*x + a) - sqrt(b*x + c))/(a - c)]","A",0
405,1,399,0,0.592061," ","integrate(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a} b c x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + a b \sqrt{c} x \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, \sqrt{b x + a} a c - 2 \, \sqrt{b x + c} a c}{2 \, {\left(a^{2} c - a c^{2}\right)} x}, -\frac{2 \, a b \sqrt{-c} x \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + \sqrt{a} b c x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} a c - 2 \, \sqrt{b x + c} a c}{2 \, {\left(a^{2} c - a c^{2}\right)} x}, \frac{2 \, \sqrt{-a} b c x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - a b \sqrt{c} x \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, \sqrt{b x + a} a c + 2 \, \sqrt{b x + c} a c}{2 \, {\left(a^{2} c - a c^{2}\right)} x}, \frac{\sqrt{-a} b c x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - a b \sqrt{-c} x \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) - \sqrt{b x + a} a c + \sqrt{b x + c} a c}{{\left(a^{2} c - a c^{2}\right)} x}\right]"," ",0,"[-1/2*(sqrt(a)*b*c*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + a*b*sqrt(c)*x*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) + 2*sqrt(b*x + a)*a*c - 2*sqrt(b*x + c)*a*c)/((a^2*c - a*c^2)*x), -1/2*(2*a*b*sqrt(-c)*x*arctan(sqrt(b*x + c)*sqrt(-c)/c) + sqrt(a)*b*c*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*a*c - 2*sqrt(b*x + c)*a*c)/((a^2*c - a*c^2)*x), 1/2*(2*sqrt(-a)*b*c*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - a*b*sqrt(c)*x*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) - 2*sqrt(b*x + a)*a*c + 2*sqrt(b*x + c)*a*c)/((a^2*c - a*c^2)*x), (sqrt(-a)*b*c*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - a*b*sqrt(-c)*x*arctan(sqrt(b*x + c)*sqrt(-c)/c) - sqrt(b*x + a)*a*c + sqrt(b*x + c)*a*c)/((a^2*c - a*c^2)*x)]","A",0
406,1,196,0,0.628821," ","integrate(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{96 \, b^{4} x^{4} + 64 \, {\left(a b^{3} + b^{3} c\right)} x^{3} - 2 \, {\left(48 \, b^{3} x^{3} + 15 \, a^{3} - 7 \, a^{2} c - 7 \, a c^{2} + 15 \, c^{3} + 8 \, {\left(a b^{2} + b^{2} c\right)} x^{2} - 2 \, {\left(5 \, a^{2} b - 2 \, a b c + 5 \, b c^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{b x + c} - 3 \, {\left(5 \, a^{4} - 4 \, a^{3} c - 2 \, a^{2} c^{2} - 4 \, a c^{3} + 5 \, c^{4}\right)} \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right)}{192 \, {\left(a^{2} b^{3} - 2 \, a b^{3} c + b^{3} c^{2}\right)}}"," ",0,"1/192*(96*b^4*x^4 + 64*(a*b^3 + b^3*c)*x^3 - 2*(48*b^3*x^3 + 15*a^3 - 7*a^2*c - 7*a*c^2 + 15*c^3 + 8*(a*b^2 + b^2*c)*x^2 - 2*(5*a^2*b - 2*a*b*c + 5*b*c^2)*x)*sqrt(b*x + a)*sqrt(b*x + c) - 3*(5*a^4 - 4*a^3*c - 2*a^2*c^2 - 4*a*c^3 + 5*c^4)*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c))/(a^2*b^3 - 2*a*b^3*c + b^3*c^2)","A",0
407,1,149,0,0.756032," ","integrate(x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{16 \, b^{3} x^{3} + 12 \, {\left(a b^{2} + b^{2} c\right)} x^{2} - 2 \, {\left(8 \, b^{2} x^{2} - 3 \, a^{2} + 2 \, a c - 3 \, c^{2} + 2 \, {\left(a b + b c\right)} x\right)} \sqrt{b x + a} \sqrt{b x + c} + 3 \, {\left(a^{3} - a^{2} c - a c^{2} + c^{3}\right)} \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right)}{24 \, {\left(a^{2} b^{2} - 2 \, a b^{2} c + b^{2} c^{2}\right)}}"," ",0,"1/24*(16*b^3*x^3 + 12*(a*b^2 + b^2*c)*x^2 - 2*(8*b^2*x^2 - 3*a^2 + 2*a*c - 3*c^2 + 2*(a*b + b*c)*x)*sqrt(b*x + a)*sqrt(b*x + c) + 3*(a^3 - a^2*c - a*c^2 + c^3)*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c))/(a^2*b^2 - 2*a*b^2*c + b^2*c^2)","A",0
408,1,103,0,0.709243," ","integrate(1/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} - 2 \, {\left(2 \, b x + a + c\right)} \sqrt{b x + a} \sqrt{b x + c} + 4 \, {\left(a b + b c\right)} x - {\left(a^{2} - 2 \, a c + c^{2}\right)} \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right)}{4 \, {\left(a^{2} b - 2 \, a b c + b c^{2}\right)}}"," ",0,"1/4*(4*b^2*x^2 - 2*(2*b*x + a + c)*sqrt(b*x + a)*sqrt(b*x + c) + 4*(a*b + b*c)*x - (a^2 - 2*a*c + c^2)*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c))/(a^2*b - 2*a*b*c + b*c^2)","B",0
409,1,290,0,0.830940," ","integrate(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{2 \, b x + {\left(a + c\right)} \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right) + {\left(a + c\right)} \log\left(x\right) + 2 \, \sqrt{a c} \log\left(\frac{2 \, a^{2} c + 2 \, a c^{2} + 2 \, {\left(2 \, a c + \sqrt{a c} {\left(a + c\right)}\right)} \sqrt{b x + a} \sqrt{b x + c} + {\left(a^{2} b + 2 \, a b c + b c^{2}\right)} x + 2 \, {\left(2 \, a c + {\left(a b + b c\right)} x\right)} \sqrt{a c}}{x}\right) - 2 \, \sqrt{b x + a} \sqrt{b x + c}}{a^{2} - 2 \, a c + c^{2}}, \frac{2 \, b x + {\left(a + c\right)} \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right) + {\left(a + c\right)} \log\left(x\right) - 4 \, \sqrt{-a c} \arctan\left(-\frac{\sqrt{-a c} b x - \sqrt{-a c} \sqrt{b x + a} \sqrt{b x + c}}{a c}\right) - 2 \, \sqrt{b x + a} \sqrt{b x + c}}{a^{2} - 2 \, a c + c^{2}}\right]"," ",0,"[(2*b*x + (a + c)*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c) + (a + c)*log(x) + 2*sqrt(a*c)*log((2*a^2*c + 2*a*c^2 + 2*(2*a*c + sqrt(a*c)*(a + c))*sqrt(b*x + a)*sqrt(b*x + c) + (a^2*b + 2*a*b*c + b*c^2)*x + 2*(2*a*c + (a*b + b*c)*x)*sqrt(a*c))/x) - 2*sqrt(b*x + a)*sqrt(b*x + c))/(a^2 - 2*a*c + c^2), (2*b*x + (a + c)*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c) + (a + c)*log(x) - 4*sqrt(-a*c)*arctan(-(sqrt(-a*c)*b*x - sqrt(-a*c)*sqrt(b*x + a)*sqrt(b*x + c))/(a*c)) - 2*sqrt(b*x + a)*sqrt(b*x + c))/(a^2 - 2*a*c + c^2)]","A",0
410,1,367,0,0.661717," ","integrate(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b c x \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right) + 2 \, a b c x \log\left(x\right) + 2 \, a b c x + {\left(a b + b c\right)} \sqrt{a c} x \log\left(\frac{2 \, a^{2} c + 2 \, a c^{2} + 2 \, {\left(2 \, a c + \sqrt{a c} {\left(a + c\right)}\right)} \sqrt{b x + a} \sqrt{b x + c} + {\left(a^{2} b + 2 \, a b c + b c^{2}\right)} x + 2 \, {\left(2 \, a c + {\left(a b + b c\right)} x\right)} \sqrt{a c}}{x}\right) + 2 \, \sqrt{b x + a} \sqrt{b x + c} a c - a^{2} c - a c^{2}}{{\left(a^{3} c - 2 \, a^{2} c^{2} + a c^{3}\right)} x}, \frac{2 \, a b c x \log\left(-2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b x + c} - a - c\right) + 2 \, a b c x \log\left(x\right) + 2 \, a b c x - 2 \, {\left(a b + b c\right)} \sqrt{-a c} x \arctan\left(-\frac{\sqrt{-a c} b x - \sqrt{-a c} \sqrt{b x + a} \sqrt{b x + c}}{a c}\right) + 2 \, \sqrt{b x + a} \sqrt{b x + c} a c - a^{2} c - a c^{2}}{{\left(a^{3} c - 2 \, a^{2} c^{2} + a c^{3}\right)} x}\right]"," ",0,"[(2*a*b*c*x*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c) + 2*a*b*c*x*log(x) + 2*a*b*c*x + (a*b + b*c)*sqrt(a*c)*x*log((2*a^2*c + 2*a*c^2 + 2*(2*a*c + sqrt(a*c)*(a + c))*sqrt(b*x + a)*sqrt(b*x + c) + (a^2*b + 2*a*b*c + b*c^2)*x + 2*(2*a*c + (a*b + b*c)*x)*sqrt(a*c))/x) + 2*sqrt(b*x + a)*sqrt(b*x + c)*a*c - a^2*c - a*c^2)/((a^3*c - 2*a^2*c^2 + a*c^3)*x), (2*a*b*c*x*log(-2*b*x + 2*sqrt(b*x + a)*sqrt(b*x + c) - a - c) + 2*a*b*c*x*log(x) + 2*a*b*c*x - 2*(a*b + b*c)*sqrt(-a*c)*x*arctan(-(sqrt(-a*c)*b*x - sqrt(-a*c)*sqrt(b*x + a)*sqrt(b*x + c))/(a*c)) + 2*sqrt(b*x + a)*sqrt(b*x + c)*a*c - a^2*c - a*c^2)/((a^3*c - 2*a^2*c^2 + a*c^3)*x)]","A",0
411,1,208,0,0.548927," ","integrate(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(140 \, b^{4} x^{4} - 40 \, a^{4} + 72 \, a^{3} c + 5 \, {\left(13 \, a b^{3} + 27 \, b^{3} c\right)} x^{3} - 3 \, {\left(5 \, a^{2} b^{2} - 9 \, a b^{2} c\right)} x^{2} + 4 \, {\left(5 \, a^{3} b - 9 \, a^{2} b c\right)} x\right)} \sqrt{b x + a} - {\left(140 \, b^{4} x^{4} + 72 \, a c^{3} - 40 \, c^{4} + 5 \, {\left(27 \, a b^{3} + 13 \, b^{3} c\right)} x^{3} + 3 \, {\left(9 \, a b^{2} c - 5 \, b^{2} c^{2}\right)} x^{2} - 4 \, {\left(9 \, a b c^{2} - 5 \, b c^{3}\right)} x\right)} \sqrt{b x + c}\right)}}{315 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{3} c + 3 \, a b^{3} c^{2} - b^{3} c^{3}\right)}}"," ",0,"2/315*((140*b^4*x^4 - 40*a^4 + 72*a^3*c + 5*(13*a*b^3 + 27*b^3*c)*x^3 - 3*(5*a^2*b^2 - 9*a*b^2*c)*x^2 + 4*(5*a^3*b - 9*a^2*b*c)*x)*sqrt(b*x + a) - (140*b^4*x^4 + 72*a*c^3 - 40*c^4 + 5*(27*a*b^3 + 13*b^3*c)*x^3 + 3*(9*a*b^2*c - 5*b^2*c^2)*x^2 - 4*(9*a*b*c^2 - 5*b*c^3)*x)*sqrt(b*x + c))/(a^3*b^3 - 3*a^2*b^3*c + 3*a*b^3*c^2 - b^3*c^3)","A",0
412,1,159,0,0.712671," ","integrate(x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(20 \, b^{3} x^{3} + 6 \, a^{3} - 14 \, a^{2} c + {\left(11 \, a b^{2} + 21 \, b^{2} c\right)} x^{2} - {\left(3 \, a^{2} b - 7 \, a b c\right)} x\right)} \sqrt{b x + a} - {\left(20 \, b^{3} x^{3} - 14 \, a c^{2} + 6 \, c^{3} + {\left(21 \, a b^{2} + 11 \, b^{2} c\right)} x^{2} + {\left(7 \, a b c - 3 \, b c^{2}\right)} x\right)} \sqrt{b x + c}\right)}}{35 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{2} c + 3 \, a b^{2} c^{2} - b^{2} c^{3}\right)}}"," ",0,"2/35*((20*b^3*x^3 + 6*a^3 - 14*a^2*c + (11*a*b^2 + 21*b^2*c)*x^2 - (3*a^2*b - 7*a*b*c)*x)*sqrt(b*x + a) - (20*b^3*x^3 - 14*a*c^2 + 6*c^3 + (21*a*b^2 + 11*b^2*c)*x^2 + (7*a*b*c - 3*b*c^2)*x)*sqrt(b*x + c))/(a^3*b^2 - 3*a^2*b^2*c + 3*a*b^2*c^2 - b^2*c^3)","A",0
413,1,106,0,0.633655," ","integrate(1/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(4 \, b^{2} x^{2} - a^{2} + 5 \, a c + {\left(3 \, a b + 5 \, b c\right)} x\right)} \sqrt{b x + a} - {\left(4 \, b^{2} x^{2} + 5 \, a c - c^{2} + {\left(5 \, a b + 3 \, b c\right)} x\right)} \sqrt{b x + c}\right)}}{5 \, {\left(a^{3} b - 3 \, a^{2} b c + 3 \, a b c^{2} - b c^{3}\right)}}"," ",0,"2/5*((4*b^2*x^2 - a^2 + 5*a*c + (3*a*b + 5*b*c)*x)*sqrt(b*x + a) - (4*b^2*x^2 + 5*a*c - c^2 + (5*a*b + 3*b*c)*x)*sqrt(b*x + c))/(a^3*b - 3*a^2*b*c + 3*a*b*c^2 - b*c^3)","B",0
414,1,516,0,0.747637," ","integrate(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a + 3 \, c\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 3 \, {\left(3 \, a + c\right)} \sqrt{c} \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(4 \, b x + 7 \, a + 9 \, c\right)} \sqrt{b x + a} + 2 \, {\left(4 \, b x + 9 \, a + 7 \, c\right)} \sqrt{b x + c}}{3 \, {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}, -\frac{6 \, {\left(3 \, a + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + 3 \, {\left(a + 3 \, c\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(4 \, b x + 7 \, a + 9 \, c\right)} \sqrt{b x + a} + 2 \, {\left(4 \, b x + 9 \, a + 7 \, c\right)} \sqrt{b x + c}}{3 \, {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}, \frac{6 \, \sqrt{-a} {\left(a + 3 \, c\right)} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 3 \, {\left(3 \, a + c\right)} \sqrt{c} \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(4 \, b x + 7 \, a + 9 \, c\right)} \sqrt{b x + a} - 2 \, {\left(4 \, b x + 9 \, a + 7 \, c\right)} \sqrt{b x + c}}{3 \, {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}, \frac{2 \, {\left(3 \, \sqrt{-a} {\left(a + 3 \, c\right)} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 3 \, {\left(3 \, a + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + {\left(4 \, b x + 7 \, a + 9 \, c\right)} \sqrt{b x + a} - {\left(4 \, b x + 9 \, a + 7 \, c\right)} \sqrt{b x + c}\right)}}{3 \, {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}\right]"," ",0,"[-1/3*(3*(a + 3*c)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 3*(3*a + c)*sqrt(c)*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) - 2*(4*b*x + 7*a + 9*c)*sqrt(b*x + a) + 2*(4*b*x + 9*a + 7*c)*sqrt(b*x + c))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3), -1/3*(6*(3*a + c)*sqrt(-c)*arctan(sqrt(b*x + c)*sqrt(-c)/c) + 3*(a + 3*c)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(4*b*x + 7*a + 9*c)*sqrt(b*x + a) + 2*(4*b*x + 9*a + 7*c)*sqrt(b*x + c))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3), 1/3*(6*sqrt(-a)*(a + 3*c)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 3*(3*a + c)*sqrt(c)*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) + 2*(4*b*x + 7*a + 9*c)*sqrt(b*x + a) - 2*(4*b*x + 9*a + 7*c)*sqrt(b*x + c))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3), 2/3*(3*sqrt(-a)*(a + 3*c)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 3*(3*a + c)*sqrt(-c)*arctan(sqrt(b*x + c)*sqrt(-c)/c) + (4*b*x + 7*a + 9*c)*sqrt(b*x + a) - (4*b*x + 9*a + 7*c)*sqrt(b*x + c))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3)]","A",0
415,1,675,0,0.913736," ","integrate(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, a b c + b c^{2}\right)} \sqrt{a} x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 3 \, {\left(a^{2} b + 3 \, a b c\right)} \sqrt{c} x \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(8 \, a b c x - a^{2} c - 3 \, a c^{2}\right)} \sqrt{b x + a} + 2 \, {\left(8 \, a b c x - 3 \, a^{2} c - a c^{2}\right)} \sqrt{b x + c}}{2 \, {\left(a^{4} c - 3 \, a^{3} c^{2} + 3 \, a^{2} c^{3} - a c^{4}\right)} x}, -\frac{6 \, {\left(a^{2} b + 3 \, a b c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + 3 \, {\left(3 \, a b c + b c^{2}\right)} \sqrt{a} x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(8 \, a b c x - a^{2} c - 3 \, a c^{2}\right)} \sqrt{b x + a} + 2 \, {\left(8 \, a b c x - 3 \, a^{2} c - a c^{2}\right)} \sqrt{b x + c}}{2 \, {\left(a^{4} c - 3 \, a^{3} c^{2} + 3 \, a^{2} c^{3} - a c^{4}\right)} x}, \frac{6 \, {\left(3 \, a b c + b c^{2}\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 3 \, {\left(a^{2} b + 3 \, a b c\right)} \sqrt{c} x \log\left(\frac{b x - 2 \, \sqrt{b x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(8 \, a b c x - a^{2} c - 3 \, a c^{2}\right)} \sqrt{b x + a} - 2 \, {\left(8 \, a b c x - 3 \, a^{2} c - a c^{2}\right)} \sqrt{b x + c}}{2 \, {\left(a^{4} c - 3 \, a^{3} c^{2} + 3 \, a^{2} c^{3} - a c^{4}\right)} x}, \frac{3 \, {\left(3 \, a b c + b c^{2}\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 3 \, {\left(a^{2} b + 3 \, a b c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{b x + c} \sqrt{-c}}{c}\right) + {\left(8 \, a b c x - a^{2} c - 3 \, a c^{2}\right)} \sqrt{b x + a} - {\left(8 \, a b c x - 3 \, a^{2} c - a c^{2}\right)} \sqrt{b x + c}}{{\left(a^{4} c - 3 \, a^{3} c^{2} + 3 \, a^{2} c^{3} - a c^{4}\right)} x}\right]"," ",0,"[-1/2*(3*(3*a*b*c + b*c^2)*sqrt(a)*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 3*(a^2*b + 3*a*b*c)*sqrt(c)*x*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) - 2*(8*a*b*c*x - a^2*c - 3*a*c^2)*sqrt(b*x + a) + 2*(8*a*b*c*x - 3*a^2*c - a*c^2)*sqrt(b*x + c))/((a^4*c - 3*a^3*c^2 + 3*a^2*c^3 - a*c^4)*x), -1/2*(6*(a^2*b + 3*a*b*c)*sqrt(-c)*x*arctan(sqrt(b*x + c)*sqrt(-c)/c) + 3*(3*a*b*c + b*c^2)*sqrt(a)*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(8*a*b*c*x - a^2*c - 3*a*c^2)*sqrt(b*x + a) + 2*(8*a*b*c*x - 3*a^2*c - a*c^2)*sqrt(b*x + c))/((a^4*c - 3*a^3*c^2 + 3*a^2*c^3 - a*c^4)*x), 1/2*(6*(3*a*b*c + b*c^2)*sqrt(-a)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 3*(a^2*b + 3*a*b*c)*sqrt(c)*x*log((b*x - 2*sqrt(b*x + c)*sqrt(c) + 2*c)/x) + 2*(8*a*b*c*x - a^2*c - 3*a*c^2)*sqrt(b*x + a) - 2*(8*a*b*c*x - 3*a^2*c - a*c^2)*sqrt(b*x + c))/((a^4*c - 3*a^3*c^2 + 3*a^2*c^3 - a*c^4)*x), (3*(3*a*b*c + b*c^2)*sqrt(-a)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 3*(a^2*b + 3*a*b*c)*sqrt(-c)*x*arctan(sqrt(b*x + c)*sqrt(-c)/c) + (8*a*b*c*x - a^2*c - 3*a*c^2)*sqrt(b*x + a) - (8*a*b*c*x - 3*a^2*c - a*c^2)*sqrt(b*x + c))/((a^4*c - 3*a^3*c^2 + 3*a^2*c^3 - a*c^4)*x)]","A",0
416,1,13,0,0.635647," ","integrate(1/(x^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, x^{\frac{3}{2}}"," ",0,"2/3*(x + 1)^(3/2) - 2/3*x^(3/2)","A",0
417,1,13,0,0.673517," ","integrate(1/((-1+x)^(1/2)+x^(1/2)),x, algorithm=""fricas"")","-\frac{2}{3} \, {\left(x - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, x^{\frac{3}{2}}"," ",0,"-2/3*(x - 1)^(3/2) + 2/3*x^(3/2)","A",0
418,1,15,0,0.727387," ","integrate(1/((-1+x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{1}{3} \, {\left(x - 1\right)}^{\frac{3}{2}}"," ",0,"1/3*(x + 1)^(3/2) - 1/3*(x - 1)^(3/2)","A",0
419,1,32,0,0.809717," ","integrate(x^3*((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""fricas"")","\frac{1}{2} \, x^{4} + \frac{2}{15} \, {\left(3 \, x^{4} - x^{2} - 2\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"1/2*x^4 + 2/15*(3*x^4 - x^2 - 2)*sqrt(x + 1)*sqrt(-x + 1)","A",0
420,1,51,0,0.661673," ","integrate(x^2*((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""fricas"")","\frac{2}{3} \, x^{3} + \frac{1}{4} \, {\left(2 \, x^{3} - x\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{1}{2} \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"2/3*x^3 + 1/4*(2*x^3 - x)*sqrt(x + 1)*sqrt(-x + 1) - 1/2*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
421,1,23,0,0.613625," ","integrate(x*((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""fricas"")","x^{2} + \frac{2}{3} \, {\left(x^{2} - 1\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"x^2 + 2/3*(x^2 - 1)*sqrt(x + 1)*sqrt(-x + 1)","A",0
422,1,40,0,0.592269," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""fricas"")","\sqrt{x + 1} x \sqrt{-x + 1} + 2 \, x - 2 \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"sqrt(x + 1)*x*sqrt(-x + 1) + 2*x - 2*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","B",0
423,1,41,0,0.466144," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2/x,x, algorithm=""fricas"")","2 \, \sqrt{x + 1} \sqrt{-x + 1} + 2 \, \log\left(x\right) + 2 \, \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"2*sqrt(x + 1)*sqrt(-x + 1) + 2*log(x) + 2*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
424,1,44,0,0.542775," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2/x^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, x \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - \sqrt{x + 1} \sqrt{-x + 1} - 1\right)}}{x}"," ",0,"2*(2*x*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - sqrt(x + 1)*sqrt(-x + 1) - 1)/x","A",0
425,1,44,0,0.396140," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2/x^3,x, algorithm=""fricas"")","-\frac{x^{2} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + \sqrt{x + 1} \sqrt{-x + 1} + 1}{x^{2}}"," ",0,"-(x^2*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + sqrt(x + 1)*sqrt(-x + 1) + 1)/x^2","A",0
426,1,122,0,0.414262," ","integrate(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(15 \, b^{3} c^{3} x^{3} + 3 \, a b^{2} c^{3} x^{2} - 4 \, a^{2} b c^{3} x + 8 \, a^{3} c^{3}\right)} \sqrt{b x + a} - {\left(15 \, b^{3} c^{3} x^{3} + 3 \, a b^{3} c^{2} x^{2} - 4 \, a^{2} b^{3} c x + 8 \, a^{3} b^{3}\right)} \sqrt{c x + a}\right)}}{105 \, {\left(b^{4} c^{3} - b^{3} c^{4}\right)}}"," ",0,"2/105*((15*b^3*c^3*x^3 + 3*a*b^2*c^3*x^2 - 4*a^2*b*c^3*x + 8*a^3*c^3)*sqrt(b*x + a) - (15*b^3*c^3*x^3 + 3*a*b^3*c^2*x^2 - 4*a^2*b^3*c*x + 8*a^3*b^3)*sqrt(c*x + a))/(b^4*c^3 - b^3*c^4)","A",0
427,1,92,0,0.395326," ","integrate(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(3 \, b^{2} c^{2} x^{2} + a b c^{2} x - 2 \, a^{2} c^{2}\right)} \sqrt{b x + a} - {\left(3 \, b^{2} c^{2} x^{2} + a b^{2} c x - 2 \, a^{2} b^{2}\right)} \sqrt{c x + a}\right)}}{15 \, {\left(b^{3} c^{2} - b^{2} c^{3}\right)}}"," ",0,"2/15*((3*b^2*c^2*x^2 + a*b*c^2*x - 2*a^2*c^2)*sqrt(b*x + a) - (3*b^2*c^2*x^2 + a*b^2*c*x - 2*a^2*b^2)*sqrt(c*x + a))/(b^3*c^2 - b^2*c^3)","A",0
428,1,50,0,0.411271," ","integrate(x/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(b c x + a c\right)} \sqrt{b x + a} - {\left(b c x + a b\right)} \sqrt{c x + a}\right)}}{3 \, {\left(b^{2} c - b c^{2}\right)}}"," ",0,"2/3*((b*c*x + a*c)*sqrt(b*x + a) - (b*c*x + a*b)*sqrt(c*x + a))/(b^2*c - b*c^2)","A",0
429,1,158,0,0.424277," ","integrate(1/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + \sqrt{a} \log\left(\frac{c x - 2 \, \sqrt{c x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, \sqrt{b x + a} + 2 \, \sqrt{c x + a}}{b - c}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{-a} \arctan\left(\frac{\sqrt{c x + a} \sqrt{-a}}{a}\right) + \sqrt{b x + a} - \sqrt{c x + a}\right)}}{b - c}\right]"," ",0,"[-(sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + sqrt(a)*log((c*x - 2*sqrt(c*x + a)*sqrt(a) + 2*a)/x) - 2*sqrt(b*x + a) + 2*sqrt(c*x + a))/(b - c), 2*(sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(-a)*arctan(sqrt(c*x + a)*sqrt(-a)/a) + sqrt(b*x + a) - sqrt(c*x + a))/(b - c)]","A",0
430,1,182,0,0.416638," ","integrate(1/x/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a} b x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + \sqrt{a} c x \log\left(\frac{c x - 2 \, \sqrt{c x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} a - 2 \, \sqrt{c x + a} a}{2 \, {\left(a b - a c\right)} x}, \frac{\sqrt{-a} b x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x + a} \sqrt{-a}}{a}\right) - \sqrt{b x + a} a + \sqrt{c x + a} a}{{\left(a b - a c\right)} x}\right]"," ",0,"[-1/2*(sqrt(a)*b*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + sqrt(a)*c*x*log((c*x - 2*sqrt(c*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*a - 2*sqrt(c*x + a)*a)/((a*b - a*c)*x), (sqrt(-a)*b*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(-a)*c*x*arctan(sqrt(c*x + a)*sqrt(-a)/a) - sqrt(b*x + a)*a + sqrt(c*x + a)*a)/((a*b - a*c)*x)]","A",0
431,1,243,0,0.451391," ","integrate(1/x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a} b^{2} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + \sqrt{a} c^{2} x^{2} \log\left(\frac{c x + 2 \, \sqrt{c x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(a b x + 2 \, a^{2}\right)} \sqrt{b x + a} - 2 \, {\left(a c x + 2 \, a^{2}\right)} \sqrt{c x + a}}{8 \, {\left(a^{2} b - a^{2} c\right)} x^{2}}, -\frac{\sqrt{-a} b^{2} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{-a} c^{2} x^{2} \arctan\left(\frac{\sqrt{c x + a} \sqrt{-a}}{a}\right) + {\left(a b x + 2 \, a^{2}\right)} \sqrt{b x + a} - {\left(a c x + 2 \, a^{2}\right)} \sqrt{c x + a}}{4 \, {\left(a^{2} b - a^{2} c\right)} x^{2}}\right]"," ",0,"[-1/8*(sqrt(a)*b^2*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + sqrt(a)*c^2*x^2*log((c*x + 2*sqrt(c*x + a)*sqrt(a) + 2*a)/x) + 2*(a*b*x + 2*a^2)*sqrt(b*x + a) - 2*(a*c*x + 2*a^2)*sqrt(c*x + a))/((a^2*b - a^2*c)*x^2), -1/4*(sqrt(-a)*b^2*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(-a)*c^2*x^2*arctan(sqrt(c*x + a)*sqrt(-a)/a) + (a*b*x + 2*a^2)*sqrt(b*x + a) - (a*c*x + 2*a^2)*sqrt(c*x + a))/((a^2*b - a^2*c)*x^2)]","A",0
432,1,479,0,0.427100," ","integrate(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{24 \, a b^{3} c^{3} x^{2} + 8 \, {\left(b^{4} c^{3} + b^{3} c^{4}\right)} x^{3} + 3 \, {\left(a^{3} b^{3} - a^{3} b^{2} c - a^{3} b c^{2} + a^{3} c^{3}\right)} \sqrt{b c} \log\left(a b^{2} + 2 \, a b c + a c^{2} + 2 \, {\left(2 \, b c - \sqrt{b c} {\left(b + c\right)}\right)} \sqrt{b x + a} \sqrt{c x + a} + 2 \, {\left(b^{2} c + b c^{2}\right)} x - 2 \, {\left(2 \, b c x + a b + a c\right)} \sqrt{b c}\right) - 2 \, {\left(8 \, b^{3} c^{3} x^{2} - 3 \, a^{2} b^{3} c + 2 \, a^{2} b^{2} c^{2} - 3 \, a^{2} b c^{3} + 2 \, {\left(a b^{3} c^{2} + a b^{2} c^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{c x + a}}{24 \, {\left(b^{5} c^{3} - 2 \, b^{4} c^{4} + b^{3} c^{5}\right)}}, \frac{12 \, a b^{3} c^{3} x^{2} + 4 \, {\left(b^{4} c^{3} + b^{3} c^{4}\right)} x^{3} + 3 \, {\left(a^{3} b^{3} - a^{3} b^{2} c - a^{3} b c^{2} + a^{3} c^{3}\right)} \sqrt{-b c} \arctan\left(\frac{\sqrt{-b c} \sqrt{b x + a} \sqrt{c x + a} - \sqrt{-b c} a}{b c x}\right) - {\left(8 \, b^{3} c^{3} x^{2} - 3 \, a^{2} b^{3} c + 2 \, a^{2} b^{2} c^{2} - 3 \, a^{2} b c^{3} + 2 \, {\left(a b^{3} c^{2} + a b^{2} c^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{c x + a}}{12 \, {\left(b^{5} c^{3} - 2 \, b^{4} c^{4} + b^{3} c^{5}\right)}}\right]"," ",0,"[1/24*(24*a*b^3*c^3*x^2 + 8*(b^4*c^3 + b^3*c^4)*x^3 + 3*(a^3*b^3 - a^3*b^2*c - a^3*b*c^2 + a^3*c^3)*sqrt(b*c)*log(a*b^2 + 2*a*b*c + a*c^2 + 2*(2*b*c - sqrt(b*c)*(b + c))*sqrt(b*x + a)*sqrt(c*x + a) + 2*(b^2*c + b*c^2)*x - 2*(2*b*c*x + a*b + a*c)*sqrt(b*c)) - 2*(8*b^3*c^3*x^2 - 3*a^2*b^3*c + 2*a^2*b^2*c^2 - 3*a^2*b*c^3 + 2*(a*b^3*c^2 + a*b^2*c^3)*x)*sqrt(b*x + a)*sqrt(c*x + a))/(b^5*c^3 - 2*b^4*c^4 + b^3*c^5), 1/12*(12*a*b^3*c^3*x^2 + 4*(b^4*c^3 + b^3*c^4)*x^3 + 3*(a^3*b^3 - a^3*b^2*c - a^3*b*c^2 + a^3*c^3)*sqrt(-b*c)*arctan((sqrt(-b*c)*sqrt(b*x + a)*sqrt(c*x + a) - sqrt(-b*c)*a)/(b*c*x)) - (8*b^3*c^3*x^2 - 3*a^2*b^3*c + 2*a^2*b^2*c^2 - 3*a^2*b*c^3 + 2*(a*b^3*c^2 + a*b^2*c^3)*x)*sqrt(b*x + a)*sqrt(c*x + a))/(b^5*c^3 - 2*b^4*c^4 + b^3*c^5)]","A",0
433,1,372,0,0.435435," ","integrate(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{8 \, a b^{2} c^{2} x + 2 \, {\left(b^{3} c^{2} + b^{2} c^{3}\right)} x^{2} + {\left(a^{2} b^{2} - 2 \, a^{2} b c + a^{2} c^{2}\right)} \sqrt{b c} \log\left(a b^{2} + 2 \, a b c + a c^{2} + 2 \, {\left(2 \, b c + \sqrt{b c} {\left(b + c\right)}\right)} \sqrt{b x + a} \sqrt{c x + a} + 2 \, {\left(b^{2} c + b c^{2}\right)} x + 2 \, {\left(2 \, b c x + a b + a c\right)} \sqrt{b c}\right) - 2 \, {\left(2 \, b^{2} c^{2} x + a b^{2} c + a b c^{2}\right)} \sqrt{b x + a} \sqrt{c x + a}}{4 \, {\left(b^{4} c^{2} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)}}, \frac{4 \, a b^{2} c^{2} x + {\left(b^{3} c^{2} + b^{2} c^{3}\right)} x^{2} - {\left(a^{2} b^{2} - 2 \, a^{2} b c + a^{2} c^{2}\right)} \sqrt{-b c} \arctan\left(\frac{\sqrt{-b c} \sqrt{b x + a} \sqrt{c x + a} - \sqrt{-b c} a}{b c x}\right) - {\left(2 \, b^{2} c^{2} x + a b^{2} c + a b c^{2}\right)} \sqrt{b x + a} \sqrt{c x + a}}{2 \, {\left(b^{4} c^{2} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)}}\right]"," ",0,"[1/4*(8*a*b^2*c^2*x + 2*(b^3*c^2 + b^2*c^3)*x^2 + (a^2*b^2 - 2*a^2*b*c + a^2*c^2)*sqrt(b*c)*log(a*b^2 + 2*a*b*c + a*c^2 + 2*(2*b*c + sqrt(b*c)*(b + c))*sqrt(b*x + a)*sqrt(c*x + a) + 2*(b^2*c + b*c^2)*x + 2*(2*b*c*x + a*b + a*c)*sqrt(b*c)) - 2*(2*b^2*c^2*x + a*b^2*c + a*b*c^2)*sqrt(b*x + a)*sqrt(c*x + a))/(b^4*c^2 - 2*b^3*c^3 + b^2*c^4), 1/2*(4*a*b^2*c^2*x + (b^3*c^2 + b^2*c^3)*x^2 - (a^2*b^2 - 2*a^2*b*c + a^2*c^2)*sqrt(-b*c)*arctan((sqrt(-b*c)*sqrt(b*x + a)*sqrt(c*x + a) - sqrt(-b*c)*a)/(b*c*x)) - (2*b^2*c^2*x + a*b^2*c + a*b*c^2)*sqrt(b*x + a)*sqrt(c*x + a))/(b^4*c^2 - 2*b^3*c^3 + b^2*c^4)]","A",0
434,1,346,0,0.446521," ","integrate(x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b c \log\left(x\right) - 2 \, a b c \log\left(-\frac{{\left(b + c\right)} x - 2 \, \sqrt{b x + a} \sqrt{c x + a} + 2 \, a}{x}\right) - 2 \, \sqrt{b x + a} \sqrt{c x + a} b c + {\left(a b + a c\right)} \sqrt{b c} \log\left(a b^{2} + 2 \, a b c + a c^{2} + 2 \, {\left(2 \, b c - \sqrt{b c} {\left(b + c\right)}\right)} \sqrt{b x + a} \sqrt{c x + a} + 2 \, {\left(b^{2} c + b c^{2}\right)} x - 2 \, {\left(2 \, b c x + a b + a c\right)} \sqrt{b c}\right) + {\left(b^{2} c + b c^{2}\right)} x}{b^{3} c - 2 \, b^{2} c^{2} + b c^{3}}, \frac{2 \, a b c \log\left(x\right) - 2 \, a b c \log\left(-\frac{{\left(b + c\right)} x - 2 \, \sqrt{b x + a} \sqrt{c x + a} + 2 \, a}{x}\right) - 2 \, \sqrt{b x + a} \sqrt{c x + a} b c + 2 \, {\left(a b + a c\right)} \sqrt{-b c} \arctan\left(\frac{\sqrt{-b c} \sqrt{b x + a} \sqrt{c x + a} - \sqrt{-b c} a}{b c x}\right) + {\left(b^{2} c + b c^{2}\right)} x}{b^{3} c - 2 \, b^{2} c^{2} + b c^{3}}\right]"," ",0,"[(2*a*b*c*log(x) - 2*a*b*c*log(-((b + c)*x - 2*sqrt(b*x + a)*sqrt(c*x + a) + 2*a)/x) - 2*sqrt(b*x + a)*sqrt(c*x + a)*b*c + (a*b + a*c)*sqrt(b*c)*log(a*b^2 + 2*a*b*c + a*c^2 + 2*(2*b*c - sqrt(b*c)*(b + c))*sqrt(b*x + a)*sqrt(c*x + a) + 2*(b^2*c + b*c^2)*x - 2*(2*b*c*x + a*b + a*c)*sqrt(b*c)) + (b^2*c + b*c^2)*x)/(b^3*c - 2*b^2*c^2 + b*c^3), (2*a*b*c*log(x) - 2*a*b*c*log(-((b + c)*x - 2*sqrt(b*x + a)*sqrt(c*x + a) + 2*a)/x) - 2*sqrt(b*x + a)*sqrt(c*x + a)*b*c + 2*(a*b + a*c)*sqrt(-b*c)*arctan((sqrt(-b*c)*sqrt(b*x + a)*sqrt(c*x + a) - sqrt(-b*c)*a)/(b*c*x)) + (b^2*c + b*c^2)*x)/(b^3*c - 2*b^2*c^2 + b*c^3)]","A",0
435,1,317,0,0.442234," ","integrate(1/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b + c\right)} x \log\left(x\right) - 2 \, {\left(b + c\right)} x \log\left(-\frac{{\left(b + c\right)} x - 2 \, \sqrt{b x + a} \sqrt{c x + a} + 2 \, a}{x}\right) + 4 \, \sqrt{b c} x \log\left(a b^{2} + 2 \, a b c + a c^{2} + 2 \, {\left(2 \, b c - \sqrt{b c} {\left(b + c\right)}\right)} \sqrt{b x + a} \sqrt{c x + a} + 2 \, {\left(b^{2} c + b c^{2}\right)} x - 2 \, {\left(2 \, b c x + a b + a c\right)} \sqrt{b c}\right) + {\left(b + c\right)} x + 4 \, \sqrt{b x + a} \sqrt{c x + a} - 4 \, a}{2 \, {\left(b^{2} - 2 \, b c + c^{2}\right)} x}, \frac{2 \, {\left(b + c\right)} x \log\left(x\right) - 2 \, {\left(b + c\right)} x \log\left(-\frac{{\left(b + c\right)} x - 2 \, \sqrt{b x + a} \sqrt{c x + a} + 2 \, a}{x}\right) + 8 \, \sqrt{-b c} x \arctan\left(\frac{\sqrt{-b c} \sqrt{b x + a} \sqrt{c x + a} - \sqrt{-b c} a}{b c x}\right) + {\left(b + c\right)} x + 4 \, \sqrt{b x + a} \sqrt{c x + a} - 4 \, a}{2 \, {\left(b^{2} - 2 \, b c + c^{2}\right)} x}\right]"," ",0,"[1/2*(2*(b + c)*x*log(x) - 2*(b + c)*x*log(-((b + c)*x - 2*sqrt(b*x + a)*sqrt(c*x + a) + 2*a)/x) + 4*sqrt(b*c)*x*log(a*b^2 + 2*a*b*c + a*c^2 + 2*(2*b*c - sqrt(b*c)*(b + c))*sqrt(b*x + a)*sqrt(c*x + a) + 2*(b^2*c + b*c^2)*x - 2*(2*b*c*x + a*b + a*c)*sqrt(b*c)) + (b + c)*x + 4*sqrt(b*x + a)*sqrt(c*x + a) - 4*a)/((b^2 - 2*b*c + c^2)*x), 1/2*(2*(b + c)*x*log(x) - 2*(b + c)*x*log(-((b + c)*x - 2*sqrt(b*x + a)*sqrt(c*x + a) + 2*a)/x) + 8*sqrt(-b*c)*x*arctan((sqrt(-b*c)*sqrt(b*x + a)*sqrt(c*x + a) - sqrt(-b*c)*a)/(b*c*x)) + (b + c)*x + 4*sqrt(b*x + a)*sqrt(c*x + a) - 4*a)/((b^2 - 2*b*c + c^2)*x)]","A",0
436,1,126,0,0.406682," ","integrate(1/x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} - 2 \, b c + c^{2}\right)} x^{2} \log\left(-\frac{{\left(b + c\right)} x - 2 \, \sqrt{b x + a} \sqrt{c x + a} + 2 \, a}{x}\right) + {\left(b^{2} + 2 \, b c + c^{2}\right)} x^{2} + 8 \, {\left({\left(b + c\right)} x + 2 \, a\right)} \sqrt{b x + a} \sqrt{c x + a} - 16 \, a^{2} - 16 \, {\left(a b + a c\right)} x}{16 \, {\left(a b^{2} - 2 \, a b c + a c^{2}\right)} x^{2}}"," ",0,"1/16*(4*(b^2 - 2*b*c + c^2)*x^2*log(-((b + c)*x - 2*sqrt(b*x + a)*sqrt(c*x + a) + 2*a)/x) + (b^2 + 2*b*c + c^2)*x^2 + 8*((b + c)*x + 2*a)*sqrt(b*x + a)*sqrt(c*x + a) - 16*a^2 - 16*(a*b + a*c)*x)/((a*b^2 - 2*a*b*c + a*c^2)*x^2)","A",0
437,1,182,0,0.410964," ","integrate(1/x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(b^{3} - b^{2} c - b c^{2} + c^{3}\right)} x^{3} \log\left(-\frac{{\left(b + c\right)} x - 2 \, \sqrt{b x + a} \sqrt{c x + a} + 2 \, a}{x}\right) + {\left(5 \, b^{3} + 3 \, b^{2} c + 3 \, b c^{2} + 5 \, c^{3}\right)} x^{3} + 64 \, a^{3} + 8 \, {\left({\left(3 \, b^{2} - 2 \, b c + 3 \, c^{2}\right)} x^{2} - 8 \, a^{2} - 2 \, {\left(a b + a c\right)} x\right)} \sqrt{b x + a} \sqrt{c x + a} + 48 \, {\left(a^{2} b + a^{2} c\right)} x}{96 \, {\left(a^{2} b^{2} - 2 \, a^{2} b c + a^{2} c^{2}\right)} x^{3}}"," ",0,"-1/96*(12*(b^3 - b^2*c - b*c^2 + c^3)*x^3*log(-((b + c)*x - 2*sqrt(b*x + a)*sqrt(c*x + a) + 2*a)/x) + (5*b^3 + 3*b^2*c + 3*b*c^2 + 5*c^3)*x^3 + 64*a^3 + 8*((3*b^2 - 2*b*c + 3*c^2)*x^2 - 8*a^2 - 2*(a*b + a*c)*x)*sqrt(b*x + a)*sqrt(c*x + a) + 48*(a^2*b + a^2*c)*x)/((a^2*b^2 - 2*a^2*b*c + a^2*c^2)*x^3)","A",0
438,1,225,0,0.422697," ","integrate(x^4/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(16 \, a^{3} b c^{3} - 8 \, a^{3} c^{4} - 5 \, {\left(b^{4} c^{3} + 3 \, b^{3} c^{4}\right)} x^{3} - {\left(29 \, a b^{3} c^{3} + 3 \, a b^{2} c^{4}\right)} x^{2} - 4 \, {\left(2 \, a^{2} b^{2} c^{3} - a^{2} b c^{4}\right)} x\right)} \sqrt{b x + a} + {\left(8 \, a^{3} b^{4} - 16 \, a^{3} b^{3} c + 5 \, {\left(3 \, b^{4} c^{3} + b^{3} c^{4}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} + 29 \, a b^{3} c^{3}\right)} x^{2} - 4 \, {\left(a^{2} b^{4} c - 2 \, a^{2} b^{3} c^{2}\right)} x\right)} \sqrt{c x + a}\right)}}{35 \, {\left(b^{6} c^{3} - 3 \, b^{5} c^{4} + 3 \, b^{4} c^{5} - b^{3} c^{6}\right)}}"," ",0,"-2/35*((16*a^3*b*c^3 - 8*a^3*c^4 - 5*(b^4*c^3 + 3*b^3*c^4)*x^3 - (29*a*b^3*c^3 + 3*a*b^2*c^4)*x^2 - 4*(2*a^2*b^2*c^3 - a^2*b*c^4)*x)*sqrt(b*x + a) + (8*a^3*b^4 - 16*a^3*b^3*c + 5*(3*b^4*c^3 + b^3*c^4)*x^3 + (3*a*b^4*c^2 + 29*a*b^3*c^3)*x^2 - 4*(a^2*b^4*c - 2*a^2*b^3*c^2)*x)*sqrt(c*x + a))/(b^6*c^3 - 3*b^5*c^4 + 3*b^4*c^5 - b^3*c^6)","A",0
439,1,167,0,0.393252," ","integrate(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(6 \, a^{2} b c^{2} - 2 \, a^{2} c^{3} + {\left(b^{3} c^{2} + 3 \, b^{2} c^{3}\right)} x^{2} + {\left(7 \, a b^{2} c^{2} + a b c^{3}\right)} x\right)} \sqrt{b x + a} + {\left(2 \, a^{2} b^{3} - 6 \, a^{2} b^{2} c - {\left(3 \, b^{3} c^{2} + b^{2} c^{3}\right)} x^{2} - {\left(a b^{3} c + 7 \, a b^{2} c^{2}\right)} x\right)} \sqrt{c x + a}\right)}}{5 \, {\left(b^{5} c^{2} - 3 \, b^{4} c^{3} + 3 \, b^{3} c^{4} - b^{2} c^{5}\right)}}"," ",0,"2/5*((6*a^2*b*c^2 - 2*a^2*c^3 + (b^3*c^2 + 3*b^2*c^3)*x^2 + (7*a*b^2*c^2 + a*b*c^3)*x)*sqrt(b*x + a) + (2*a^2*b^3 - 6*a^2*b^2*c - (3*b^3*c^2 + b^2*c^3)*x^2 - (a*b^3*c + 7*a*b^2*c^2)*x)*sqrt(c*x + a))/(b^5*c^2 - 3*b^4*c^3 + 3*b^3*c^4 - b^2*c^5)","A",0
440,1,321,0,0.420145," ","integrate(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(6 \, a^{\frac{3}{2}} b c \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 6 \, a^{\frac{3}{2}} b c \log\left(\frac{c x - 2 \, \sqrt{c x + a} \sqrt{a} + 2 \, a}{x}\right) - {\left(13 \, a b c + 3 \, a c^{2} + {\left(b^{2} c + 3 \, b c^{2}\right)} x\right)} \sqrt{b x + a} + {\left(3 \, a b^{2} + 13 \, a b c + {\left(3 \, b^{2} c + b c^{2}\right)} x\right)} \sqrt{c x + a}\right)}}{3 \, {\left(b^{4} c - 3 \, b^{3} c^{2} + 3 \, b^{2} c^{3} - b c^{4}\right)}}, \frac{2 \, {\left(12 \, \sqrt{-a} a b c \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 12 \, \sqrt{-a} a b c \arctan\left(\frac{\sqrt{c x + a} \sqrt{-a}}{a}\right) + {\left(13 \, a b c + 3 \, a c^{2} + {\left(b^{2} c + 3 \, b c^{2}\right)} x\right)} \sqrt{b x + a} - {\left(3 \, a b^{2} + 13 \, a b c + {\left(3 \, b^{2} c + b c^{2}\right)} x\right)} \sqrt{c x + a}\right)}}{3 \, {\left(b^{4} c - 3 \, b^{3} c^{2} + 3 \, b^{2} c^{3} - b c^{4}\right)}}\right]"," ",0,"[-2/3*(6*a^(3/2)*b*c*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 6*a^(3/2)*b*c*log((c*x - 2*sqrt(c*x + a)*sqrt(a) + 2*a)/x) - (13*a*b*c + 3*a*c^2 + (b^2*c + 3*b*c^2)*x)*sqrt(b*x + a) + (3*a*b^2 + 13*a*b*c + (3*b^2*c + b*c^2)*x)*sqrt(c*x + a))/(b^4*c - 3*b^3*c^2 + 3*b^2*c^3 - b*c^4), 2/3*(12*sqrt(-a)*a*b*c*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 12*sqrt(-a)*a*b*c*arctan(sqrt(c*x + a)*sqrt(-a)/a) + (13*a*b*c + 3*a*c^2 + (b^2*c + 3*b*c^2)*x)*sqrt(b*x + a) - (3*a*b^2 + 13*a*b*c + (3*b^2*c + b*c^2)*x)*sqrt(c*x + a))/(b^4*c - 3*b^3*c^2 + 3*b^2*c^3 - b*c^4)]","A",0
441,1,260,0,0.418368," ","integrate(x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{a} {\left(b + c\right)} x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 3 \, \sqrt{a} {\left(b + c\right)} x \log\left(\frac{c x - 2 \, \sqrt{c x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left({\left(b + 3 \, c\right)} x - 2 \, a\right)} \sqrt{b x + a} + 2 \, {\left({\left(3 \, b + c\right)} x - 2 \, a\right)} \sqrt{c x + a}}{{\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)} x}, \frac{2 \, {\left(3 \, \sqrt{-a} {\left(b + c\right)} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 3 \, \sqrt{-a} {\left(b + c\right)} x \arctan\left(\frac{\sqrt{c x + a} \sqrt{-a}}{a}\right) + {\left({\left(b + 3 \, c\right)} x - 2 \, a\right)} \sqrt{b x + a} - {\left({\left(3 \, b + c\right)} x - 2 \, a\right)} \sqrt{c x + a}\right)}}{{\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)} x}\right]"," ",0,"[-(3*sqrt(a)*(b + c)*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 3*sqrt(a)*(b + c)*x*log((c*x - 2*sqrt(c*x + a)*sqrt(a) + 2*a)/x) - 2*((b + 3*c)*x - 2*a)*sqrt(b*x + a) + 2*((3*b + c)*x - 2*a)*sqrt(c*x + a))/((b^3 - 3*b^2*c + 3*b*c^2 - c^3)*x), 2*(3*sqrt(-a)*(b + c)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 3*sqrt(-a)*(b + c)*x*arctan(sqrt(c*x + a)*sqrt(-a)/a) + ((b + 3*c)*x - 2*a)*sqrt(b*x + a) - ((3*b + c)*x - 2*a)*sqrt(c*x + a))/((b^3 - 3*b^2*c + 3*b*c^2 - c^3)*x)]","A",0
442,1,297,0,0.448072," ","integrate(1/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{a} b c x^{2} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 3 \, \sqrt{a} b c x^{2} \log\left(\frac{c x - 2 \, \sqrt{c x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, a^{2} + {\left(2 \, a b + 3 \, a c\right)} x\right)} \sqrt{b x + a} - 2 \, {\left(2 \, a^{2} + {\left(3 \, a b + 2 \, a c\right)} x\right)} \sqrt{c x + a}}{2 \, {\left(a b^{3} - 3 \, a b^{2} c + 3 \, a b c^{2} - a c^{3}\right)} x^{2}}, \frac{3 \, \sqrt{-a} b c x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - 3 \, \sqrt{-a} b c x^{2} \arctan\left(\frac{\sqrt{c x + a} \sqrt{-a}}{a}\right) - {\left(2 \, a^{2} + {\left(2 \, a b + 3 \, a c\right)} x\right)} \sqrt{b x + a} + {\left(2 \, a^{2} + {\left(3 \, a b + 2 \, a c\right)} x\right)} \sqrt{c x + a}}{{\left(a b^{3} - 3 \, a b^{2} c + 3 \, a b c^{2} - a c^{3}\right)} x^{2}}\right]"," ",0,"[-1/2*(3*sqrt(a)*b*c*x^2*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 3*sqrt(a)*b*c*x^2*log((c*x - 2*sqrt(c*x + a)*sqrt(a) + 2*a)/x) + 2*(2*a^2 + (2*a*b + 3*a*c)*x)*sqrt(b*x + a) - 2*(2*a^2 + (3*a*b + 2*a*c)*x)*sqrt(c*x + a))/((a*b^3 - 3*a*b^2*c + 3*a*b*c^2 - a*c^3)*x^2), (3*sqrt(-a)*b*c*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) - 3*sqrt(-a)*b*c*x^2*arctan(sqrt(c*x + a)*sqrt(-a)/a) - (2*a^2 + (2*a*b + 3*a*c)*x)*sqrt(b*x + a) + (2*a^2 + (3*a*b + 2*a*c)*x)*sqrt(c*x + a))/((a*b^3 - 3*a*b^2*c + 3*a*b*c^2 - a*c^3)*x^2)]","A",0
443,1,44,0,0.400405," ","integrate((1-x)^(1/2)*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, x^{2} + \frac{1}{2} \, \sqrt{x + 1} x \sqrt{-x + 1} + x - \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-1/2*x^2 + 1/2*sqrt(x + 1)*x*sqrt(-x + 1) + x - arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
444,1,32,0,0.394597," ","integrate(x^3*(-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, x^{4} - \frac{2}{15} \, {\left(3 \, x^{4} - x^{2} - 2\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"-1/2*x^4 - 2/15*(3*x^4 - x^2 - 2)*sqrt(x + 1)*sqrt(-x + 1)","A",0
445,1,51,0,0.394084," ","integrate(x^2*(-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","-\frac{2}{3} \, x^{3} - \frac{1}{4} \, {\left(2 \, x^{3} - x\right)} \sqrt{x + 1} \sqrt{-x + 1} + \frac{1}{2} \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-2/3*x^3 - 1/4*(2*x^3 - x)*sqrt(x + 1)*sqrt(-x + 1) + 1/2*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
446,1,25,0,0.416083," ","integrate(x*(-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","-x^{2} - \frac{2}{3} \, {\left(x^{2} - 1\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"-x^2 - 2/3*(x^2 - 1)*sqrt(x + 1)*sqrt(-x + 1)","A",0
447,1,41,0,0.391846," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","-\sqrt{x + 1} x \sqrt{-x + 1} - 2 \, x + 2 \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-sqrt(x + 1)*x*sqrt(-x + 1) - 2*x + 2*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","B",0
448,1,41,0,0.398763," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x,x, algorithm=""fricas"")","-2 \, \sqrt{x + 1} \sqrt{-x + 1} - 2 \, \log\left(x\right) - 2 \, \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-2*sqrt(x + 1)*sqrt(-x + 1) - 2*log(x) - 2*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
449,1,44,0,0.409272," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, x \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - \sqrt{x + 1} \sqrt{-x + 1} - 1\right)}}{x}"," ",0,"-2*(2*x*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - sqrt(x + 1)*sqrt(-x + 1) - 1)/x","A",0
450,1,43,0,0.399923," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x^3,x, algorithm=""fricas"")","\frac{x^{2} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + \sqrt{x + 1} \sqrt{-x + 1} + 1}{x^{2}}"," ",0,"(x^2*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + sqrt(x + 1)*sqrt(-x + 1) + 1)/x^2","A",0
451,1,36,0,0.381798," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))/(-(1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","\sqrt{x + 1} \sqrt{-x + 1} + \log\left(x\right) + \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"sqrt(x + 1)*sqrt(-x + 1) + log(x) + log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
452,1,37,0,0.414839," ","integrate((-(-1+x)^(1/2)+(1+x)^(1/2))/((-1+x)^(1/2)+(1+x)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{x + 1} \sqrt{x - 1} x + \frac{1}{2} \, x^{2} - \frac{1}{2} \, \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"-1/2*sqrt(x + 1)*sqrt(x - 1)*x + 1/2*x^2 - 1/2*log(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
453,0,0,0,0.574890," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d\right)}^{n}, x\right)"," ",0,"integral((e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)^n, x)","F",0
454,1,161,0,0.414531," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""fricas"")","\frac{2 \, e^{4} x^{4} + 4 \, d e^{3} x^{3} - 3 \, a d^{2} f^{2} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 3 \, {\left(a e^{2} f^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(3 \, a d e f^{2} + d^{3} e\right)} x + {\left(2 \, e^{3} f x^{3} + 4 \, d e^{2} f x^{2} + 4 \, a d f^{3} + {\left(2 \, a e f^{3} + 3 \, d^{2} e f\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}}{2 \, e}"," ",0,"1/2*(2*e^4*x^4 + 4*d*e^3*x^3 - 3*a*d^2*f^2*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2)) + 3*(a*e^2*f^2 + d^2*e^2)*x^2 + 2*(3*a*d*e*f^2 + d^3*e)*x + (2*e^3*f*x^3 + 4*d*e^2*f*x^2 + 4*a*d*f^3 + (2*a*e*f^3 + 3*d^2*e*f)*x)*sqrt((e^2*x^2 + a*f^2)/f^2))/e","A",0
455,1,114,0,0.398265," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""fricas"")","\frac{2 \, e^{3} x^{3} + 3 \, d e^{2} x^{2} - 3 \, a d f^{2} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 3 \, {\left(a e f^{2} + d^{2} e\right)} x + {\left(2 \, e^{2} f x^{2} + 2 \, a f^{3} + 3 \, d e f x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}}{3 \, e}"," ",0,"1/3*(2*e^3*x^3 + 3*d*e^2*x^2 - 3*a*d*f^2*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2)) + 3*(a*e*f^2 + d^2*e)*x + (2*e^2*f*x^2 + 2*a*f^3 + 3*d*e*f*x)*sqrt((e^2*x^2 + a*f^2)/f^2))/e","A",0
456,1,74,0,0.400825," ","integrate(d+e*x+f*(a+e^2*x^2/f^2)^(1/2),x, algorithm=""fricas"")","\frac{e^{2} x^{2} - a f^{2} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + e f x \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, d e x}{2 \, e}"," ",0,"1/2*(e^2*x^2 - a*f^2*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2)) + e*f*x*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*d*e*x)/e","A",0
457,1,187,0,0.455759," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, d e x - 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + {\left(a f^{2} + d^{2}\right)} \log\left(a f^{2} - d e x + d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + {\left(a f^{2} + d^{2}\right)} \log\left(-a f^{2} + 2 \, d e x + d^{2}\right) - {\left(a f^{2} + d^{2}\right)} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} - d\right) + {\left(a f^{2} - d^{2}\right)} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)}{4 \, d^{2} e}"," ",0,"1/4*(2*d*e*x - 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + (a*f^2 + d^2)*log(a*f^2 - d*e*x + d*f*sqrt((e^2*x^2 + a*f^2)/f^2)) + (a*f^2 + d^2)*log(-a*f^2 + 2*d*e*x + d^2) - (a*f^2 + d^2)*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) - d) + (a*f^2 - d^2)*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2)))/(d^2*e)","A",0
458,1,284,0,0.468326," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""fricas"")","\frac{a^{2} f^{4} - 2 \, d^{2} e^{2} x^{2} + a d^{2} f^{2} - 2 \, d^{3} e x + {\left(a^{2} f^{4} - 2 \, a d e f^{2} x - a d^{2} f^{2}\right)} \log\left(-a e f^{2} x + 2 \, d e^{2} x^{2} + a d f^{2} + {\left(a f^{3} - 2 \, d e f x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + {\left(a^{2} f^{4} - 2 \, a d e f^{2} x - a d^{2} f^{2}\right)} \log\left(-a f^{2} + 2 \, d e x + d^{2}\right) - {\left(a^{2} f^{4} - 2 \, a d e f^{2} x - a d^{2} f^{2}\right)} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} - d\right) - 2 \, {\left(a d f^{3} - d^{2} e f x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}}{2 \, {\left(a d^{3} e f^{2} - 2 \, d^{4} e^{2} x - d^{5} e\right)}}"," ",0,"1/2*(a^2*f^4 - 2*d^2*e^2*x^2 + a*d^2*f^2 - 2*d^3*e*x + (a^2*f^4 - 2*a*d*e*f^2*x - a*d^2*f^2)*log(-a*e*f^2*x + 2*d*e^2*x^2 + a*d*f^2 + (a*f^3 - 2*d*e*f*x)*sqrt((e^2*x^2 + a*f^2)/f^2)) + (a^2*f^4 - 2*a*d*e*f^2*x - a*d^2*f^2)*log(-a*f^2 + 2*d*e*x + d^2) - (a^2*f^4 - 2*a*d*e*f^2*x - a*d^2*f^2)*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) - d) - 2*(a*d*f^3 - d^2*e*f*x)*sqrt((e^2*x^2 + a*f^2)/f^2))/(a*d^3*e*f^2 - 2*d^4*e^2*x - d^5*e)","B",0
459,1,536,0,0.709444," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""fricas"")","\frac{5 \, a^{3} f^{6} + 8 \, d^{3} e^{3} x^{3} - 6 \, a^{2} d^{2} f^{4} - 3 \, a d^{4} f^{2} + 2 \, {\left(a d^{2} e^{2} f^{2} + 5 \, d^{4} e^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{2} d e f^{4} + a d^{3} e f^{2} - 2 \, d^{5} e\right)} x + 3 \, {\left(a^{3} f^{6} + 4 \, a d^{2} e^{2} f^{2} x^{2} - 2 \, a^{2} d^{2} f^{4} + a d^{4} f^{2} - 4 \, {\left(a^{2} d e f^{4} - a d^{3} e f^{2}\right)} x\right)} \log\left(-a e f^{2} x + 2 \, d e^{2} x^{2} + a d f^{2} + {\left(a f^{3} - 2 \, d e f x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 3 \, {\left(a^{3} f^{6} + 4 \, a d^{2} e^{2} f^{2} x^{2} - 2 \, a^{2} d^{2} f^{4} + a d^{4} f^{2} - 4 \, {\left(a^{2} d e f^{4} - a d^{3} e f^{2}\right)} x\right)} \log\left(-a f^{2} + 2 \, d e x + d^{2}\right) - 3 \, {\left(a^{3} f^{6} + 4 \, a d^{2} e^{2} f^{2} x^{2} - 2 \, a^{2} d^{2} f^{4} + a d^{4} f^{2} - 4 \, {\left(a^{2} d e f^{4} - a d^{3} e f^{2}\right)} x\right)} \log\left(-e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} - d\right) - 2 \, {\left(3 \, a^{2} d f^{5} + 4 \, d^{3} e^{2} f x^{2} - 5 \, a d^{3} f^{3} - 3 \, {\left(3 \, a d^{2} e f^{3} - d^{4} e f\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}}{4 \, {\left(a^{2} d^{4} e f^{4} + 4 \, d^{6} e^{3} x^{2} - 2 \, a d^{6} e f^{2} + d^{8} e - 4 \, {\left(a d^{5} e^{2} f^{2} - d^{7} e^{2}\right)} x\right)}}"," ",0,"1/4*(5*a^3*f^6 + 8*d^3*e^3*x^3 - 6*a^2*d^2*f^4 - 3*a*d^4*f^2 + 2*(a*d^2*e^2*f^2 + 5*d^4*e^2)*x^2 - 2*(7*a^2*d*e*f^4 + a*d^3*e*f^2 - 2*d^5*e)*x + 3*(a^3*f^6 + 4*a*d^2*e^2*f^2*x^2 - 2*a^2*d^2*f^4 + a*d^4*f^2 - 4*(a^2*d*e*f^4 - a*d^3*e*f^2)*x)*log(-a*e*f^2*x + 2*d*e^2*x^2 + a*d*f^2 + (a*f^3 - 2*d*e*f*x)*sqrt((e^2*x^2 + a*f^2)/f^2)) + 3*(a^3*f^6 + 4*a*d^2*e^2*f^2*x^2 - 2*a^2*d^2*f^4 + a*d^4*f^2 - 4*(a^2*d*e*f^4 - a*d^3*e*f^2)*x)*log(-a*f^2 + 2*d*e*x + d^2) - 3*(a^3*f^6 + 4*a*d^2*e^2*f^2*x^2 - 2*a^2*d^2*f^4 + a*d^4*f^2 - 4*(a^2*d*e*f^4 - a*d^3*e*f^2)*x)*log(-e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) - d) - 2*(3*a^2*d*f^5 + 4*d^3*e^2*f*x^2 - 5*a*d^3*f^3 - 3*(3*a*d^2*e*f^3 - d^4*e*f)*x)*sqrt((e^2*x^2 + a*f^2)/f^2))/(a^2*d^4*e*f^4 + 4*d^6*e^3*x^2 - 2*a*d^6*e*f^2 + d^8*e - 4*(a*d^5*e^2*f^2 - d^7*e^2)*x)","B",0
460,1,416,0,0.497246," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, a d^{\frac{3}{2}} f^{2} \log\left(a f^{2} - 2 \, d e x + 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, {\left(\sqrt{d} e x - \sqrt{d} f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}\right) + 2 \, {\left(24 \, e^{3} x^{3} + 36 \, d e^{2} x^{2} + 116 \, a d f^{2} + 6 \, d^{3} + {\left(32 \, a e f^{2} + 39 \, d^{2} e\right)} x + {\left(24 \, e^{2} f x^{2} + 20 \, a f^{3} + 36 \, d e f x - 3 \, d^{2} f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{84 \, e}, \frac{105 \, a \sqrt{-d} d f^{2} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d} \sqrt{-d}}{d}\right) + {\left(24 \, e^{3} x^{3} + 36 \, d e^{2} x^{2} + 116 \, a d f^{2} + 6 \, d^{3} + {\left(32 \, a e f^{2} + 39 \, d^{2} e\right)} x + {\left(24 \, e^{2} f x^{2} + 20 \, a f^{3} + 36 \, d e f x - 3 \, d^{2} f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{42 \, e}\right]"," ",0,"[1/84*(105*a*d^(3/2)*f^2*log(a*f^2 - 2*d*e*x + 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*(sqrt(d)*e*x - sqrt(d)*f*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)) + 2*(24*e^3*x^3 + 36*d*e^2*x^2 + 116*a*d*f^2 + 6*d^3 + (32*a*e*f^2 + 39*d^2*e)*x + (24*e^2*f*x^2 + 20*a*f^3 + 36*d*e*f*x - 3*d^2*f)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/e, 1/42*(105*a*sqrt(-d)*d*f^2*arctan(sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)*sqrt(-d)/d) + (24*e^3*x^3 + 36*d*e^2*x^2 + 116*a*d*f^2 + 6*d^3 + (32*a*e*f^2 + 39*d^2*e)*x + (24*e^2*f*x^2 + 20*a*f^3 + 36*d*e*f*x - 3*d^2*f)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/e]","A",0
461,1,337,0,0.494308," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, a \sqrt{d} f^{2} \log\left(a f^{2} - 2 \, d e x + 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, {\left(\sqrt{d} e x - \sqrt{d} f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}\right) + 2 \, {\left(4 \, e^{2} x^{2} + 12 \, a f^{2} + 9 \, d e x + 2 \, d^{2} + {\left(4 \, e f x - d f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{20 \, e}, \frac{15 \, a \sqrt{-d} f^{2} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d} \sqrt{-d}}{d}\right) + {\left(4 \, e^{2} x^{2} + 12 \, a f^{2} + 9 \, d e x + 2 \, d^{2} + {\left(4 \, e f x - d f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{10 \, e}\right]"," ",0,"[1/20*(15*a*sqrt(d)*f^2*log(a*f^2 - 2*d*e*x + 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*(sqrt(d)*e*x - sqrt(d)*f*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)) + 2*(4*e^2*x^2 + 12*a*f^2 + 9*d*e*x + 2*d^2 + (4*e*f*x - d*f)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/e, 1/10*(15*a*sqrt(-d)*f^2*arctan(sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)*sqrt(-d)/d) + (4*e^2*x^2 + 12*a*f^2 + 9*d*e*x + 2*d^2 + (4*e*f*x - d*f)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/e]","A",0
462,1,301,0,0.498043," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{d} f^{2} \log\left(a f^{2} - 2 \, d e x + 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, {\left(\sqrt{d} e x - \sqrt{d} f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}\right) + 2 \, {\left(5 \, d e x - d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, d^{2}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{12 \, d e}, \frac{3 \, a \sqrt{-d} f^{2} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d} \sqrt{-d}}{d}\right) + {\left(5 \, d e x - d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, d^{2}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{6 \, d e}\right]"," ",0,"[1/12*(3*a*sqrt(d)*f^2*log(a*f^2 - 2*d*e*x + 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*(sqrt(d)*e*x - sqrt(d)*f*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)) + 2*(5*d*e*x - d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*d^2)*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(d*e), 1/6*(3*a*sqrt(-d)*f^2*arctan(sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)*sqrt(-d)/d) + (5*d*e*x - d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*d^2)*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(d*e)]","A",0
463,1,298,0,0.507870," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{d} f^{2} \log\left(a f^{2} - 2 \, d e x + 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} - 2 \, {\left(\sqrt{d} e x - \sqrt{d} f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}\right) + 2 \, {\left(d e x - d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, d^{2}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{4 \, d^{2} e}, -\frac{a \sqrt{-d} f^{2} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d} \sqrt{-d}}{d}\right) - {\left(d e x - d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + 2 \, d^{2}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{2 \, d^{2} e}\right]"," ",0,"[1/4*(a*sqrt(d)*f^2*log(a*f^2 - 2*d*e*x + 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) - 2*(sqrt(d)*e*x - sqrt(d)*f*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)) + 2*(d*e*x - d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*d^2)*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(d^2*e), -1/2*(a*sqrt(-d)*f^2*arctan(sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)*sqrt(-d)/d) - (d*e*x - d*f*sqrt((e^2*x^2 + a*f^2)/f^2) + 2*d^2)*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(d^2*e)]","A",0
464,1,487,0,0.519561," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} f^{4} - 2 \, a d e f^{2} x - a d^{2} f^{2}\right)} \sqrt{d} \log\left(a f^{2} - 2 \, d e x + 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} - 2 \, {\left(\sqrt{d} e x - \sqrt{d} f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}\right) - 2 \, {\left(2 \, d^{2} e^{2} x^{2} - 2 \, a d^{2} f^{2} - 2 \, d^{4} - {\left(3 \, a d e f^{2} + d^{3} e\right)} x + {\left(3 \, a d f^{3} - 2 \, d^{2} e f x + d^{3} f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{4 \, {\left(a d^{3} e f^{2} - 2 \, d^{4} e^{2} x - d^{5} e\right)}}, -\frac{3 \, {\left(a^{2} f^{4} - 2 \, a d e f^{2} x - a d^{2} f^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d} \sqrt{-d}}{d}\right) + {\left(2 \, d^{2} e^{2} x^{2} - 2 \, a d^{2} f^{2} - 2 \, d^{4} - {\left(3 \, a d e f^{2} + d^{3} e\right)} x + {\left(3 \, a d f^{3} - 2 \, d^{2} e f x + d^{3} f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{2 \, {\left(a d^{3} e f^{2} - 2 \, d^{4} e^{2} x - d^{5} e\right)}}\right]"," ",0,"[1/4*(3*(a^2*f^4 - 2*a*d*e*f^2*x - a*d^2*f^2)*sqrt(d)*log(a*f^2 - 2*d*e*x + 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) - 2*(sqrt(d)*e*x - sqrt(d)*f*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)) - 2*(2*d^2*e^2*x^2 - 2*a*d^2*f^2 - 2*d^4 - (3*a*d*e*f^2 + d^3*e)*x + (3*a*d*f^3 - 2*d^2*e*f*x + d^3*f)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(a*d^3*e*f^2 - 2*d^4*e^2*x - d^5*e), -1/2*(3*(a^2*f^4 - 2*a*d*e*f^2*x - a*d^2*f^2)*sqrt(-d)*arctan(sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)*sqrt(-d)/d) + (2*d^2*e^2*x^2 - 2*a*d^2*f^2 - 2*d^4 - (3*a*d*e*f^2 + d^3*e)*x + (3*a*d*f^3 - 2*d^2*e*f*x + d^3*f)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(a*d^3*e*f^2 - 2*d^4*e^2*x - d^5*e)]","A",0
465,1,812,0,0.544140," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} f^{6} + 4 \, a d^{2} e^{2} f^{2} x^{2} - 2 \, a^{2} d^{2} f^{4} + a d^{4} f^{2} - 4 \, {\left(a^{2} d e f^{4} - a d^{3} e f^{2}\right)} x\right)} \sqrt{d} \log\left(a f^{2} - 2 \, d e x + 2 \, d f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} - 2 \, {\left(\sqrt{d} e x - \sqrt{d} f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}\right) + 2 \, {\left(12 \, d^{3} e^{3} x^{3} + 10 \, a^{2} d^{2} f^{4} - 16 \, a d^{4} f^{2} - 2 \, d^{6} - 8 \, {\left(5 \, a d^{2} e^{2} f^{2} - d^{4} e^{2}\right)} x^{2} + {\left(15 \, a^{2} d e f^{4} - 46 \, a d^{3} e f^{2} - d^{5} e\right)} x - {\left(15 \, a^{2} d f^{5} + 12 \, d^{3} e^{2} f x^{2} - 22 \, a d^{3} f^{3} - d^{5} f - 8 \, {\left(5 \, a d^{2} e f^{3} - d^{4} e f\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{12 \, {\left(a^{2} d^{4} e f^{4} + 4 \, d^{6} e^{3} x^{2} - 2 \, a d^{6} e f^{2} + d^{8} e - 4 \, {\left(a d^{5} e^{2} f^{2} - d^{7} e^{2}\right)} x\right)}}, -\frac{15 \, {\left(a^{3} f^{6} + 4 \, a d^{2} e^{2} f^{2} x^{2} - 2 \, a^{2} d^{2} f^{4} + a d^{4} f^{2} - 4 \, {\left(a^{2} d e f^{4} - a d^{3} e f^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d} \sqrt{-d}}{d}\right) - {\left(12 \, d^{3} e^{3} x^{3} + 10 \, a^{2} d^{2} f^{4} - 16 \, a d^{4} f^{2} - 2 \, d^{6} - 8 \, {\left(5 \, a d^{2} e^{2} f^{2} - d^{4} e^{2}\right)} x^{2} + {\left(15 \, a^{2} d e f^{4} - 46 \, a d^{3} e f^{2} - d^{5} e\right)} x - {\left(15 \, a^{2} d f^{5} + 12 \, d^{3} e^{2} f x^{2} - 22 \, a d^{3} f^{3} - d^{5} f - 8 \, {\left(5 \, a d^{2} e f^{3} - d^{4} e f\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{6 \, {\left(a^{2} d^{4} e f^{4} + 4 \, d^{6} e^{3} x^{2} - 2 \, a d^{6} e f^{2} + d^{8} e - 4 \, {\left(a d^{5} e^{2} f^{2} - d^{7} e^{2}\right)} x\right)}}\right]"," ",0,"[1/12*(15*(a^3*f^6 + 4*a*d^2*e^2*f^2*x^2 - 2*a^2*d^2*f^4 + a*d^4*f^2 - 4*(a^2*d*e*f^4 - a*d^3*e*f^2)*x)*sqrt(d)*log(a*f^2 - 2*d*e*x + 2*d*f*sqrt((e^2*x^2 + a*f^2)/f^2) - 2*(sqrt(d)*e*x - sqrt(d)*f*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)) + 2*(12*d^3*e^3*x^3 + 10*a^2*d^2*f^4 - 16*a*d^4*f^2 - 2*d^6 - 8*(5*a*d^2*e^2*f^2 - d^4*e^2)*x^2 + (15*a^2*d*e*f^4 - 46*a*d^3*e*f^2 - d^5*e)*x - (15*a^2*d*f^5 + 12*d^3*e^2*f*x^2 - 22*a*d^3*f^3 - d^5*f - 8*(5*a*d^2*e*f^3 - d^4*e*f)*x)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(a^2*d^4*e*f^4 + 4*d^6*e^3*x^2 - 2*a*d^6*e*f^2 + d^8*e - 4*(a*d^5*e^2*f^2 - d^7*e^2)*x), -1/6*(15*(a^3*f^6 + 4*a*d^2*e^2*f^2*x^2 - 2*a^2*d^2*f^4 + a*d^4*f^2 - 4*(a^2*d*e*f^4 - a*d^3*e*f^2)*x)*sqrt(-d)*arctan(sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d)*sqrt(-d)/d) - (12*d^3*e^3*x^3 + 10*a^2*d^2*f^4 - 16*a*d^4*f^2 - 2*d^6 - 8*(5*a*d^2*e^2*f^2 - d^4*e^2)*x^2 + (15*a^2*d*e*f^4 - 46*a*d^3*e*f^2 - d^5*e)*x - (15*a^2*d*f^5 + 12*d^3*e^2*f*x^2 - 22*a*d^3*f^3 - d^5*f - 8*(5*a*d^2*e*f^3 - d^4*e*f)*x)*sqrt((e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((e^2*x^2 + a*f^2)/f^2) + d))/(a^2*d^4*e*f^4 + 4*d^6*e^3*x^2 - 2*a*d^6*e*f^2 + d^8*e - 4*(a*d^5*e^2*f^2 - d^7*e^2)*x)]","B",0
466,1,26,0,0.395163," ","integrate((x-(x^2-4)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(2 \, x + \sqrt{x^{2} - 4}\right)} \sqrt{x - \sqrt{x^{2} - 4}}"," ",0,"2/3*(2*x + sqrt(x^2 - 4))*sqrt(x - sqrt(x^2 - 4))","A",0
467,1,59,0,0.414584," ","integrate((a*x+b*(c+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a x - b \sqrt{\frac{a^{2} x^{2} + b^{2} c}{b^{2}}}\right)} \sqrt{a x + b \sqrt{\frac{a^{2} x^{2} + b^{2} c}{b^{2}}}}}{3 \, a}"," ",0,"2/3*(2*a*x - b*sqrt((a^2*x^2 + b^2*c)/b^2))*sqrt(a*x + b*sqrt((a^2*x^2 + b^2*c)/b^2))/a","A",0
468,1,34,0,0.421366," ","integrate((1+(-x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} - \sqrt{-x^{2} + 1} + 1\right)} \sqrt{\sqrt{-x^{2} + 1} + 1}}{3 \, x}"," ",0,"2/3*(x^2 - sqrt(-x^2 + 1) + 1)*sqrt(sqrt(-x^2 + 1) + 1)/x","A",0
469,1,28,0,0.446475," ","integrate(((x^2+1)^(1/2)+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + \sqrt{x^{2} + 1} - 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}{3 \, x}"," ",0,"2/3*(x^2 + sqrt(x^2 + 1) - 1)*sqrt(sqrt(x^2 + 1) + 1)/x","A",0
470,1,30,0,0.426109," ","integrate((5+(x^2+25)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 5 \, \sqrt{x^{2} + 25} - 25\right)} \sqrt{\sqrt{x^{2} + 25} + 5}}{3 \, x}"," ",0,"2/3*(x^2 + 5*sqrt(x^2 + 25) - 25)*sqrt(sqrt(x^2 + 25) + 5)/x","A",0
471,1,70,0,0.496426," ","integrate((a+b*(1/b^2*a^2+c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} c x^{2} + a b \sqrt{\frac{b^{2} c x^{2} + a^{2}}{b^{2}}} - a^{2}\right)} \sqrt{b \sqrt{\frac{b^{2} c x^{2} + a^{2}}{b^{2}}} + a}}{3 \, b^{2} c x}"," ",0,"2/3*(b^2*c*x^2 + a*b*sqrt((b^2*c*x^2 + a^2)/b^2) - a^2)*sqrt(b*sqrt((b^2*c*x^2 + a^2)/b^2) + a)/(b^2*c*x)","A",0
472,-1,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,1,345,0,0.813924," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""fricas"")","\frac{32 \, e^{8} x^{4} + 32 \, {\left(b e^{6} f^{2} + 2 \, d e^{7}\right)} x^{3} + 48 \, {\left(d^{2} e^{6} + {\left(b d e^{5} + a e^{6}\right)} f^{2}\right)} x^{2} + 32 \, {\left(3 \, a d e^{5} f^{2} + d^{3} e^{5}\right)} x + 3 \, {\left(b^{4} f^{8} - 16 \, a d^{2} e^{4} f^{2} - 4 \, {\left(b^{3} d e + a b^{2} e^{2}\right)} f^{6} + 4 \, {\left(b^{2} d^{2} e^{2} + 4 \, a b d e^{3}\right)} f^{4}\right)} \log\left(-b f^{2} - 2 \, e^{2} x + 2 \, e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 2 \, {\left(3 \, b^{3} e f^{7} + 16 \, e^{7} f x^{3} - 4 \, {\left(3 \, b^{2} d e^{2} + 2 \, a b e^{3}\right)} f^{5} + 4 \, {\left(3 \, b d^{2} e^{3} + 8 \, a d e^{4}\right)} f^{3} + 8 \, {\left(b e^{5} f^{3} + 4 \, d e^{6} f\right)} x^{2} - 2 \, {\left(b^{2} e^{3} f^{5} - 12 \, d^{2} e^{5} f - 4 \, {\left(b d e^{4} + 2 \, a e^{5}\right)} f^{3}\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}}{32 \, e^{5}}"," ",0,"1/32*(32*e^8*x^4 + 32*(b*e^6*f^2 + 2*d*e^7)*x^3 + 48*(d^2*e^6 + (b*d*e^5 + a*e^6)*f^2)*x^2 + 32*(3*a*d*e^5*f^2 + d^3*e^5)*x + 3*(b^4*f^8 - 16*a*d^2*e^4*f^2 - 4*(b^3*d*e + a*b^2*e^2)*f^6 + 4*(b^2*d^2*e^2 + 4*a*b*d*e^3)*f^4)*log(-b*f^2 - 2*e^2*x + 2*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 2*(3*b^3*e*f^7 + 16*e^7*f*x^3 - 4*(3*b^2*d*e^2 + 2*a*b*e^3)*f^5 + 4*(3*b*d^2*e^3 + 8*a*d*e^4)*f^3 + 8*(b*e^5*f^3 + 4*d*e^6*f)*x^2 - 2*(b^2*e^3*f^5 - 12*d^2*e^5*f - 4*(b*d*e^4 + 2*a*e^5)*f^3)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))/e^5","A",0
474,1,219,0,0.638277," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""fricas"")","\frac{16 \, e^{6} x^{3} + 12 \, {\left(b e^{4} f^{2} + 2 \, d e^{5}\right)} x^{2} + 24 \, {\left(a e^{4} f^{2} + d^{2} e^{4}\right)} x - 3 \, {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} \log\left(-b f^{2} - 2 \, e^{2} x + 2 \, e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) - 2 \, {\left(3 \, b^{2} e f^{5} - 8 \, e^{5} f x^{2} - 2 \, {\left(3 \, b d e^{2} + 4 \, a e^{3}\right)} f^{3} - 2 \, {\left(b e^{3} f^{3} + 6 \, d e^{4} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}}{24 \, e^{4}}"," ",0,"1/24*(16*e^6*x^3 + 12*(b*e^4*f^2 + 2*d*e^5)*x^2 + 24*(a*e^4*f^2 + d^2*e^4)*x - 3*(b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*log(-b*f^2 - 2*e^2*x + 2*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) - 2*(3*b^2*e*f^5 - 8*e^5*f*x^2 - 2*(3*b*d*e^2 + 4*a*e^3)*f^3 - 2*(b*e^3*f^3 + 6*d*e^4*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))/e^4","A",0
475,1,123,0,0.611220," ","integrate(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2),x, algorithm=""fricas"")","\frac{4 \, e^{4} x^{2} + 8 \, d e^{3} x + {\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \log\left(-b f^{2} - 2 \, e^{2} x + 2 \, e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 2 \, {\left(b e f^{3} + 2 \, e^{3} f x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}}{8 \, e^{3}}"," ",0,"1/8*(4*e^4*x^2 + 8*d*e^3*x + (b^2*f^4 - 4*a*e^2*f^2)*log(-b*f^2 - 2*e^2*x + 2*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 2*(b*e*f^3 + 2*e^3*f*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))/e^3","A",0
476,1,371,0,8.118674," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x - 2 \, {\left(d^{2} e^{2} - {\left(b d e - a e^{2}\right)} f^{2}\right)} \log\left({\left(b d - 2 \, a e\right)} f^{2} - {\left(b e f^{2} - 2 \, d e^{2}\right)} x + {\left(b f^{3} - 2 \, d e f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) - 2 \, {\left(d^{2} e^{2} - {\left(b d e - a e^{2}\right)} f^{2}\right)} \log\left(a f^{2} - d^{2} + {\left(b f^{2} - 2 \, d e\right)} x\right) + {\left(b^{2} f^{4} + 2 \, d^{2} e^{2} - 2 \, {\left(b d e + a e^{2}\right)} f^{2}\right)} \log\left(-b f^{2} - 2 \, e^{2} x + 2 \, e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 2 \, {\left(d^{2} e^{2} - {\left(b d e - a e^{2}\right)} f^{2}\right)} \log\left(-e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - d\right) - 2 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}}{2 \, {\left(b^{2} e f^{4} - 4 \, b d e^{2} f^{2} + 4 \, d^{2} e^{3}\right)}}"," ",0,"-1/2*(2*(b*e^2*f^2 - 2*d*e^3)*x - 2*(d^2*e^2 - (b*d*e - a*e^2)*f^2)*log((b*d - 2*a*e)*f^2 - (b*e*f^2 - 2*d*e^2)*x + (b*f^3 - 2*d*e*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) - 2*(d^2*e^2 - (b*d*e - a*e^2)*f^2)*log(a*f^2 - d^2 + (b*f^2 - 2*d*e)*x) + (b^2*f^4 + 2*d^2*e^2 - 2*(b*d*e + a*e^2)*f^2)*log(-b*f^2 - 2*e^2*x + 2*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 2*(d^2*e^2 - (b*d*e - a*e^2)*f^2)*log(-e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - d) - 2*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))/(b^2*e*f^4 - 4*b*d*e^2*f^2 + 4*d^2*e^3)","A",0
477,1,826,0,3.686164," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""fricas"")","-\frac{a b^{2} f^{6} + {\left(3 \, b^{2} d^{2} - 14 \, a b d e + 8 \, a^{2} e^{2}\right)} f^{4} - 2 \, {\left(b d^{3} e - 4 \, a d^{2} e^{2}\right)} f^{2} - 4 \, {\left(b^{2} e^{2} f^{4} - 4 \, b d e^{3} f^{2} + 4 \, d^{2} e^{4}\right)} x^{2} + {\left(b^{3} f^{6} - 8 \, b^{2} d e f^{4} + 20 \, b d^{2} e^{2} f^{2} - 16 \, d^{3} e^{3}\right)} x - 2 \, {\left(a b^{2} f^{6} + 4 \, a d^{2} e^{2} f^{2} - {\left(b^{2} d^{2} + 4 \, a^{2} e^{2}\right)} f^{4} + {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} x\right)} \log\left(-4 \, a d e^{2} f^{2} - {\left(b^{2} d - 4 \, a b e\right)} f^{4} + 4 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)} x^{2} + {\left(3 \, b^{2} e f^{4} - 4 \, {\left(2 \, b d e^{2} - a e^{3}\right)} f^{2}\right)} x - {\left(b^{2} f^{5} - 4 \, {\left(b d e - a e^{2}\right)} f^{3} + 4 \, {\left(b e^{2} f^{3} - 2 \, d e^{3} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) - 2 \, {\left(a b^{2} f^{6} + 4 \, a d^{2} e^{2} f^{2} - {\left(b^{2} d^{2} + 4 \, a^{2} e^{2}\right)} f^{4} + {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} x\right)} \log\left(a f^{2} - d^{2} + {\left(b f^{2} - 2 \, d e\right)} x\right) + 2 \, {\left(a b^{2} f^{6} + 4 \, a d^{2} e^{2} f^{2} - {\left(b^{2} d^{2} + 4 \, a^{2} e^{2}\right)} f^{4} + {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} x\right)} \log\left(-e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - d\right) - 4 \, {\left({\left(b^{2} d - 2 \, a b e\right)} f^{5} - 2 \, {\left(b d^{2} e - 2 \, a d e^{2}\right)} f^{3} - {\left(b^{2} e f^{5} - 4 \, b d e^{2} f^{3} + 4 \, d^{2} e^{3} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}}{2 \, {\left(a b^{3} f^{8} + 8 \, d^{5} e^{3} - {\left(b^{3} d^{2} + 6 \, a b^{2} d e\right)} f^{6} + 6 \, {\left(b^{2} d^{3} e + 2 \, a b d^{2} e^{2}\right)} f^{4} - 4 \, {\left(3 \, b d^{4} e^{2} + 2 \, a d^{3} e^{3}\right)} f^{2} + {\left(b^{4} f^{8} - 8 \, b^{3} d e f^{6} + 24 \, b^{2} d^{2} e^{2} f^{4} - 32 \, b d^{3} e^{3} f^{2} + 16 \, d^{4} e^{4}\right)} x\right)}}"," ",0,"-1/2*(a*b^2*f^6 + (3*b^2*d^2 - 14*a*b*d*e + 8*a^2*e^2)*f^4 - 2*(b*d^3*e - 4*a*d^2*e^2)*f^2 - 4*(b^2*e^2*f^4 - 4*b*d*e^3*f^2 + 4*d^2*e^4)*x^2 + (b^3*f^6 - 8*b^2*d*e*f^4 + 20*b*d^2*e^2*f^2 - 16*d^3*e^3)*x - 2*(a*b^2*f^6 + 4*a*d^2*e^2*f^2 - (b^2*d^2 + 4*a^2*e^2)*f^4 + (b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*x)*log(-4*a*d*e^2*f^2 - (b^2*d - 4*a*b*e)*f^4 + 4*(b*e^3*f^2 - 2*d*e^4)*x^2 + (3*b^2*e*f^4 - 4*(2*b*d*e^2 - a*e^3)*f^2)*x - (b^2*f^5 - 4*(b*d*e - a*e^2)*f^3 + 4*(b*e^2*f^3 - 2*d*e^3*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) - 2*(a*b^2*f^6 + 4*a*d^2*e^2*f^2 - (b^2*d^2 + 4*a^2*e^2)*f^4 + (b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*x)*log(a*f^2 - d^2 + (b*f^2 - 2*d*e)*x) + 2*(a*b^2*f^6 + 4*a*d^2*e^2*f^2 - (b^2*d^2 + 4*a^2*e^2)*f^4 + (b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*x)*log(-e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - d) - 4*((b^2*d - 2*a*b*e)*f^5 - 2*(b*d^2*e - 2*a*d*e^2)*f^3 - (b^2*e*f^5 - 4*b*d*e^2*f^3 + 4*d^2*e^3*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))/(a*b^3*f^8 + 8*d^5*e^3 - (b^3*d^2 + 6*a*b^2*d*e)*f^6 + 6*(b^2*d^3*e + 2*a*b*d^2*e^2)*f^4 - 4*(3*b*d^4*e^2 + 2*a*d^3*e^3)*f^2 + (b^4*f^8 - 8*b^3*d*e*f^6 + 24*b^2*d^2*e^2*f^4 - 32*b*d^3*e^3*f^2 + 16*d^4*e^4)*x)","B",0
478,1,1954,0,32.344055," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a b^{3} d - 4 \, a^{2} b^{2} e\right)} f^{8} - {\left(b^{3} d^{3} + 4 \, a b^{2} d^{2} e + 10 \, a^{2} b d e^{2} - 20 \, a^{3} e^{3}\right)} f^{6} - 4 \, {\left(b^{2} d^{4} e - 8 \, a b d^{3} e^{2} + 6 \, a^{2} d^{2} e^{3}\right)} f^{4} - 4 \, {\left(b^{3} e^{3} f^{6} - 6 \, b^{2} d e^{4} f^{4} + 12 \, b d^{2} e^{5} f^{2} - 8 \, d^{3} e^{6}\right)} x^{3} + 2 \, {\left(b d^{5} e^{2} - 6 \, a d^{4} e^{3}\right)} f^{2} - {\left(b^{4} e f^{8} - 2 \, a b^{2} e^{3} f^{6} - 40 \, d^{4} e^{5} - 2 \, {\left(11 \, b^{2} d^{2} e^{3} - 4 \, a b d e^{4}\right)} f^{4} + 8 \, {\left(7 \, b d^{3} e^{4} - a d^{2} e^{5}\right)} f^{2}\right)} x^{2} + {\left(16 \, d^{5} e^{4} + {\left(3 \, b^{4} d - 5 \, a b^{3} e\right)} f^{8} - {\left(7 \, b^{3} d^{2} e + 10 \, a b^{2} d e^{2} - 28 \, a^{2} b e^{3}\right)} f^{6} + 2 \, {\left(5 \, b^{2} d^{3} e^{2} + 22 \, a b d^{2} e^{3} - 28 \, a^{2} d e^{4}\right)} f^{4} - 8 \, {\left(3 \, b d^{4} e^{3} + a d^{3} e^{4}\right)} f^{2}\right)} x - 3 \, {\left(a^{2} b^{2} e f^{8} - 4 \, a d^{4} e^{3} f^{2} - 2 \, {\left(a b^{2} d^{2} e + 2 \, a^{3} e^{3}\right)} f^{6} + {\left(b^{2} d^{4} e + 8 \, a^{2} d^{2} e^{3}\right)} f^{4} + {\left(b^{4} e f^{8} - 16 \, a d^{2} e^{5} f^{2} - 4 \, {\left(b^{3} d e^{2} + a b^{2} e^{3}\right)} f^{6} + 4 \, {\left(b^{2} d^{2} e^{3} + 4 \, a b d e^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(a b^{3} e f^{8} - 8 \, a d^{3} e^{4} f^{2} - {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} + 4 \, a^{2} b e^{3}\right)} f^{6} + 2 \, {\left(b^{2} d^{3} e^{2} + 2 \, a b d^{2} e^{3} + 4 \, a^{2} d e^{4}\right)} f^{4}\right)} x\right)} \log\left(-4 \, a d e^{2} f^{2} - {\left(b^{2} d - 4 \, a b e\right)} f^{4} + 4 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)} x^{2} + {\left(3 \, b^{2} e f^{4} - 4 \, {\left(2 \, b d e^{2} - a e^{3}\right)} f^{2}\right)} x - {\left(b^{2} f^{5} - 4 \, {\left(b d e - a e^{2}\right)} f^{3} + 4 \, {\left(b e^{2} f^{3} - 2 \, d e^{3} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) - 3 \, {\left(a^{2} b^{2} e f^{8} - 4 \, a d^{4} e^{3} f^{2} - 2 \, {\left(a b^{2} d^{2} e + 2 \, a^{3} e^{3}\right)} f^{6} + {\left(b^{2} d^{4} e + 8 \, a^{2} d^{2} e^{3}\right)} f^{4} + {\left(b^{4} e f^{8} - 16 \, a d^{2} e^{5} f^{2} - 4 \, {\left(b^{3} d e^{2} + a b^{2} e^{3}\right)} f^{6} + 4 \, {\left(b^{2} d^{2} e^{3} + 4 \, a b d e^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(a b^{3} e f^{8} - 8 \, a d^{3} e^{4} f^{2} - {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} + 4 \, a^{2} b e^{3}\right)} f^{6} + 2 \, {\left(b^{2} d^{3} e^{2} + 2 \, a b d^{2} e^{3} + 4 \, a^{2} d e^{4}\right)} f^{4}\right)} x\right)} \log\left(a f^{2} - d^{2} + {\left(b f^{2} - 2 \, d e\right)} x\right) + 3 \, {\left(a^{2} b^{2} e f^{8} - 4 \, a d^{4} e^{3} f^{2} - 2 \, {\left(a b^{2} d^{2} e + 2 \, a^{3} e^{3}\right)} f^{6} + {\left(b^{2} d^{4} e + 8 \, a^{2} d^{2} e^{3}\right)} f^{4} + {\left(b^{4} e f^{8} - 16 \, a d^{2} e^{5} f^{2} - 4 \, {\left(b^{3} d e^{2} + a b^{2} e^{3}\right)} f^{6} + 4 \, {\left(b^{2} d^{2} e^{3} + 4 \, a b d e^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(a b^{3} e f^{8} - 8 \, a d^{3} e^{4} f^{2} - {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} + 4 \, a^{2} b e^{3}\right)} f^{6} + 2 \, {\left(b^{2} d^{3} e^{2} + 2 \, a b d^{2} e^{3} + 4 \, a^{2} d e^{4}\right)} f^{4}\right)} x\right)} \log\left(-e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - d\right) - 2 \, {\left(a b^{3} f^{9} - 3 \, {\left(a b^{2} d e + 2 \, a^{2} b e^{2}\right)} f^{7} - 3 \, {\left(b^{2} d^{3} e - 4 \, a b d^{2} e^{2} - 4 \, a^{2} d e^{3}\right)} f^{5} + 2 \, {\left(3 \, b d^{4} e^{2} - 10 \, a d^{3} e^{3}\right)} f^{3} - 2 \, {\left(b^{3} e^{2} f^{7} - 6 \, b^{2} d e^{3} f^{5} + 12 \, b d^{2} e^{4} f^{3} - 8 \, d^{3} e^{5} f\right)} x^{2} + {\left(b^{4} f^{9} + 12 \, d^{4} e^{4} f - 3 \, {\left(b^{3} d e + 3 \, a b^{2} e^{2}\right)} f^{7} + 3 \, {\left(b^{2} d^{2} e^{2} + 12 \, a b d e^{3}\right)} f^{5} - 4 \, {\left(2 \, b d^{3} e^{3} + 9 \, a d^{2} e^{4}\right)} f^{3}\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}}{a^{2} b^{4} f^{12} + 16 \, d^{8} e^{4} - 2 \, {\left(a b^{4} d^{2} + 4 \, a^{2} b^{3} d e\right)} f^{10} + {\left(b^{4} d^{4} + 16 \, a b^{3} d^{3} e + 24 \, a^{2} b^{2} d^{2} e^{2}\right)} f^{8} - 8 \, {\left(b^{3} d^{5} e + 6 \, a b^{2} d^{4} e^{2} + 4 \, a^{2} b d^{3} e^{3}\right)} f^{6} + 8 \, {\left(3 \, b^{2} d^{6} e^{2} + 8 \, a b d^{5} e^{3} + 2 \, a^{2} d^{4} e^{4}\right)} f^{4} - 32 \, {\left(b d^{7} e^{3} + a d^{6} e^{4}\right)} f^{2} + {\left(b^{6} f^{12} - 12 \, b^{5} d e f^{10} + 60 \, b^{4} d^{2} e^{2} f^{8} - 160 \, b^{3} d^{3} e^{3} f^{6} + 240 \, b^{2} d^{4} e^{4} f^{4} - 192 \, b d^{5} e^{5} f^{2} + 64 \, d^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} f^{12} + 32 \, d^{7} e^{5} - {\left(b^{5} d^{2} + 10 \, a b^{4} d e\right)} f^{10} + 10 \, {\left(b^{4} d^{3} e + 4 \, a b^{3} d^{2} e^{2}\right)} f^{8} - 40 \, {\left(b^{3} d^{4} e^{2} + 2 \, a b^{2} d^{3} e^{3}\right)} f^{6} + 80 \, {\left(b^{2} d^{5} e^{3} + a b d^{4} e^{4}\right)} f^{4} - 16 \, {\left(5 \, b d^{6} e^{4} + 2 \, a d^{5} e^{5}\right)} f^{2}\right)} x}"," ",0,"((3*a*b^3*d - 4*a^2*b^2*e)*f^8 - (b^3*d^3 + 4*a*b^2*d^2*e + 10*a^2*b*d*e^2 - 20*a^3*e^3)*f^6 - 4*(b^2*d^4*e - 8*a*b*d^3*e^2 + 6*a^2*d^2*e^3)*f^4 - 4*(b^3*e^3*f^6 - 6*b^2*d*e^4*f^4 + 12*b*d^2*e^5*f^2 - 8*d^3*e^6)*x^3 + 2*(b*d^5*e^2 - 6*a*d^4*e^3)*f^2 - (b^4*e*f^8 - 2*a*b^2*e^3*f^6 - 40*d^4*e^5 - 2*(11*b^2*d^2*e^3 - 4*a*b*d*e^4)*f^4 + 8*(7*b*d^3*e^4 - a*d^2*e^5)*f^2)*x^2 + (16*d^5*e^4 + (3*b^4*d - 5*a*b^3*e)*f^8 - (7*b^3*d^2*e + 10*a*b^2*d*e^2 - 28*a^2*b*e^3)*f^6 + 2*(5*b^2*d^3*e^2 + 22*a*b*d^2*e^3 - 28*a^2*d*e^4)*f^4 - 8*(3*b*d^4*e^3 + a*d^3*e^4)*f^2)*x - 3*(a^2*b^2*e*f^8 - 4*a*d^4*e^3*f^2 - 2*(a*b^2*d^2*e + 2*a^3*e^3)*f^6 + (b^2*d^4*e + 8*a^2*d^2*e^3)*f^4 + (b^4*e*f^8 - 16*a*d^2*e^5*f^2 - 4*(b^3*d*e^2 + a*b^2*e^3)*f^6 + 4*(b^2*d^2*e^3 + 4*a*b*d*e^4)*f^4)*x^2 + 2*(a*b^3*e*f^8 - 8*a*d^3*e^4*f^2 - (b^3*d^2*e + 2*a*b^2*d*e^2 + 4*a^2*b*e^3)*f^6 + 2*(b^2*d^3*e^2 + 2*a*b*d^2*e^3 + 4*a^2*d*e^4)*f^4)*x)*log(-4*a*d*e^2*f^2 - (b^2*d - 4*a*b*e)*f^4 + 4*(b*e^3*f^2 - 2*d*e^4)*x^2 + (3*b^2*e*f^4 - 4*(2*b*d*e^2 - a*e^3)*f^2)*x - (b^2*f^5 - 4*(b*d*e - a*e^2)*f^3 + 4*(b*e^2*f^3 - 2*d*e^3*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) - 3*(a^2*b^2*e*f^8 - 4*a*d^4*e^3*f^2 - 2*(a*b^2*d^2*e + 2*a^3*e^3)*f^6 + (b^2*d^4*e + 8*a^2*d^2*e^3)*f^4 + (b^4*e*f^8 - 16*a*d^2*e^5*f^2 - 4*(b^3*d*e^2 + a*b^2*e^3)*f^6 + 4*(b^2*d^2*e^3 + 4*a*b*d*e^4)*f^4)*x^2 + 2*(a*b^3*e*f^8 - 8*a*d^3*e^4*f^2 - (b^3*d^2*e + 2*a*b^2*d*e^2 + 4*a^2*b*e^3)*f^6 + 2*(b^2*d^3*e^2 + 2*a*b*d^2*e^3 + 4*a^2*d*e^4)*f^4)*x)*log(a*f^2 - d^2 + (b*f^2 - 2*d*e)*x) + 3*(a^2*b^2*e*f^8 - 4*a*d^4*e^3*f^2 - 2*(a*b^2*d^2*e + 2*a^3*e^3)*f^6 + (b^2*d^4*e + 8*a^2*d^2*e^3)*f^4 + (b^4*e*f^8 - 16*a*d^2*e^5*f^2 - 4*(b^3*d*e^2 + a*b^2*e^3)*f^6 + 4*(b^2*d^2*e^3 + 4*a*b*d*e^4)*f^4)*x^2 + 2*(a*b^3*e*f^8 - 8*a*d^3*e^4*f^2 - (b^3*d^2*e + 2*a*b^2*d*e^2 + 4*a^2*b*e^3)*f^6 + 2*(b^2*d^3*e^2 + 2*a*b*d^2*e^3 + 4*a^2*d*e^4)*f^4)*x)*log(-e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - d) - 2*(a*b^3*f^9 - 3*(a*b^2*d*e + 2*a^2*b*e^2)*f^7 - 3*(b^2*d^3*e - 4*a*b*d^2*e^2 - 4*a^2*d*e^3)*f^5 + 2*(3*b*d^4*e^2 - 10*a*d^3*e^3)*f^3 - 2*(b^3*e^2*f^7 - 6*b^2*d*e^3*f^5 + 12*b*d^2*e^4*f^3 - 8*d^3*e^5*f)*x^2 + (b^4*f^9 + 12*d^4*e^4*f - 3*(b^3*d*e + 3*a*b^2*e^2)*f^7 + 3*(b^2*d^2*e^2 + 12*a*b*d*e^3)*f^5 - 4*(2*b*d^3*e^3 + 9*a*d^2*e^4)*f^3)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))/(a^2*b^4*f^12 + 16*d^8*e^4 - 2*(a*b^4*d^2 + 4*a^2*b^3*d*e)*f^10 + (b^4*d^4 + 16*a*b^3*d^3*e + 24*a^2*b^2*d^2*e^2)*f^8 - 8*(b^3*d^5*e + 6*a*b^2*d^4*e^2 + 4*a^2*b*d^3*e^3)*f^6 + 8*(3*b^2*d^6*e^2 + 8*a*b*d^5*e^3 + 2*a^2*d^4*e^4)*f^4 - 32*(b*d^7*e^3 + a*d^6*e^4)*f^2 + (b^6*f^12 - 12*b^5*d*e*f^10 + 60*b^4*d^2*e^2*f^8 - 160*b^3*d^3*e^3*f^6 + 240*b^2*d^4*e^4*f^4 - 192*b*d^5*e^5*f^2 + 64*d^6*e^6)*x^2 + 2*(a*b^5*f^12 + 32*d^7*e^5 - (b^5*d^2 + 10*a*b^4*d*e)*f^10 + 10*(b^4*d^3*e + 4*a*b^3*d^2*e^2)*f^8 - 40*(b^3*d^4*e^2 + 2*a*b^2*d^3*e^3)*f^6 + 80*(b^2*d^5*e^3 + a*b*d^4*e^4)*f^4 - 16*(5*b*d^6*e^4 + 2*a*d^5*e^5)*f^2)*x)","B",0
479,1,923,0,1.052197," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{\frac{1}{2}} {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} \sqrt{-\frac{b f^{2} - 2 \, d e}{e}} \log\left(-b^{2} f^{4} + 4 \, {\left(b d e - a e^{2}\right)} f^{2} - 4 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x + 4 \, {\left(2 \, \sqrt{\frac{1}{2}} e^{2} f \sqrt{-\frac{b f^{2} - 2 \, d e}{e}} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{\frac{1}{2}} {\left(b e f^{2} + 2 \, e^{3} x\right)} \sqrt{-\frac{b f^{2} - 2 \, d e}{e}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} + 4 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 2 \, {\left(105 \, b^{3} f^{6} + 192 \, e^{6} x^{3} + 48 \, d^{3} e^{3} - 56 \, {\left(5 \, b^{2} d e + 6 \, a b e^{2}\right)} f^{4} + 4 \, {\left(21 \, b d^{2} e^{2} + 232 \, a d e^{3}\right)} f^{2} + 144 \, {\left(b e^{4} f^{2} + 2 \, d e^{5}\right)} x^{2} + 2 \, {\left(7 \, b^{2} e^{2} f^{4} + 156 \, d^{2} e^{4} - 4 \, {\left(3 \, b d e^{3} - 32 \, a e^{4}\right)} f^{2}\right)} x - 2 \, {\left(35 \, b^{2} e f^{5} - 96 \, e^{5} f x^{2} + 12 \, d^{2} e^{3} f - 4 \, {\left(21 \, b d e^{2} + 20 \, a e^{3}\right)} f^{3} - 24 \, {\left(b e^{3} f^{3} + 6 \, d e^{4} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{672 \, e^{4}}, -\frac{105 \, \sqrt{\frac{1}{2}} {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} \sqrt{\frac{b f^{2} - 2 \, d e}{e}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} e \sqrt{\frac{b f^{2} - 2 \, d e}{e}}}{b f^{2} - 2 \, d e}\right) - {\left(105 \, b^{3} f^{6} + 192 \, e^{6} x^{3} + 48 \, d^{3} e^{3} - 56 \, {\left(5 \, b^{2} d e + 6 \, a b e^{2}\right)} f^{4} + 4 \, {\left(21 \, b d^{2} e^{2} + 232 \, a d e^{3}\right)} f^{2} + 144 \, {\left(b e^{4} f^{2} + 2 \, d e^{5}\right)} x^{2} + 2 \, {\left(7 \, b^{2} e^{2} f^{4} + 156 \, d^{2} e^{4} - 4 \, {\left(3 \, b d e^{3} - 32 \, a e^{4}\right)} f^{2}\right)} x - 2 \, {\left(35 \, b^{2} e f^{5} - 96 \, e^{5} f x^{2} + 12 \, d^{2} e^{3} f - 4 \, {\left(21 \, b d e^{2} + 20 \, a e^{3}\right)} f^{3} - 24 \, {\left(b e^{3} f^{3} + 6 \, d e^{4} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{336 \, e^{4}}\right]"," ",0,"[1/672*(105*sqrt(1/2)*(b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*sqrt(-(b*f^2 - 2*d*e)/e)*log(-b^2*f^4 + 4*(b*d*e - a*e^2)*f^2 - 4*(b*e^2*f^2 - 2*d*e^3)*x + 4*(2*sqrt(1/2)*e^2*f*sqrt(-(b*f^2 - 2*d*e)/e)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(1/2)*(b*e*f^2 + 2*e^3*x)*sqrt(-(b*f^2 - 2*d*e)/e))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d) + 4*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 2*(105*b^3*f^6 + 192*e^6*x^3 + 48*d^3*e^3 - 56*(5*b^2*d*e + 6*a*b*e^2)*f^4 + 4*(21*b*d^2*e^2 + 232*a*d*e^3)*f^2 + 144*(b*e^4*f^2 + 2*d*e^5)*x^2 + 2*(7*b^2*e^2*f^4 + 156*d^2*e^4 - 4*(3*b*d*e^3 - 32*a*e^4)*f^2)*x - 2*(35*b^2*e*f^5 - 96*e^5*f*x^2 + 12*d^2*e^3*f - 4*(21*b*d*e^2 + 20*a*e^3)*f^3 - 24*(b*e^3*f^3 + 6*d*e^4*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/e^4, -1/336*(105*sqrt(1/2)*(b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*sqrt((b*f^2 - 2*d*e)/e)*arctan(2*sqrt(1/2)*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d)*e*sqrt((b*f^2 - 2*d*e)/e)/(b*f^2 - 2*d*e)) - (105*b^3*f^6 + 192*e^6*x^3 + 48*d^3*e^3 - 56*(5*b^2*d*e + 6*a*b*e^2)*f^4 + 4*(21*b*d^2*e^2 + 232*a*d*e^3)*f^2 + 144*(b*e^4*f^2 + 2*d*e^5)*x^2 + 2*(7*b^2*e^2*f^4 + 156*d^2*e^4 - 4*(3*b*d*e^3 - 32*a*e^4)*f^2)*x - 2*(35*b^2*e*f^5 - 96*e^5*f*x^2 + 12*d^2*e^3*f - 4*(21*b*d*e^2 + 20*a*e^3)*f^3 - 24*(b*e^3*f^3 + 6*d*e^4*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/e^4]","A",0
480,1,657,0,0.829925," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{\frac{1}{2}} {\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \sqrt{-\frac{b f^{2} - 2 \, d e}{e}} \log\left(-b^{2} f^{4} + 4 \, {\left(b d e - a e^{2}\right)} f^{2} - 4 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x + 4 \, {\left(2 \, \sqrt{\frac{1}{2}} e^{2} f \sqrt{-\frac{b f^{2} - 2 \, d e}{e}} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{\frac{1}{2}} {\left(b e f^{2} + 2 \, e^{3} x\right)} \sqrt{-\frac{b f^{2} - 2 \, d e}{e}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} + 4 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 2 \, {\left(15 \, b^{2} f^{4} - 16 \, e^{4} x^{2} - 8 \, d^{2} e^{2} - 2 \, {\left(5 \, b d e + 24 \, a e^{2}\right)} f^{2} + 2 \, {\left(b e^{2} f^{2} - 18 \, d e^{3}\right)} x - 2 \, {\left(5 \, b e f^{3} + 8 \, e^{3} f x - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{80 \, e^{3}}, \frac{15 \, \sqrt{\frac{1}{2}} {\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \sqrt{\frac{b f^{2} - 2 \, d e}{e}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} e \sqrt{\frac{b f^{2} - 2 \, d e}{e}}}{b f^{2} - 2 \, d e}\right) - {\left(15 \, b^{2} f^{4} - 16 \, e^{4} x^{2} - 8 \, d^{2} e^{2} - 2 \, {\left(5 \, b d e + 24 \, a e^{2}\right)} f^{2} + 2 \, {\left(b e^{2} f^{2} - 18 \, d e^{3}\right)} x - 2 \, {\left(5 \, b e f^{3} + 8 \, e^{3} f x - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{40 \, e^{3}}\right]"," ",0,"[-1/80*(15*sqrt(1/2)*(b^2*f^4 - 4*a*e^2*f^2)*sqrt(-(b*f^2 - 2*d*e)/e)*log(-b^2*f^4 + 4*(b*d*e - a*e^2)*f^2 - 4*(b*e^2*f^2 - 2*d*e^3)*x + 4*(2*sqrt(1/2)*e^2*f*sqrt(-(b*f^2 - 2*d*e)/e)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(1/2)*(b*e*f^2 + 2*e^3*x)*sqrt(-(b*f^2 - 2*d*e)/e))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d) + 4*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 2*(15*b^2*f^4 - 16*e^4*x^2 - 8*d^2*e^2 - 2*(5*b*d*e + 24*a*e^2)*f^2 + 2*(b*e^2*f^2 - 18*d*e^3)*x - 2*(5*b*e*f^3 + 8*e^3*f*x - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/e^3, 1/40*(15*sqrt(1/2)*(b^2*f^4 - 4*a*e^2*f^2)*sqrt((b*f^2 - 2*d*e)/e)*arctan(2*sqrt(1/2)*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d)*e*sqrt((b*f^2 - 2*d*e)/e)/(b*f^2 - 2*d*e)) - (15*b^2*f^4 - 16*e^4*x^2 - 8*d^2*e^2 - 2*(5*b*d*e + 24*a*e^2)*f^2 + 2*(b*e^2*f^2 - 18*d*e^3)*x - 2*(5*b*e*f^3 + 8*e^3*f*x - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/e^3]","A",0
481,1,692,0,0.975317," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} \log\left(-b^{2} f^{4} + 4 \, {\left(b d e - a e^{2}\right)} f^{2} - 4 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x - 2 \, {\left(2 \, \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} {\left(b f^{2} + 2 \, e^{2} x\right)}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} + 4 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) - 4 \, {\left(3 \, b^{2} e f^{4} - 2 \, b d e^{2} f^{2} - 8 \, d^{2} e^{3} + 10 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)} x - 2 \, {\left(b e^{2} f^{3} - 2 \, d e^{3} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{48 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)}}, \frac{3 \, {\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \sqrt{2 \, b e f^{2} - 4 \, d e^{2}} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} {\left(\sqrt{2 \, b e f^{2} - 4 \, d e^{2}} f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{2 \, b e f^{2} - 4 \, d e^{2}} {\left(e x + d\right)}\right)}}{2 \, {\left(a e f^{2} - d^{2} e + {\left(b e f^{2} - 2 \, d e^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, b^{2} e f^{4} - 2 \, b d e^{2} f^{2} - 8 \, d^{2} e^{3} + 10 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)} x - 2 \, {\left(b e^{2} f^{3} - 2 \, d e^{3} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{24 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)}}\right]"," ",0,"[-1/48*(3*(b^2*f^4 - 4*a*e^2*f^2)*sqrt(-2*b*e*f^2 + 4*d*e^2)*log(-b^2*f^4 + 4*(b*d*e - a*e^2)*f^2 - 4*(b*e^2*f^2 - 2*d*e^3)*x - 2*(2*sqrt(-2*b*e*f^2 + 4*d*e^2)*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(-2*b*e*f^2 + 4*d*e^2)*(b*f^2 + 2*e^2*x))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d) + 4*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) - 4*(3*b^2*e*f^4 - 2*b*d*e^2*f^2 - 8*d^2*e^3 + 10*(b*e^3*f^2 - 2*d*e^4)*x - 2*(b*e^2*f^3 - 2*d*e^3*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(b*e^3*f^2 - 2*d*e^4), 1/24*(3*(b^2*f^4 - 4*a*e^2*f^2)*sqrt(2*b*e*f^2 - 4*d*e^2)*arctan(1/2*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d)*(sqrt(2*b*e*f^2 - 4*d*e^2)*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(2*b*e*f^2 - 4*d*e^2)*(e*x + d))/(a*e*f^2 - d^2*e + (b*e*f^2 - 2*d*e^2)*x)) + 2*(3*b^2*e*f^4 - 2*b*d*e^2*f^2 - 8*d^2*e^3 + 10*(b*e^3*f^2 - 2*d*e^4)*x - 2*(b*e^2*f^3 - 2*d*e^3*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(b*e^3*f^2 - 2*d*e^4)]","A",0
482,1,716,0,1.140051," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} \log\left(-b^{2} f^{4} + 4 \, {\left(b d e - a e^{2}\right)} f^{2} - 4 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x + 2 \, {\left(2 \, \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} {\left(b f^{2} + 2 \, e^{2} x\right)}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} + 4 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 4 \, {\left(b^{2} e f^{4} - 6 \, b d e^{2} f^{2} + 8 \, d^{2} e^{3} - 2 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)} x + 2 \, {\left(b e^{2} f^{3} - 2 \, d e^{3} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{8 \, {\left(b^{2} e^{2} f^{4} - 4 \, b d e^{3} f^{2} + 4 \, d^{2} e^{4}\right)}}, \frac{{\left(b^{2} f^{4} - 4 \, a e^{2} f^{2}\right)} \sqrt{2 \, b e f^{2} - 4 \, d e^{2}} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} {\left(\sqrt{2 \, b e f^{2} - 4 \, d e^{2}} f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{2 \, b e f^{2} - 4 \, d e^{2}} {\left(e x + d\right)}\right)}}{2 \, {\left(a e f^{2} - d^{2} e + {\left(b e f^{2} - 2 \, d e^{2}\right)} x\right)}}\right) + 2 \, {\left(b^{2} e f^{4} - 6 \, b d e^{2} f^{2} + 8 \, d^{2} e^{3} - 2 \, {\left(b e^{3} f^{2} - 2 \, d e^{4}\right)} x + 2 \, {\left(b e^{2} f^{3} - 2 \, d e^{3} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{4 \, {\left(b^{2} e^{2} f^{4} - 4 \, b d e^{3} f^{2} + 4 \, d^{2} e^{4}\right)}}\right]"," ",0,"[1/8*((b^2*f^4 - 4*a*e^2*f^2)*sqrt(-2*b*e*f^2 + 4*d*e^2)*log(-b^2*f^4 + 4*(b*d*e - a*e^2)*f^2 - 4*(b*e^2*f^2 - 2*d*e^3)*x + 2*(2*sqrt(-2*b*e*f^2 + 4*d*e^2)*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(-2*b*e*f^2 + 4*d*e^2)*(b*f^2 + 2*e^2*x))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d) + 4*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 4*(b^2*e*f^4 - 6*b*d*e^2*f^2 + 8*d^2*e^3 - 2*(b*e^3*f^2 - 2*d*e^4)*x + 2*(b*e^2*f^3 - 2*d*e^3*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(b^2*e^2*f^4 - 4*b*d*e^3*f^2 + 4*d^2*e^4), 1/4*((b^2*f^4 - 4*a*e^2*f^2)*sqrt(2*b*e*f^2 - 4*d*e^2)*arctan(1/2*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d)*(sqrt(2*b*e*f^2 - 4*d*e^2)*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(2*b*e*f^2 - 4*d*e^2)*(e*x + d))/(a*e*f^2 - d^2*e + (b*e*f^2 - 2*d*e^2)*x)) + 2*(b^2*e*f^4 - 6*b*d*e^2*f^2 + 8*d^2*e^3 - 2*(b*e^3*f^2 - 2*d*e^4)*x + 2*(b*e^2*f^3 - 2*d*e^3*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(b^2*e^2*f^4 - 4*b*d*e^3*f^2 + 4*d^2*e^4)]","A",0
483,1,1456,0,1.418231," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{2} f^{6} + 4 \, a d^{2} e^{2} f^{2} - {\left(b^{2} d^{2} + 4 \, a^{2} e^{2}\right)} f^{4} + {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} x\right)} \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} \log\left(-b^{2} f^{4} + 4 \, {\left(b d e - a e^{2}\right)} f^{2} - 4 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x - 2 \, {\left(2 \, \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} e f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{-2 \, b e f^{2} + 4 \, d e^{2}} {\left(b f^{2} + 2 \, e^{2} x\right)}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} + 4 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) + 4 \, {\left(a b^{2} e f^{6} - 8 \, d^{4} e^{3} - {\left(5 \, b^{2} d^{2} e - 2 \, a b d e^{2}\right)} f^{4} + 2 \, {\left(7 \, b d^{3} e^{2} - 4 \, a d^{2} e^{3}\right)} f^{2} + 2 \, {\left(b^{2} e^{3} f^{4} - 4 \, b d e^{4} f^{2} + 4 \, d^{2} e^{5}\right)} x^{2} + {\left(b^{3} e f^{6} - 4 \, d^{3} e^{4} - 2 \, {\left(4 \, b^{2} d e^{2} - 3 \, a b e^{3}\right)} f^{4} + 2 \, {\left(7 \, b d^{2} e^{3} - 6 \, a d e^{4}\right)} f^{2}\right)} x + 2 \, {\left(2 \, d^{3} e^{3} f + {\left(2 \, b^{2} d e - 3 \, a b e^{2}\right)} f^{5} - {\left(5 \, b d^{2} e^{2} - 6 \, a d e^{3}\right)} f^{3} - {\left(b^{2} e^{2} f^{5} - 4 \, b d e^{3} f^{3} + 4 \, d^{2} e^{4} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{4 \, {\left(a b^{3} e f^{8} + 8 \, d^{5} e^{4} - {\left(b^{3} d^{2} e + 6 \, a b^{2} d e^{2}\right)} f^{6} + 6 \, {\left(b^{2} d^{3} e^{2} + 2 \, a b d^{2} e^{3}\right)} f^{4} - 4 \, {\left(3 \, b d^{4} e^{3} + 2 \, a d^{3} e^{4}\right)} f^{2} + {\left(b^{4} e f^{8} - 8 \, b^{3} d e^{2} f^{6} + 24 \, b^{2} d^{2} e^{3} f^{4} - 32 \, b d^{3} e^{4} f^{2} + 16 \, d^{4} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(a b^{2} f^{6} + 4 \, a d^{2} e^{2} f^{2} - {\left(b^{2} d^{2} + 4 \, a^{2} e^{2}\right)} f^{4} + {\left(b^{3} f^{6} + 8 \, a d e^{3} f^{2} - 2 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} f^{4}\right)} x\right)} \sqrt{2 \, b e f^{2} - 4 \, d e^{2}} \arctan\left(\frac{\sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} {\left(\sqrt{2 \, b e f^{2} - 4 \, d e^{2}} f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{2 \, b e f^{2} - 4 \, d e^{2}} {\left(e x + d\right)}\right)}}{2 \, {\left(a e f^{2} - d^{2} e + {\left(b e f^{2} - 2 \, d e^{2}\right)} x\right)}}\right) - 2 \, {\left(a b^{2} e f^{6} - 8 \, d^{4} e^{3} - {\left(5 \, b^{2} d^{2} e - 2 \, a b d e^{2}\right)} f^{4} + 2 \, {\left(7 \, b d^{3} e^{2} - 4 \, a d^{2} e^{3}\right)} f^{2} + 2 \, {\left(b^{2} e^{3} f^{4} - 4 \, b d e^{4} f^{2} + 4 \, d^{2} e^{5}\right)} x^{2} + {\left(b^{3} e f^{6} - 4 \, d^{3} e^{4} - 2 \, {\left(4 \, b^{2} d e^{2} - 3 \, a b e^{3}\right)} f^{4} + 2 \, {\left(7 \, b d^{2} e^{3} - 6 \, a d e^{4}\right)} f^{2}\right)} x + 2 \, {\left(2 \, d^{3} e^{3} f + {\left(2 \, b^{2} d e - 3 \, a b e^{2}\right)} f^{5} - {\left(5 \, b d^{2} e^{2} - 6 \, a d e^{3}\right)} f^{3} - {\left(b^{2} e^{2} f^{5} - 4 \, b d e^{3} f^{3} + 4 \, d^{2} e^{4} f\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{2 \, {\left(a b^{3} e f^{8} + 8 \, d^{5} e^{4} - {\left(b^{3} d^{2} e + 6 \, a b^{2} d e^{2}\right)} f^{6} + 6 \, {\left(b^{2} d^{3} e^{2} + 2 \, a b d^{2} e^{3}\right)} f^{4} - 4 \, {\left(3 \, b d^{4} e^{3} + 2 \, a d^{3} e^{4}\right)} f^{2} + {\left(b^{4} e f^{8} - 8 \, b^{3} d e^{2} f^{6} + 24 \, b^{2} d^{2} e^{3} f^{4} - 32 \, b d^{3} e^{4} f^{2} + 16 \, d^{4} e^{5}\right)} x\right)}}\right]"," ",0,"[1/4*(3*(a*b^2*f^6 + 4*a*d^2*e^2*f^2 - (b^2*d^2 + 4*a^2*e^2)*f^4 + (b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*x)*sqrt(-2*b*e*f^2 + 4*d*e^2)*log(-b^2*f^4 + 4*(b*d*e - a*e^2)*f^2 - 4*(b*e^2*f^2 - 2*d*e^3)*x - 2*(2*sqrt(-2*b*e*f^2 + 4*d*e^2)*e*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(-2*b*e*f^2 + 4*d*e^2)*(b*f^2 + 2*e^2*x))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d) + 4*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) + 4*(a*b^2*e*f^6 - 8*d^4*e^3 - (5*b^2*d^2*e - 2*a*b*d*e^2)*f^4 + 2*(7*b*d^3*e^2 - 4*a*d^2*e^3)*f^2 + 2*(b^2*e^3*f^4 - 4*b*d*e^4*f^2 + 4*d^2*e^5)*x^2 + (b^3*e*f^6 - 4*d^3*e^4 - 2*(4*b^2*d*e^2 - 3*a*b*e^3)*f^4 + 2*(7*b*d^2*e^3 - 6*a*d*e^4)*f^2)*x + 2*(2*d^3*e^3*f + (2*b^2*d*e - 3*a*b*e^2)*f^5 - (5*b*d^2*e^2 - 6*a*d*e^3)*f^3 - (b^2*e^2*f^5 - 4*b*d*e^3*f^3 + 4*d^2*e^4*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(a*b^3*e*f^8 + 8*d^5*e^4 - (b^3*d^2*e + 6*a*b^2*d*e^2)*f^6 + 6*(b^2*d^3*e^2 + 2*a*b*d^2*e^3)*f^4 - 4*(3*b*d^4*e^3 + 2*a*d^3*e^4)*f^2 + (b^4*e*f^8 - 8*b^3*d*e^2*f^6 + 24*b^2*d^2*e^3*f^4 - 32*b*d^3*e^4*f^2 + 16*d^4*e^5)*x), -1/2*(3*(a*b^2*f^6 + 4*a*d^2*e^2*f^2 - (b^2*d^2 + 4*a^2*e^2)*f^4 + (b^3*f^6 + 8*a*d*e^3*f^2 - 2*(b^2*d*e + 2*a*b*e^2)*f^4)*x)*sqrt(2*b*e*f^2 - 4*d*e^2)*arctan(1/2*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d)*(sqrt(2*b*e*f^2 - 4*d*e^2)*f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(2*b*e*f^2 - 4*d*e^2)*(e*x + d))/(a*e*f^2 - d^2*e + (b*e*f^2 - 2*d*e^2)*x)) - 2*(a*b^2*e*f^6 - 8*d^4*e^3 - (5*b^2*d^2*e - 2*a*b*d*e^2)*f^4 + 2*(7*b*d^3*e^2 - 4*a*d^2*e^3)*f^2 + 2*(b^2*e^3*f^4 - 4*b*d*e^4*f^2 + 4*d^2*e^5)*x^2 + (b^3*e*f^6 - 4*d^3*e^4 - 2*(4*b^2*d*e^2 - 3*a*b*e^3)*f^4 + 2*(7*b*d^2*e^3 - 6*a*d*e^4)*f^2)*x + 2*(2*d^3*e^3*f + (2*b^2*d*e - 3*a*b*e^2)*f^5 - (5*b*d^2*e^2 - 6*a*d*e^3)*f^3 - (b^2*e^2*f^5 - 4*b*d*e^3*f^3 + 4*d^2*e^4*f)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(a*b^3*e*f^8 + 8*d^5*e^4 - (b^3*d^2*e + 6*a*b^2*d*e^2)*f^6 + 6*(b^2*d^3*e^2 + 2*a*b*d^2*e^3)*f^4 - 4*(3*b*d^4*e^3 + 2*a*d^3*e^4)*f^2 + (b^4*e*f^8 - 8*b^3*d*e^2*f^6 + 24*b^2*d^2*e^3*f^4 - 32*b*d^3*e^4*f^2 + 16*d^4*e^5)*x)]","B",0
484,1,2514,0,2.086829," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left(a^{2} b^{2} f^{8} - 4 \, a d^{4} e^{2} f^{2} - 2 \, {\left(a b^{2} d^{2} + 2 \, a^{3} e^{2}\right)} f^{6} + {\left(b^{2} d^{4} + 8 \, a^{2} d^{2} e^{2}\right)} f^{4} + {\left(b^{4} f^{8} - 16 \, a d^{2} e^{4} f^{2} - 4 \, {\left(b^{3} d e + a b^{2} e^{2}\right)} f^{6} + 4 \, {\left(b^{2} d^{2} e^{2} + 4 \, a b d e^{3}\right)} f^{4}\right)} x^{2} + 2 \, {\left(a b^{3} f^{8} - 8 \, a d^{3} e^{3} f^{2} - {\left(b^{3} d^{2} + 2 \, a b^{2} d e + 4 \, a^{2} b e^{2}\right)} f^{6} + 2 \, {\left(b^{2} d^{3} e + 2 \, a b d^{2} e^{2} + 4 \, a^{2} d e^{3}\right)} f^{4}\right)} x\right)} \sqrt{-\frac{e}{b f^{2} - 2 \, d e}} \log\left(-b^{2} f^{4} + 4 \, {\left(b d e - a e^{2}\right)} f^{2} - 4 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x - 2 \, {\left(2 \, \sqrt{2} {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{-\frac{e}{b f^{2} - 2 \, d e}} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{2} {\left(b^{2} f^{4} - 2 \, b d e f^{2} + 2 \, {\left(b e^{2} f^{2} - 2 \, d e^{3}\right)} x\right)} \sqrt{-\frac{e}{b f^{2} - 2 \, d e}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d} + 4 \, {\left(b e f^{3} - 2 \, d e^{2} f\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right) - 4 \, {\left(4 \, d^{5} e^{2} + {\left(8 \, a b^{2} d - 5 \, a^{2} b e\right)} f^{6} - 2 \, {\left(2 \, b^{2} d^{3} + a b d^{2} e + 10 \, a^{2} d e^{2}\right)} f^{4} - 6 \, {\left(b^{2} e^{3} f^{4} - 4 \, b d e^{4} f^{2} + 4 \, d^{2} e^{5}\right)} x^{3} - {\left(9 \, b d^{4} e - 32 \, a d^{3} e^{2}\right)} f^{2} + {\left(3 \, b^{3} e f^{6} - 16 \, d^{3} e^{4} + 4 \, {\left(b^{2} d e^{2} - 10 \, a b e^{3}\right)} f^{4} - 4 \, {\left(3 \, b d^{2} e^{3} - 20 \, a d e^{4}\right)} f^{2}\right)} x^{2} + 2 \, {\left(d^{4} e^{3} + {\left(4 \, b^{3} d - a b^{2} e\right)} f^{6} - {\left(7 \, b^{2} d^{2} e + 6 \, a b d e^{2} + 15 \, a^{2} e^{3}\right)} f^{4} - 2 \, {\left(5 \, b d^{3} e^{2} - 23 \, a d^{2} e^{3}\right)} f^{2}\right)} x - 2 \, {\left(3 \, a b^{2} f^{7} + d^{4} e^{2} f - {\left(b^{2} d^{2} + 2 \, a b d e + 15 \, a^{2} e^{2}\right)} f^{5} - 2 \, {\left(3 \, b d^{3} e - 11 \, a d^{2} e^{2}\right)} f^{3} - 3 \, {\left(b^{2} e^{2} f^{5} - 4 \, b d e^{3} f^{3} + 4 \, d^{2} e^{4} f\right)} x^{2} + {\left(3 \, b^{3} f^{7} + 40 \, a d e^{3} f^{3} - 8 \, d^{3} e^{3} f - 4 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} f^{5}\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{6 \, {\left(a^{2} b^{3} f^{10} - 8 \, d^{7} e^{3} - 2 \, {\left(a b^{3} d^{2} + 3 \, a^{2} b^{2} d e\right)} f^{8} + {\left(b^{3} d^{4} + 12 \, a b^{2} d^{3} e + 12 \, a^{2} b d^{2} e^{2}\right)} f^{6} - 2 \, {\left(3 \, b^{2} d^{5} e + 12 \, a b d^{4} e^{2} + 4 \, a^{2} d^{3} e^{3}\right)} f^{4} + 4 \, {\left(3 \, b d^{6} e^{2} + 4 \, a d^{5} e^{3}\right)} f^{2} + {\left(b^{5} f^{10} - 10 \, b^{4} d e f^{8} + 40 \, b^{3} d^{2} e^{2} f^{6} - 80 \, b^{2} d^{3} e^{3} f^{4} + 80 \, b d^{4} e^{4} f^{2} - 32 \, d^{5} e^{5}\right)} x^{2} + 2 \, {\left(a b^{4} f^{10} - 16 \, d^{6} e^{4} - {\left(b^{4} d^{2} + 8 \, a b^{3} d e\right)} f^{8} + 8 \, {\left(b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2}\right)} f^{6} - 8 \, {\left(3 \, b^{2} d^{4} e^{2} + 4 \, a b d^{3} e^{3}\right)} f^{4} + 16 \, {\left(2 \, b d^{5} e^{3} + a d^{4} e^{4}\right)} f^{2}\right)} x\right)}}, \frac{15 \, \sqrt{2} {\left(a^{2} b^{2} f^{8} - 4 \, a d^{4} e^{2} f^{2} - 2 \, {\left(a b^{2} d^{2} + 2 \, a^{3} e^{2}\right)} f^{6} + {\left(b^{2} d^{4} + 8 \, a^{2} d^{2} e^{2}\right)} f^{4} + {\left(b^{4} f^{8} - 16 \, a d^{2} e^{4} f^{2} - 4 \, {\left(b^{3} d e + a b^{2} e^{2}\right)} f^{6} + 4 \, {\left(b^{2} d^{2} e^{2} + 4 \, a b d e^{3}\right)} f^{4}\right)} x^{2} + 2 \, {\left(a b^{3} f^{8} - 8 \, a d^{3} e^{3} f^{2} - {\left(b^{3} d^{2} + 2 \, a b^{2} d e + 4 \, a^{2} b e^{2}\right)} f^{6} + 2 \, {\left(b^{2} d^{3} e + 2 \, a b d^{2} e^{2} + 4 \, a^{2} d e^{3}\right)} f^{4}\right)} x\right)} \sqrt{\frac{e}{b f^{2} - 2 \, d e}} \arctan\left(\frac{{\left(\sqrt{2} {\left(b f^{3} - 2 \, d e f\right)} \sqrt{\frac{e}{b f^{2} - 2 \, d e}} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} - \sqrt{2} {\left(b d f^{2} - 2 \, d^{2} e + {\left(b e f^{2} - 2 \, d e^{2}\right)} x\right)} \sqrt{\frac{e}{b f^{2} - 2 \, d e}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{2 \, {\left(a e f^{2} - d^{2} e + {\left(b e f^{2} - 2 \, d e^{2}\right)} x\right)}}\right) + 2 \, {\left(4 \, d^{5} e^{2} + {\left(8 \, a b^{2} d - 5 \, a^{2} b e\right)} f^{6} - 2 \, {\left(2 \, b^{2} d^{3} + a b d^{2} e + 10 \, a^{2} d e^{2}\right)} f^{4} - 6 \, {\left(b^{2} e^{3} f^{4} - 4 \, b d e^{4} f^{2} + 4 \, d^{2} e^{5}\right)} x^{3} - {\left(9 \, b d^{4} e - 32 \, a d^{3} e^{2}\right)} f^{2} + {\left(3 \, b^{3} e f^{6} - 16 \, d^{3} e^{4} + 4 \, {\left(b^{2} d e^{2} - 10 \, a b e^{3}\right)} f^{4} - 4 \, {\left(3 \, b d^{2} e^{3} - 20 \, a d e^{4}\right)} f^{2}\right)} x^{2} + 2 \, {\left(d^{4} e^{3} + {\left(4 \, b^{3} d - a b^{2} e\right)} f^{6} - {\left(7 \, b^{2} d^{2} e + 6 \, a b d e^{2} + 15 \, a^{2} e^{3}\right)} f^{4} - 2 \, {\left(5 \, b d^{3} e^{2} - 23 \, a d^{2} e^{3}\right)} f^{2}\right)} x - 2 \, {\left(3 \, a b^{2} f^{7} + d^{4} e^{2} f - {\left(b^{2} d^{2} + 2 \, a b d e + 15 \, a^{2} e^{2}\right)} f^{5} - 2 \, {\left(3 \, b d^{3} e - 11 \, a d^{2} e^{2}\right)} f^{3} - 3 \, {\left(b^{2} e^{2} f^{5} - 4 \, b d e^{3} f^{3} + 4 \, d^{2} e^{4} f\right)} x^{2} + {\left(3 \, b^{3} f^{7} + 40 \, a d e^{3} f^{3} - 8 \, d^{3} e^{3} f - 4 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} f^{5}\right)} x\right)} \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}}\right)} \sqrt{e x + f \sqrt{\frac{b f^{2} x + e^{2} x^{2} + a f^{2}}{f^{2}}} + d}}{3 \, {\left(a^{2} b^{3} f^{10} - 8 \, d^{7} e^{3} - 2 \, {\left(a b^{3} d^{2} + 3 \, a^{2} b^{2} d e\right)} f^{8} + {\left(b^{3} d^{4} + 12 \, a b^{2} d^{3} e + 12 \, a^{2} b d^{2} e^{2}\right)} f^{6} - 2 \, {\left(3 \, b^{2} d^{5} e + 12 \, a b d^{4} e^{2} + 4 \, a^{2} d^{3} e^{3}\right)} f^{4} + 4 \, {\left(3 \, b d^{6} e^{2} + 4 \, a d^{5} e^{3}\right)} f^{2} + {\left(b^{5} f^{10} - 10 \, b^{4} d e f^{8} + 40 \, b^{3} d^{2} e^{2} f^{6} - 80 \, b^{2} d^{3} e^{3} f^{4} + 80 \, b d^{4} e^{4} f^{2} - 32 \, d^{5} e^{5}\right)} x^{2} + 2 \, {\left(a b^{4} f^{10} - 16 \, d^{6} e^{4} - {\left(b^{4} d^{2} + 8 \, a b^{3} d e\right)} f^{8} + 8 \, {\left(b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2}\right)} f^{6} - 8 \, {\left(3 \, b^{2} d^{4} e^{2} + 4 \, a b d^{3} e^{3}\right)} f^{4} + 16 \, {\left(2 \, b d^{5} e^{3} + a d^{4} e^{4}\right)} f^{2}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*sqrt(2)*(a^2*b^2*f^8 - 4*a*d^4*e^2*f^2 - 2*(a*b^2*d^2 + 2*a^3*e^2)*f^6 + (b^2*d^4 + 8*a^2*d^2*e^2)*f^4 + (b^4*f^8 - 16*a*d^2*e^4*f^2 - 4*(b^3*d*e + a*b^2*e^2)*f^6 + 4*(b^2*d^2*e^2 + 4*a*b*d*e^3)*f^4)*x^2 + 2*(a*b^3*f^8 - 8*a*d^3*e^3*f^2 - (b^3*d^2 + 2*a*b^2*d*e + 4*a^2*b*e^2)*f^6 + 2*(b^2*d^3*e + 2*a*b*d^2*e^2 + 4*a^2*d*e^3)*f^4)*x)*sqrt(-e/(b*f^2 - 2*d*e))*log(-b^2*f^4 + 4*(b*d*e - a*e^2)*f^2 - 4*(b*e^2*f^2 - 2*d*e^3)*x - 2*(2*sqrt(2)*(b*e*f^3 - 2*d*e^2*f)*sqrt(-e/(b*f^2 - 2*d*e))*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(2)*(b^2*f^4 - 2*b*d*e*f^2 + 2*(b*e^2*f^2 - 2*d*e^3)*x)*sqrt(-e/(b*f^2 - 2*d*e)))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d) + 4*(b*e*f^3 - 2*d*e^2*f)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2)) - 4*(4*d^5*e^2 + (8*a*b^2*d - 5*a^2*b*e)*f^6 - 2*(2*b^2*d^3 + a*b*d^2*e + 10*a^2*d*e^2)*f^4 - 6*(b^2*e^3*f^4 - 4*b*d*e^4*f^2 + 4*d^2*e^5)*x^3 - (9*b*d^4*e - 32*a*d^3*e^2)*f^2 + (3*b^3*e*f^6 - 16*d^3*e^4 + 4*(b^2*d*e^2 - 10*a*b*e^3)*f^4 - 4*(3*b*d^2*e^3 - 20*a*d*e^4)*f^2)*x^2 + 2*(d^4*e^3 + (4*b^3*d - a*b^2*e)*f^6 - (7*b^2*d^2*e + 6*a*b*d*e^2 + 15*a^2*e^3)*f^4 - 2*(5*b*d^3*e^2 - 23*a*d^2*e^3)*f^2)*x - 2*(3*a*b^2*f^7 + d^4*e^2*f - (b^2*d^2 + 2*a*b*d*e + 15*a^2*e^2)*f^5 - 2*(3*b*d^3*e - 11*a*d^2*e^2)*f^3 - 3*(b^2*e^2*f^5 - 4*b*d*e^3*f^3 + 4*d^2*e^4*f)*x^2 + (3*b^3*f^7 + 40*a*d*e^3*f^3 - 8*d^3*e^3*f - 4*(b^2*d*e + 5*a*b*e^2)*f^5)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(a^2*b^3*f^10 - 8*d^7*e^3 - 2*(a*b^3*d^2 + 3*a^2*b^2*d*e)*f^8 + (b^3*d^4 + 12*a*b^2*d^3*e + 12*a^2*b*d^2*e^2)*f^6 - 2*(3*b^2*d^5*e + 12*a*b*d^4*e^2 + 4*a^2*d^3*e^3)*f^4 + 4*(3*b*d^6*e^2 + 4*a*d^5*e^3)*f^2 + (b^5*f^10 - 10*b^4*d*e*f^8 + 40*b^3*d^2*e^2*f^6 - 80*b^2*d^3*e^3*f^4 + 80*b*d^4*e^4*f^2 - 32*d^5*e^5)*x^2 + 2*(a*b^4*f^10 - 16*d^6*e^4 - (b^4*d^2 + 8*a*b^3*d*e)*f^8 + 8*(b^3*d^3*e + 3*a*b^2*d^2*e^2)*f^6 - 8*(3*b^2*d^4*e^2 + 4*a*b*d^3*e^3)*f^4 + 16*(2*b*d^5*e^3 + a*d^4*e^4)*f^2)*x), 1/3*(15*sqrt(2)*(a^2*b^2*f^8 - 4*a*d^4*e^2*f^2 - 2*(a*b^2*d^2 + 2*a^3*e^2)*f^6 + (b^2*d^4 + 8*a^2*d^2*e^2)*f^4 + (b^4*f^8 - 16*a*d^2*e^4*f^2 - 4*(b^3*d*e + a*b^2*e^2)*f^6 + 4*(b^2*d^2*e^2 + 4*a*b*d*e^3)*f^4)*x^2 + 2*(a*b^3*f^8 - 8*a*d^3*e^3*f^2 - (b^3*d^2 + 2*a*b^2*d*e + 4*a^2*b*e^2)*f^6 + 2*(b^2*d^3*e + 2*a*b*d^2*e^2 + 4*a^2*d*e^3)*f^4)*x)*sqrt(e/(b*f^2 - 2*d*e))*arctan(1/2*(sqrt(2)*(b*f^3 - 2*d*e*f)*sqrt(e/(b*f^2 - 2*d*e))*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) - sqrt(2)*(b*d*f^2 - 2*d^2*e + (b*e*f^2 - 2*d*e^2)*x)*sqrt(e/(b*f^2 - 2*d*e)))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d)/(a*e*f^2 - d^2*e + (b*e*f^2 - 2*d*e^2)*x)) + 2*(4*d^5*e^2 + (8*a*b^2*d - 5*a^2*b*e)*f^6 - 2*(2*b^2*d^3 + a*b*d^2*e + 10*a^2*d*e^2)*f^4 - 6*(b^2*e^3*f^4 - 4*b*d*e^4*f^2 + 4*d^2*e^5)*x^3 - (9*b*d^4*e - 32*a*d^3*e^2)*f^2 + (3*b^3*e*f^6 - 16*d^3*e^4 + 4*(b^2*d*e^2 - 10*a*b*e^3)*f^4 - 4*(3*b*d^2*e^3 - 20*a*d*e^4)*f^2)*x^2 + 2*(d^4*e^3 + (4*b^3*d - a*b^2*e)*f^6 - (7*b^2*d^2*e + 6*a*b*d*e^2 + 15*a^2*e^3)*f^4 - 2*(5*b*d^3*e^2 - 23*a*d^2*e^3)*f^2)*x - 2*(3*a*b^2*f^7 + d^4*e^2*f - (b^2*d^2 + 2*a*b*d*e + 15*a^2*e^2)*f^5 - 2*(3*b*d^3*e - 11*a*d^2*e^2)*f^3 - 3*(b^2*e^2*f^5 - 4*b*d*e^3*f^3 + 4*d^2*e^4*f)*x^2 + (3*b^3*f^7 + 40*a*d*e^3*f^3 - 8*d^3*e^3*f - 4*(b^2*d*e + 5*a*b*e^2)*f^5)*x)*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2))*sqrt(e*x + f*sqrt((b*f^2*x + e^2*x^2 + a*f^2)/f^2) + d))/(a^2*b^3*f^10 - 8*d^7*e^3 - 2*(a*b^3*d^2 + 3*a^2*b^2*d*e)*f^8 + (b^3*d^4 + 12*a*b^2*d^3*e + 12*a^2*b*d^2*e^2)*f^6 - 2*(3*b^2*d^5*e + 12*a*b*d^4*e^2 + 4*a^2*d^3*e^3)*f^4 + 4*(3*b*d^6*e^2 + 4*a*d^5*e^3)*f^2 + (b^5*f^10 - 10*b^4*d*e*f^8 + 40*b^3*d^2*e^2*f^6 - 80*b^2*d^3*e^3*f^4 + 80*b*d^4*e^4*f^2 - 32*d^5*e^5)*x^2 + 2*(a*b^4*f^10 - 16*d^6*e^4 - (b^4*d^2 + 8*a*b^3*d*e)*f^8 + 8*(b^3*d^3*e + 3*a*b^2*d^2*e^2)*f^6 - 8*(3*b^2*d^4*e^2 + 4*a*b*d^3*e^3)*f^4 + 16*(2*b*d^5*e^3 + a*d^4*e^4)*f^2)*x)]","B",0
485,1,158,0,0.736661," ","integrate((x^2+a)^2*(x+(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(5 \, {\left(n^{4} - 10 \, n^{2} + 9\right)} x^{5} + 10 \, {\left(a n^{4} - 16 \, a n^{2} + 15 \, a\right)} x^{3} + 5 \, {\left(a^{2} n^{4} - 22 \, a^{2} n^{2} + 45 \, a^{2}\right)} x - {\left(a^{2} n^{5} - 30 \, a^{2} n^{3} + {\left(n^{5} - 10 \, n^{3} + 9 \, n\right)} x^{4} + 149 \, a^{2} n + 2 \, {\left(a n^{5} - 20 \, a n^{3} + 19 \, a n\right)} x^{2}\right)} \sqrt{x^{2} + a}\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n^{6} - 35 \, n^{4} + 259 \, n^{2} - 225}"," ",0,"-(5*(n^4 - 10*n^2 + 9)*x^5 + 10*(a*n^4 - 16*a*n^2 + 15*a)*x^3 + 5*(a^2*n^4 - 22*a^2*n^2 + 45*a^2)*x - (a^2*n^5 - 30*a^2*n^3 + (n^5 - 10*n^3 + 9*n)*x^4 + 149*a^2*n + 2*(a*n^5 - 20*a*n^3 + 19*a*n)*x^2)*sqrt(x^2 + a))*(x + sqrt(x^2 + a))^n/(n^6 - 35*n^4 + 259*n^2 - 225)","A",0
486,1,78,0,0.677377," ","integrate((x^2+a)*(x+(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(n^{2} - 1\right)} x^{3} + 3 \, {\left(a n^{2} - 3 \, a\right)} x - {\left(a n^{3} + {\left(n^{3} - n\right)} x^{2} - 7 \, a n\right)} \sqrt{x^{2} + a}\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n^{4} - 10 \, n^{2} + 9}"," ",0,"-(3*(n^2 - 1)*x^3 + 3*(a*n^2 - 3*a)*x - (a*n^3 + (n^3 - n)*x^2 - 7*a*n)*sqrt(x^2 + a))*(x + sqrt(x^2 + a))^n/(n^4 - 10*n^2 + 9)","A",0
487,1,32,0,0.531113," ","integrate((x+(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(\sqrt{x^{2} + a} n - x\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n^{2} - 1}"," ",0,"(sqrt(x^2 + a)*n - x)*(x + sqrt(x^2 + a))^n/(n^2 - 1)","A",0
488,0,0,0,0.663821," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{x^{2} + a}, x\right)"," ",0,"integral((x + sqrt(x^2 + a))^n/(x^2 + a), x)","F",0
489,0,0,0,0.719560," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{x^{4} + 2 \, a x^{2} + a^{2}}, x\right)"," ",0,"integral((x + sqrt(x^2 + a))^n/(x^4 + 2*a*x^2 + a^2), x)","F",0
490,1,159,0,0.534165," ","integrate((x^2+a)^2*(x-(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(5 \, {\left(n^{4} - 10 \, n^{2} + 9\right)} x^{5} + 10 \, {\left(a n^{4} - 16 \, a n^{2} + 15 \, a\right)} x^{3} + 5 \, {\left(a^{2} n^{4} - 22 \, a^{2} n^{2} + 45 \, a^{2}\right)} x + {\left(a^{2} n^{5} - 30 \, a^{2} n^{3} + {\left(n^{5} - 10 \, n^{3} + 9 \, n\right)} x^{4} + 149 \, a^{2} n + 2 \, {\left(a n^{5} - 20 \, a n^{3} + 19 \, a n\right)} x^{2}\right)} \sqrt{x^{2} + a}\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n^{6} - 35 \, n^{4} + 259 \, n^{2} - 225}"," ",0,"-(5*(n^4 - 10*n^2 + 9)*x^5 + 10*(a*n^4 - 16*a*n^2 + 15*a)*x^3 + 5*(a^2*n^4 - 22*a^2*n^2 + 45*a^2)*x + (a^2*n^5 - 30*a^2*n^3 + (n^5 - 10*n^3 + 9*n)*x^4 + 149*a^2*n + 2*(a*n^5 - 20*a*n^3 + 19*a*n)*x^2)*sqrt(x^2 + a))*(x - sqrt(x^2 + a))^n/(n^6 - 35*n^4 + 259*n^2 - 225)","A",0
491,1,79,0,0.683588," ","integrate((x^2+a)*(x-(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(n^{2} - 1\right)} x^{3} + 3 \, {\left(a n^{2} - 3 \, a\right)} x + {\left(a n^{3} + {\left(n^{3} - n\right)} x^{2} - 7 \, a n\right)} \sqrt{x^{2} + a}\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n^{4} - 10 \, n^{2} + 9}"," ",0,"-(3*(n^2 - 1)*x^3 + 3*(a*n^2 - 3*a)*x + (a*n^3 + (n^3 - n)*x^2 - 7*a*n)*sqrt(x^2 + a))*(x - sqrt(x^2 + a))^n/(n^4 - 10*n^2 + 9)","A",0
492,1,33,0,0.581693," ","integrate((x-(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(\sqrt{x^{2} + a} n + x\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n^{2} - 1}"," ",0,"-(sqrt(x^2 + a)*n + x)*(x - sqrt(x^2 + a))^n/(n^2 - 1)","A",0
493,0,0,0,0.782928," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{x^{2} + a}, x\right)"," ",0,"integral((x - sqrt(x^2 + a))^n/(x^2 + a), x)","F",0
494,0,0,0,0.649209," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{x^{4} + 2 \, a x^{2} + a^{2}}, x\right)"," ",0,"integral((x - sqrt(x^2 + a))^n/(x^4 + 2*a*x^2 + a^2), x)","F",0
495,1,201,0,0.752990," ","integrate((x^2+a)^(5/2)*(x+(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(a^{3} n^{6} - 50 \, a^{3} n^{4} + {\left(n^{6} - 20 \, n^{4} + 64 \, n^{2}\right)} x^{6} + 544 \, a^{3} n^{2} + 3 \, {\left(a n^{6} - 30 \, a n^{4} + 104 \, a n^{2}\right)} x^{4} - 720 \, a^{3} + 3 \, {\left(a^{2} n^{6} - 40 \, a^{2} n^{4} + 264 \, a^{2} n^{2}\right)} x^{2} - 6 \, {\left({\left(n^{5} - 20 \, n^{3} + 64 \, n\right)} x^{5} + 2 \, {\left(a n^{5} - 30 \, a n^{3} + 104 \, a n\right)} x^{3} + {\left(a^{2} n^{5} - 40 \, a^{2} n^{3} + 264 \, a^{2} n\right)} x\right)} \sqrt{x^{2} + a}\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n^{7} - 56 \, n^{5} + 784 \, n^{3} - 2304 \, n}"," ",0,"(a^3*n^6 - 50*a^3*n^4 + (n^6 - 20*n^4 + 64*n^2)*x^6 + 544*a^3*n^2 + 3*(a*n^6 - 30*a*n^4 + 104*a*n^2)*x^4 - 720*a^3 + 3*(a^2*n^6 - 40*a^2*n^4 + 264*a^2*n^2)*x^2 - 6*((n^5 - 20*n^3 + 64*n)*x^5 + 2*(a*n^5 - 30*a*n^3 + 104*a*n)*x^3 + (a^2*n^5 - 40*a^2*n^3 + 264*a^2*n)*x)*sqrt(x^2 + a))*(x + sqrt(x^2 + a))^n/(n^7 - 56*n^5 + 784*n^3 - 2304*n)","A",0
496,1,110,0,0.540139," ","integrate((x^2+a)^(3/2)*(x+(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(a^{2} n^{4} + {\left(n^{4} - 4 \, n^{2}\right)} x^{4} - 16 \, a^{2} n^{2} + 2 \, {\left(a n^{4} - 10 \, a n^{2}\right)} x^{2} + 24 \, a^{2} - 4 \, {\left({\left(n^{3} - 4 \, n\right)} x^{3} + {\left(a n^{3} - 10 \, a n\right)} x\right)} \sqrt{x^{2} + a}\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n^{5} - 20 \, n^{3} + 64 \, n}"," ",0,"(a^2*n^4 + (n^4 - 4*n^2)*x^4 - 16*a^2*n^2 + 2*(a*n^4 - 10*a*n^2)*x^2 + 24*a^2 - 4*((n^3 - 4*n)*x^3 + (a*n^3 - 10*a*n)*x)*sqrt(x^2 + a))*(x + sqrt(x^2 + a))^n/(n^5 - 20*n^3 + 64*n)","A",0
497,1,48,0,0.862127," ","integrate((x^2+a)^(1/2)*(x+(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(n^{2} x^{2} + a n^{2} - 2 \, \sqrt{x^{2} + a} n x - 2 \, a\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n^{3} - 4 \, n}"," ",0,"(n^2*x^2 + a*n^2 - 2*sqrt(x^2 + a)*n*x - 2*a)*(x + sqrt(x^2 + a))^n/(n^3 - 4*n)","A",0
498,1,15,0,0.658506," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{n}"," ",0,"(x + sqrt(x^2 + a))^n/n","A",0
499,0,0,0,0.711017," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + a} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{x^{4} + 2 \, a x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(x^2 + a)*(x + sqrt(x^2 + a))^n/(x^4 + 2*a*x^2 + a^2), x)","F",0
500,0,0,0,0.826459," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + a} {\left(x + \sqrt{x^{2} + a}\right)}^{n}}{x^{6} + 3 \, a x^{4} + 3 \, a^{2} x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(x^2 + a)*(x + sqrt(x^2 + a))^n/(x^6 + 3*a*x^4 + 3*a^2*x^2 + a^3), x)","F",0
501,1,204,0,0.816974," ","integrate((x^2+a)^(5/2)*(x-(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(a^{3} n^{6} - 50 \, a^{3} n^{4} + {\left(n^{6} - 20 \, n^{4} + 64 \, n^{2}\right)} x^{6} + 544 \, a^{3} n^{2} + 3 \, {\left(a n^{6} - 30 \, a n^{4} + 104 \, a n^{2}\right)} x^{4} - 720 \, a^{3} + 3 \, {\left(a^{2} n^{6} - 40 \, a^{2} n^{4} + 264 \, a^{2} n^{2}\right)} x^{2} + 6 \, {\left({\left(n^{5} - 20 \, n^{3} + 64 \, n\right)} x^{5} + 2 \, {\left(a n^{5} - 30 \, a n^{3} + 104 \, a n\right)} x^{3} + {\left(a^{2} n^{5} - 40 \, a^{2} n^{3} + 264 \, a^{2} n\right)} x\right)} \sqrt{x^{2} + a}\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n^{7} - 56 \, n^{5} + 784 \, n^{3} - 2304 \, n}"," ",0,"-(a^3*n^6 - 50*a^3*n^4 + (n^6 - 20*n^4 + 64*n^2)*x^6 + 544*a^3*n^2 + 3*(a*n^6 - 30*a*n^4 + 104*a*n^2)*x^4 - 720*a^3 + 3*(a^2*n^6 - 40*a^2*n^4 + 264*a^2*n^2)*x^2 + 6*((n^5 - 20*n^3 + 64*n)*x^5 + 2*(a*n^5 - 30*a*n^3 + 104*a*n)*x^3 + (a^2*n^5 - 40*a^2*n^3 + 264*a^2*n)*x)*sqrt(x^2 + a))*(x - sqrt(x^2 + a))^n/(n^7 - 56*n^5 + 784*n^3 - 2304*n)","A",0
502,1,113,0,0.568211," ","integrate((x^2+a)^(3/2)*(x-(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(a^{2} n^{4} + {\left(n^{4} - 4 \, n^{2}\right)} x^{4} - 16 \, a^{2} n^{2} + 2 \, {\left(a n^{4} - 10 \, a n^{2}\right)} x^{2} + 24 \, a^{2} + 4 \, {\left({\left(n^{3} - 4 \, n\right)} x^{3} + {\left(a n^{3} - 10 \, a n\right)} x\right)} \sqrt{x^{2} + a}\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n^{5} - 20 \, n^{3} + 64 \, n}"," ",0,"-(a^2*n^4 + (n^4 - 4*n^2)*x^4 - 16*a^2*n^2 + 2*(a*n^4 - 10*a*n^2)*x^2 + 24*a^2 + 4*((n^3 - 4*n)*x^3 + (a*n^3 - 10*a*n)*x)*sqrt(x^2 + a))*(x - sqrt(x^2 + a))^n/(n^5 - 20*n^3 + 64*n)","A",0
503,1,51,0,0.826422," ","integrate((x^2+a)^(1/2)*(x-(x^2+a)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(n^{2} x^{2} + a n^{2} + 2 \, \sqrt{x^{2} + a} n x - 2 \, a\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n^{3} - 4 \, n}"," ",0,"-(n^2*x^2 + a*n^2 + 2*sqrt(x^2 + a)*n*x - 2*a)*(x - sqrt(x^2 + a))^n/(n^3 - 4*n)","A",0
504,1,18,0,0.596194," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{n}"," ",0,"-(x - sqrt(x^2 + a))^n/n","A",0
505,0,0,0,0.614531," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + a} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{x^{4} + 2 \, a x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(x^2 + a)*(x - sqrt(x^2 + a))^n/(x^4 + 2*a*x^2 + a^2), x)","F",0
506,0,0,0,0.646333," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + a} {\left(x - \sqrt{x^{2} + a}\right)}^{n}}{x^{6} + 3 \, a x^{4} + 3 \, a^{2} x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(x^2 + a)*(x - sqrt(x^2 + a))^n/(x^6 + 3*a*x^4 + 3*a^2*x^2 + a^3), x)","F",0
507,1,654,0,0.658804," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)^2*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(5 \, a^{2} d f^{4} n^{4} + 225 \, a^{2} d f^{4} - 300 \, a d^{3} f^{2} + 5 \, {\left(e^{5} n^{4} - 10 \, e^{5} n^{2} + 9 \, e^{5}\right)} x^{5} + 120 \, d^{5} + 25 \, {\left(d e^{4} n^{4} - 10 \, d e^{4} n^{2} + 9 \, d e^{4}\right)} x^{4} + 10 \, {\left(15 \, a e^{3} f^{2} + 30 \, d^{2} e^{3} + {\left(a e^{3} f^{2} + 4 \, d^{2} e^{3}\right)} n^{4} - 2 \, {\left(8 \, a e^{3} f^{2} + 17 \, d^{2} e^{3}\right)} n^{2}\right)} x^{3} - 10 \, {\left(11 \, a^{2} d f^{4} - 6 \, a d^{3} f^{2}\right)} n^{2} + 10 \, {\left(45 \, a d e^{2} f^{2} + {\left(3 \, a d e^{2} f^{2} + 2 \, d^{3} e^{2}\right)} n^{4} - 2 \, {\left(24 \, a d e^{2} f^{2} + d^{3} e^{2}\right)} n^{2}\right)} x^{2} + 5 \, {\left(45 \, a^{2} e f^{4} + {\left(a^{2} e f^{4} + 4 \, a d^{2} e f^{2}\right)} n^{4} - 2 \, {\left(11 \, a^{2} e f^{4} + 26 \, a d^{2} e f^{2} - 12 \, d^{4} e\right)} n^{2}\right)} x - {\left(a^{2} f^{5} n^{5} + {\left(e^{4} f n^{5} - 10 \, e^{4} f n^{3} + 9 \, e^{4} f n\right)} x^{4} - 10 \, {\left(3 \, a^{2} f^{5} - 2 \, a d^{2} f^{3}\right)} n^{3} + 4 \, {\left(d e^{3} f n^{5} - 10 \, d e^{3} f n^{3} + 9 \, d e^{3} f n\right)} x^{3} + 2 \, {\left({\left(a e^{2} f^{3} + 2 \, d^{2} e^{2} f\right)} n^{5} - 10 \, {\left(2 \, a e^{2} f^{3} + d^{2} e^{2} f\right)} n^{3} + {\left(19 \, a e^{2} f^{3} + 8 \, d^{2} e^{2} f\right)} n\right)} x^{2} + {\left(149 \, a^{2} f^{5} - 260 \, a d^{2} f^{3} + 120 \, d^{4} f\right)} n + 4 \, {\left(a d e f^{3} n^{5} - 10 \, {\left(2 \, a d e f^{3} - d^{3} e f\right)} n^{3} + {\left(19 \, a d e f^{3} - 10 \, d^{3} e f\right)} n\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n}}{e f^{4} n^{6} - 35 \, e f^{4} n^{4} + 259 \, e f^{4} n^{2} - 225 \, e f^{4}}"," ",0,"-(5*a^2*d*f^4*n^4 + 225*a^2*d*f^4 - 300*a*d^3*f^2 + 5*(e^5*n^4 - 10*e^5*n^2 + 9*e^5)*x^5 + 120*d^5 + 25*(d*e^4*n^4 - 10*d*e^4*n^2 + 9*d*e^4)*x^4 + 10*(15*a*e^3*f^2 + 30*d^2*e^3 + (a*e^3*f^2 + 4*d^2*e^3)*n^4 - 2*(8*a*e^3*f^2 + 17*d^2*e^3)*n^2)*x^3 - 10*(11*a^2*d*f^4 - 6*a*d^3*f^2)*n^2 + 10*(45*a*d*e^2*f^2 + (3*a*d*e^2*f^2 + 2*d^3*e^2)*n^4 - 2*(24*a*d*e^2*f^2 + d^3*e^2)*n^2)*x^2 + 5*(45*a^2*e*f^4 + (a^2*e*f^4 + 4*a*d^2*e*f^2)*n^4 - 2*(11*a^2*e*f^4 + 26*a*d^2*e*f^2 - 12*d^4*e)*n^2)*x - (a^2*f^5*n^5 + (e^4*f*n^5 - 10*e^4*f*n^3 + 9*e^4*f*n)*x^4 - 10*(3*a^2*f^5 - 2*a*d^2*f^3)*n^3 + 4*(d*e^3*f*n^5 - 10*d*e^3*f*n^3 + 9*d*e^3*f*n)*x^3 + 2*((a*e^2*f^3 + 2*d^2*e^2*f)*n^5 - 10*(2*a*e^2*f^3 + d^2*e^2*f)*n^3 + (19*a*e^2*f^3 + 8*d^2*e^2*f)*n)*x^2 + (149*a^2*f^5 - 260*a*d^2*f^3 + 120*d^4*f)*n + 4*(a*d*e*f^3*n^5 - 10*(2*a*d*e*f^3 - d^3*e*f)*n^3 + (19*a*d*e*f^3 - 10*d^3*e*f)*n)*x)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2))*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n/(e*f^4*n^6 - 35*e*f^4*n^4 + 259*e*f^4*n^2 - 225*e*f^4)","A",0
508,1,239,0,0.710929," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(3 \, a d f^{2} n^{2} - 9 \, a d f^{2} + 3 \, {\left(e^{3} n^{2} - e^{3}\right)} x^{3} + 6 \, d^{3} + 9 \, {\left(d e^{2} n^{2} - d e^{2}\right)} x^{2} - 3 \, {\left(3 \, a e f^{2} - {\left(a e f^{2} + 2 \, d^{2} e\right)} n^{2}\right)} x - {\left(a f^{3} n^{3} + {\left(e^{2} f n^{3} - e^{2} f n\right)} x^{2} - {\left(7 \, a f^{3} - 6 \, d^{2} f\right)} n + 2 \, {\left(d e f n^{3} - d e f n\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n}}{e f^{2} n^{4} - 10 \, e f^{2} n^{2} + 9 \, e f^{2}}"," ",0,"-(3*a*d*f^2*n^2 - 9*a*d*f^2 + 3*(e^3*n^2 - e^3)*x^3 + 6*d^3 + 9*(d*e^2*n^2 - d*e^2)*x^2 - 3*(3*a*e*f^2 - (a*e*f^2 + 2*d^2*e)*n^2)*x - (a*f^3*n^3 + (e^2*f*n^3 - e^2*f*n)*x^2 - (7*a*f^3 - 6*d^2*f)*n + 2*(d*e*f*n^3 - d*e*f*n)*x)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2))*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n/(e*f^2*n^4 - 10*e*f^2*n^2 + 9*e*f^2)","A",0
509,1,80,0,0.786443," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(f n \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} - e x - d\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n}}{e n^{2} - e}"," ",0,"(f*n*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) - e*x - d)*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n/(e*n^2 - e)","A",0
510,0,0,0,0.645129," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{2}}{e^{2} x^{2} + a f^{2} + 2 \, d e x}, x\right)"," ",0,"integral((e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^2/(e^2*x^2 + a*f^2 + 2*d*e*x), x)","F",0
511,0,0,0,0.777821," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{4}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + a^{2} f^{4} + 4 \, a d e f^{2} x + 2 \, {\left(a e^{2} f^{2} + 2 \, d^{2} e^{2}\right)} x^{2}}, x\right)"," ",0,"integral((e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^4/(e^4*x^4 + 4*d*e^3*x^3 + a^2*f^4 + 4*a*d*e*f^2*x + 2*(a*e^2*f^2 + 2*d^2*e^2)*x^2), x)","F",0
512,1,80,0,0.701130," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(f n \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} - e x - d\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n}}{e n^{2} - e}"," ",0,"(f*n*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) - e*x - d)*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n/(e*n^2 - e)","A",0
513,0,0,0,0.850511," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{2}}{e^{2} x^{2} + a f^{2} + 2 \, d e x}, x\right)"," ",0,"integral((e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^2/(e^2*x^2 + a*f^2 + 2*d*e*x), x)","F",0
514,1,377,0,0.704827," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)^(3/2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(a^{2} f^{4} n^{4} + 24 \, a^{2} f^{4} - 48 \, a d^{2} f^{2} + {\left(e^{4} n^{4} - 4 \, e^{4} n^{2}\right)} x^{4} + 24 \, d^{4} + 4 \, {\left(d e^{3} n^{4} - 4 \, d e^{3} n^{2}\right)} x^{3} - 4 \, {\left(4 \, a^{2} f^{4} - 3 \, a d^{2} f^{2}\right)} n^{2} + 2 \, {\left({\left(a e^{2} f^{2} + 2 \, d^{2} e^{2}\right)} n^{4} - 2 \, {\left(5 \, a e^{2} f^{2} + d^{2} e^{2}\right)} n^{2}\right)} x^{2} + 4 \, {\left(a d e f^{2} n^{4} - 2 \, {\left(5 \, a d e f^{2} - 3 \, d^{3} e\right)} n^{2}\right)} x - 4 \, {\left(a d f^{3} n^{3} + {\left(e^{3} f n^{3} - 4 \, e^{3} f n\right)} x^{3} + 3 \, {\left(d e^{2} f n^{3} - 4 \, d e^{2} f n\right)} x^{2} - 2 \, {\left(5 \, a d f^{3} - 3 \, d^{3} f\right)} n + {\left({\left(a e f^{3} + 2 \, d^{2} e f\right)} n^{3} - 2 \, {\left(5 \, a e f^{3} + d^{2} e f\right)} n\right)} x\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n}}{e f^{3} n^{5} - 20 \, e f^{3} n^{3} + 64 \, e f^{3} n}"," ",0,"(a^2*f^4*n^4 + 24*a^2*f^4 - 48*a*d^2*f^2 + (e^4*n^4 - 4*e^4*n^2)*x^4 + 24*d^4 + 4*(d*e^3*n^4 - 4*d*e^3*n^2)*x^3 - 4*(4*a^2*f^4 - 3*a*d^2*f^2)*n^2 + 2*((a*e^2*f^2 + 2*d^2*e^2)*n^4 - 2*(5*a*e^2*f^2 + d^2*e^2)*n^2)*x^2 + 4*(a*d*e*f^2*n^4 - 2*(5*a*d*e*f^2 - 3*d^3*e)*n^2)*x - 4*(a*d*f^3*n^3 + (e^3*f*n^3 - 4*e^3*f*n)*x^3 + 3*(d*e^2*f*n^3 - 4*d*e^2*f*n)*x^2 - 2*(5*a*d*f^3 - 3*d^3*f)*n + ((a*e*f^3 + 2*d^2*e*f)*n^3 - 2*(5*a*e*f^3 + d^2*e*f)*n)*x)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2))*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n/(e*f^3*n^5 - 20*e*f^3*n^3 + 64*e*f^3*n)","A",0
515,1,122,0,0.775652," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","\frac{{\left(e^{2} n^{2} x^{2} + a f^{2} n^{2} + 2 \, d e n^{2} x - 2 \, a f^{2} + 2 \, d^{2} - 2 \, {\left(e f n x + d f n\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n}}{e f n^{3} - 4 \, e f n}"," ",0,"(e^2*n^2*x^2 + a*f^2*n^2 + 2*d*e*n^2*x - 2*a*f^2 + 2*d^2 - 2*(e*f*n*x + d*f*n)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2))*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n/(e*f*n^3 - 4*e*f*n)","A",0
516,1,41,0,0.723363," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f}{e n}"," ",0,"(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f/(e*n)","A",0
517,0,0,0,0.916418," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{4} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + a^{2} f^{4} + 4 \, a d e f^{2} x + 2 \, {\left(a e^{2} f^{2} + 2 \, d^{2} e^{2}\right)} x^{2}}, x\right)"," ",0,"integral((e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^4*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2)/(e^4*x^4 + 4*d*e^3*x^3 + a^2*f^4 + 4*a*d*e*f^2*x + 2*(a*e^2*f^2 + 2*d^2*e^2)*x^2), x)","F",0
518,1,41,0,0.565894," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n/((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f}{e n}"," ",0,"(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f/(e*n)","A",0
519,1,231,0,0.752801," ","integrate((a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(1/2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""fricas"")","-\frac{{\left(2 \, e^{3} n x^{3} + 6 \, d e^{2} n x^{2} + 2 \, a d f^{2} n + 2 \, {\left(a e f^{2} + 2 \, d^{2} e\right)} n x - {\left(e^{2} f n^{2} x^{2} + a f^{3} n^{2} + 2 \, d e f n^{2} x - 2 \, a f^{3} + 2 \, d^{2} f\right)} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}\right)} {\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} \sqrt{\frac{e^{2} g x^{2} + a f^{2} g + 2 \, d e g x}{f^{2}}}}{a e f^{2} n^{3} - 4 \, a e f^{2} n + {\left(e^{3} n^{3} - 4 \, e^{3} n\right)} x^{2} + 2 \, {\left(d e^{2} n^{3} - 4 \, d e^{2} n\right)} x}"," ",0,"-(2*e^3*n*x^3 + 6*d*e^2*n*x^2 + 2*a*d*f^2*n + 2*(a*e*f^2 + 2*d^2*e)*n*x - (e^2*f*n^2*x^2 + a*f^3*n^2 + 2*d*e*f*n^2*x - 2*a*f^3 + 2*d^2*f)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2))*(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*sqrt((e^2*g*x^2 + a*f^2*g + 2*d*e*g*x)/f^2)/(a*e*f^2*n^3 - 4*a*e*f^2*n + (e^3*n^3 - 4*e^3*n)*x^2 + 2*(d*e^2*n^3 - 4*d*e^2*n)*x)","A",0
520,1,117,0,0.667549," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{3} \sqrt{\frac{e^{2} g x^{2} + a f^{2} g + 2 \, d e g x}{f^{2}}} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}}{e^{3} g n x^{2} + a e f^{2} g n + 2 \, d e^{2} g n x}"," ",0,"(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^3*sqrt((e^2*g*x^2 + a*f^2*g + 2*d*e*g*x)/f^2)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2)/(e^3*g*n*x^2 + a*e*f^2*g*n + 2*d*e^2*g*n*x)","A",0
521,0,0,0,0.917907," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{4} \sqrt{\frac{e^{2} g x^{2} + a f^{2} g + 2 \, d e g x}{f^{2}}}}{e^{4} g^{2} x^{4} + 4 \, d e^{3} g^{2} x^{3} + a^{2} f^{4} g^{2} + 4 \, a d e f^{2} g^{2} x + 2 \, {\left(a e^{2} f^{2} + 2 \, d^{2} e^{2}\right)} g^{2} x^{2}}, x\right)"," ",0,"integral((e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^4*sqrt((e^2*g*x^2 + a*f^2*g + 2*d*e*g*x)/f^2)/(e^4*g^2*x^4 + 4*d*e^3*g^2*x^3 + a^2*f^4*g^2 + 4*a*d*e*f^2*g^2*x + 2*(a*e^2*f^2 + 2*d^2*e^2)*g^2*x^2), x)","F",0
522,1,117,0,0.658065," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n/((a*f^2*g+e*g*x*(e*x+2*d))/f^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e x + f \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}} + d\right)}^{n} f^{3} \sqrt{\frac{e^{2} g x^{2} + a f^{2} g + 2 \, d e g x}{f^{2}}} \sqrt{\frac{e^{2} x^{2} + a f^{2} + 2 \, d e x}{f^{2}}}}{e^{3} g n x^{2} + a e f^{2} g n + 2 \, d e^{2} g n x}"," ",0,"(e*x + f*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2) + d)^n*f^3*sqrt((e^2*g*x^2 + a*f^2*g + 2*d*e*g*x)/f^2)*sqrt((e^2*x^2 + a*f^2 + 2*d*e*x)/f^2)/(e^3*g*n*x^2 + a*e*f^2*g*n + 2*d*e^2*g*n*x)","A",0
523,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,1,141,0,0.478606," ","integrate((-2*f*x^2+e)/(4*f^2*x^4+4*d*f*x^2+4*e*f*x^2+e^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(\frac{4 \, f^{2} x^{4} - 4 \, {\left(d - e\right)} f x^{2} + e^{2} + 4 \, {\left(2 \, f x^{3} + e x\right)} \sqrt{-d f}}{4 \, f^{2} x^{4} + 4 \, {\left(d + e\right)} f x^{2} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{\sqrt{d f} x}{d}\right) - \sqrt{d f} \arctan\left(\frac{{\left(2 \, f x^{3} + {\left(2 \, d + e\right)} x\right)} \sqrt{d f}}{d e}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log((4*f^2*x^4 - 4*(d - e)*f*x^2 + e^2 + 4*(2*f*x^3 + e*x)*sqrt(-d*f))/(4*f^2*x^4 + 4*(d + e)*f*x^2 + e^2))/(d*f), -1/2*(sqrt(d*f)*arctan(sqrt(d*f)*x/d) - sqrt(d*f)*arctan((2*f*x^3 + (2*d + e)*x)*sqrt(d*f)/(d*e)))/(d*f)]","A",0
525,1,146,0,0.651036," ","integrate((-2*f*x^2+e)/(4*f^2*x^4-4*d*f*x^2+4*e*f*x^2+e^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(\frac{4 \, f^{2} x^{4} + 4 \, {\left(d + e\right)} f x^{2} + e^{2} + 4 \, {\left(2 \, f x^{3} + e x\right)} \sqrt{d f}}{4 \, f^{2} x^{4} - 4 \, {\left(d - e\right)} f x^{2} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{\sqrt{-d f} x}{d}\right) - \sqrt{-d f} \arctan\left(\frac{{\left(2 \, f x^{3} - {\left(2 \, d - e\right)} x\right)} \sqrt{-d f}}{d e}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log((4*f^2*x^4 + 4*(d + e)*f*x^2 + e^2 + 4*(2*f*x^3 + e*x)*sqrt(d*f))/(4*f^2*x^4 - 4*(d - e)*f*x^2 + e^2))/(d*f), -1/2*(sqrt(-d*f)*arctan(sqrt(-d*f)*x/d) - sqrt(-d*f)*arctan((2*f*x^3 - (2*d - e)*x)*sqrt(-d*f)/(d*e)))/(d*f)]","A",0
526,1,153,0,0.662638," ","integrate((-4*f*x^3+e)/(4*f^2*x^6+4*e*f*x^3+4*d*f*x^2+e^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(\frac{4 \, f^{2} x^{6} + 4 \, e f x^{3} - 4 \, d f x^{2} + e^{2} + 4 \, {\left(2 \, f x^{4} + e x\right)} \sqrt{-d f}}{4 \, f^{2} x^{6} + 4 \, e f x^{3} + 4 \, d f x^{2} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{\sqrt{d f} x^{2}}{d}\right) - \sqrt{d f} \arctan\left(\frac{{\left(2 \, f x^{5} + e x^{2} + 2 \, d x\right)} \sqrt{d f}}{d e}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log((4*f^2*x^6 + 4*e*f*x^3 - 4*d*f*x^2 + e^2 + 4*(2*f*x^4 + e*x)*sqrt(-d*f))/(4*f^2*x^6 + 4*e*f*x^3 + 4*d*f*x^2 + e^2))/(d*f), -1/2*(sqrt(d*f)*arctan(sqrt(d*f)*x^2/d) - sqrt(d*f)*arctan((2*f*x^5 + e*x^2 + 2*d*x)*sqrt(d*f)/(d*e)))/(d*f)]","B",0
527,1,155,0,0.609523," ","integrate((-4*f*x^3+e)/(4*f^2*x^6+4*e*f*x^3-4*d*f*x^2+e^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(\frac{4 \, f^{2} x^{6} + 4 \, e f x^{3} + 4 \, d f x^{2} + e^{2} + 4 \, {\left(2 \, f x^{4} + e x\right)} \sqrt{d f}}{4 \, f^{2} x^{6} + 4 \, e f x^{3} - 4 \, d f x^{2} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{\sqrt{-d f} x^{2}}{d}\right) - \sqrt{-d f} \arctan\left(\frac{{\left(2 \, f x^{5} + e x^{2} - 2 \, d x\right)} \sqrt{-d f}}{d e}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log((4*f^2*x^6 + 4*e*f*x^3 + 4*d*f*x^2 + e^2 + 4*(2*f*x^4 + e*x)*sqrt(d*f))/(4*f^2*x^6 + 4*e*f*x^3 - 4*d*f*x^2 + e^2))/(d*f), -1/2*(sqrt(-d*f)*arctan(sqrt(-d*f)*x^2/d) - sqrt(-d*f)*arctan((2*f*x^5 + e*x^2 - 2*d*x)*sqrt(-d*f)/(d*e)))/(d*f)]","B",0
528,1,144,0,0.752943," ","integrate((e-2*f*(-1+n)*x^n)/(e^2+4*d*f*x^2+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(-\frac{4 \, d f x^{2} - 4 \, f^{2} x^{2 \, n} - 4 \, \sqrt{-d f} e x - e^{2} - 4 \, {\left(2 \, \sqrt{-d f} f x + e f\right)} x^{n}}{4 \, d f x^{2} + 4 \, f^{2} x^{2 \, n} + 4 \, e f x^{n} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{2 \, \sqrt{d f} f x^{n} + \sqrt{d f} e}{2 \, d f x}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log(-(4*d*f*x^2 - 4*f^2*x^(2*n) - 4*sqrt(-d*f)*e*x - e^2 - 4*(2*sqrt(-d*f)*f*x + e*f)*x^n)/(4*d*f*x^2 + 4*f^2*x^(2*n) + 4*e*f*x^n + e^2))/(d*f), -1/2*sqrt(d*f)*arctan(1/2*(2*sqrt(d*f)*f*x^n + sqrt(d*f)*e)/(d*f*x))/(d*f)]","A",0
529,1,144,0,0.417578," ","integrate((e-2*f*(-1+n)*x^n)/(e^2-4*d*f*x^2+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(-\frac{4 \, d f x^{2} + 4 \, f^{2} x^{2 \, n} + 4 \, \sqrt{d f} e x + e^{2} + 4 \, {\left(2 \, \sqrt{d f} f x + e f\right)} x^{n}}{4 \, d f x^{2} - 4 \, f^{2} x^{2 \, n} - 4 \, e f x^{n} - e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{2 \, \sqrt{-d f} f x^{n} + \sqrt{-d f} e}{2 \, d f x}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log(-(4*d*f*x^2 + 4*f^2*x^(2*n) + 4*sqrt(d*f)*e*x + e^2 + 4*(2*sqrt(d*f)*f*x + e*f)*x^n)/(4*d*f*x^2 - 4*f^2*x^(2*n) - 4*e*f*x^n - e^2))/(d*f), -1/2*sqrt(-d*f)*arctan(1/2*(2*sqrt(-d*f)*f*x^n + sqrt(-d*f)*e)/(d*f*x))/(d*f)]","A",0
530,1,155,0,0.393161," ","integrate(x/(4*d*f*x^4+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(\frac{4 \, {\left(d^{2} f + 2 \, d f^{2} + f^{3}\right)} x^{4} - d e^{2} + e^{2} f + 4 \, {\left(d e f + e f^{2}\right)} x^{2} - 2 \, {\left(2 \, {\left(d e + e f\right)} x^{2} + e^{2}\right)} \sqrt{-d f}}{4 \, {\left(d f + f^{2}\right)} x^{4} + 4 \, e f x^{2} + e^{2}}\right)}{8 \, d e f}, \frac{\sqrt{d f} \arctan\left(\frac{{\left(2 \, {\left(d + f\right)} x^{2} + e\right)} \sqrt{d f}}{d e}\right)}{4 \, d e f}\right]"," ",0,"[-1/8*sqrt(-d*f)*log((4*(d^2*f + 2*d*f^2 + f^3)*x^4 - d*e^2 + e^2*f + 4*(d*e*f + e*f^2)*x^2 - 2*(2*(d*e + e*f)*x^2 + e^2)*sqrt(-d*f))/(4*(d*f + f^2)*x^4 + 4*e*f*x^2 + e^2))/(d*e*f), 1/4*sqrt(d*f)*arctan((2*(d + f)*x^2 + e)*sqrt(d*f)/(d*e))/(d*e*f)]","A",0
531,1,168,0,0.409522," ","integrate(x/(-4*d*f*x^4+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(-\frac{4 \, {\left(d^{2} f - 2 \, d f^{2} + f^{3}\right)} x^{4} + d e^{2} + e^{2} f - 4 \, {\left(d e f - e f^{2}\right)} x^{2} + 2 \, {\left(2 \, {\left(d e - e f\right)} x^{2} - e^{2}\right)} \sqrt{d f}}{4 \, {\left(d f - f^{2}\right)} x^{4} - 4 \, e f x^{2} - e^{2}}\right)}{8 \, d e f}, \frac{\sqrt{-d f} \arctan\left(-\frac{{\left(2 \, {\left(d - f\right)} x^{2} - e\right)} \sqrt{-d f}}{d e}\right)}{4 \, d e f}\right]"," ",0,"[1/8*sqrt(d*f)*log(-(4*(d^2*f - 2*d*f^2 + f^3)*x^4 + d*e^2 + e^2*f - 4*(d*e*f - e*f^2)*x^2 + 2*(2*(d*e - e*f)*x^2 - e^2)*sqrt(d*f))/(4*(d*f - f^2)*x^4 - 4*e*f*x^2 - e^2))/(d*e*f), 1/4*sqrt(-d*f)*arctan(-(2*(d - f)*x^2 - e)*sqrt(-d*f)/(d*e))/(d*e*f)]","A",0
532,1,208,0,0.406515," ","integrate(x^2*(2*f*x^2+3*e)/(4*d*f*x^6+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(\frac{4 \, d f x^{6} - 4 \, f^{2} x^{4} - 4 \, e f x^{2} - e^{2} - 4 \, {\left(2 \, f x^{5} + e x^{3}\right)} \sqrt{-d f}}{4 \, d f x^{6} + 4 \, f^{2} x^{4} + 4 \, e f x^{2} + e^{2}}\right)}{4 \, d f}, \frac{\sqrt{d f} \arctan\left(\frac{\sqrt{d f} x}{f}\right) - \sqrt{d f} \arctan\left(\frac{2 \, {\left(2 \, d f x^{5} - {\left(d e - 2 \, f^{2}\right)} x^{3} + e f x\right)} \sqrt{d f}}{d e^{2}}\right) + \sqrt{d f} \arctan\left(\frac{{\left(2 \, d f x^{3} - {\left(d e - 2 \, f^{2}\right)} x\right)} \sqrt{d f}}{d e f}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log((4*d*f*x^6 - 4*f^2*x^4 - 4*e*f*x^2 - e^2 - 4*(2*f*x^5 + e*x^3)*sqrt(-d*f))/(4*d*f*x^6 + 4*f^2*x^4 + 4*e*f*x^2 + e^2))/(d*f), 1/2*(sqrt(d*f)*arctan(sqrt(d*f)*x/f) - sqrt(d*f)*arctan(2*(2*d*f*x^5 - (d*e - 2*f^2)*x^3 + e*f*x)*sqrt(d*f)/(d*e^2)) + sqrt(d*f)*arctan((2*d*f*x^3 - (d*e - 2*f^2)*x)*sqrt(d*f)/(d*e*f)))/(d*f)]","B",0
533,1,213,0,0.409498," ","integrate(x^2*(2*f*x^2+3*e)/(-4*d*f*x^6+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(\frac{4 \, d f x^{6} + 4 \, f^{2} x^{4} + 4 \, e f x^{2} + e^{2} + 4 \, {\left(2 \, f x^{5} + e x^{3}\right)} \sqrt{d f}}{4 \, d f x^{6} - 4 \, f^{2} x^{4} - 4 \, e f x^{2} - e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{\sqrt{-d f} x}{f}\right) - \sqrt{-d f} \arctan\left(\frac{2 \, {\left(2 \, d f x^{5} - {\left(d e + 2 \, f^{2}\right)} x^{3} - e f x\right)} \sqrt{-d f}}{d e^{2}}\right) + \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x^{3} - {\left(d e + 2 \, f^{2}\right)} x\right)} \sqrt{-d f}}{d e f}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log((4*d*f*x^6 + 4*f^2*x^4 + 4*e*f*x^2 + e^2 + 4*(2*f*x^5 + e*x^3)*sqrt(d*f))/(4*d*f*x^6 - 4*f^2*x^4 - 4*e*f*x^2 - e^2))/(d*f), -1/2*(sqrt(-d*f)*arctan(sqrt(-d*f)*x/f) - sqrt(-d*f)*arctan(2*(2*d*f*x^5 - (d*e + 2*f^2)*x^3 - e*f*x)*sqrt(-d*f)/(d*e^2)) + sqrt(-d*f)*arctan((2*d*f*x^3 - (d*e + 2*f^2)*x)*sqrt(-d*f)/(d*e*f)))/(d*f)]","B",0
534,1,146,0,0.440211," ","integrate(x^m*(e*(1+m)+2*f*(-1+m)*x^2)/(e^2+4*e*f*x^2+4*f^2*x^4+4*d*f*x^(2+2*m)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(-\frac{4 \, f^{2} x^{4} - 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{2} + 4 \, {\left(2 \, f x^{3} + e x\right)} \sqrt{-d f} x^{m} + e^{2}}{4 \, f^{2} x^{4} + 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{2} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{{\left(2 \, f x^{2} + e\right)} \sqrt{d f}}{2 \, d f x x^{m}}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log(-(4*f^2*x^4 - 4*d*f*x^2*x^(2*m) + 4*e*f*x^2 + 4*(2*f*x^3 + e*x)*sqrt(-d*f)*x^m + e^2)/(4*f^2*x^4 + 4*d*f*x^2*x^(2*m) + 4*e*f*x^2 + e^2))/(d*f), -1/2*sqrt(d*f)*arctan(1/2*(2*f*x^2 + e)*sqrt(d*f)/(d*f*x*x^m))/(d*f)]","A",0
535,1,146,0,0.432291," ","integrate(x^m*(e*(1+m)+2*f*(-1+m)*x^2)/(e^2+4*e*f*x^2+4*f^2*x^4-4*d*f*x^(2+2*m)),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(-\frac{4 \, f^{2} x^{4} + 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{2} + 4 \, {\left(2 \, f x^{3} + e x\right)} \sqrt{d f} x^{m} + e^{2}}{4 \, f^{2} x^{4} - 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{2} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{{\left(2 \, f x^{2} + e\right)} \sqrt{-d f}}{2 \, d f x x^{m}}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log(-(4*f^2*x^4 + 4*d*f*x^2*x^(2*m) + 4*e*f*x^2 + 4*(2*f*x^3 + e*x)*sqrt(d*f)*x^m + e^2)/(4*f^2*x^4 - 4*d*f*x^2*x^(2*m) + 4*e*f*x^2 + e^2))/(d*f), -1/2*sqrt(-d*f)*arctan(1/2*(2*f*x^2 + e)*sqrt(-d*f)/(d*f*x*x^m))/(d*f)]","A",0
536,1,153,0,0.435744," ","integrate(x*(-2*f*x^3+2*e)/(4*f^2*x^6+4*d*f*x^4+4*e*f*x^3+e^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(\frac{4 \, f^{2} x^{6} - 4 \, d f x^{4} + 4 \, e f x^{3} + e^{2} + 4 \, {\left(2 \, f x^{5} + e x^{2}\right)} \sqrt{-d f}}{4 \, f^{2} x^{6} + 4 \, d f x^{4} + 4 \, e f x^{3} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{\sqrt{d f} x}{d}\right) - \sqrt{d f} \arctan\left(\frac{{\left(2 \, f x^{4} + 2 \, d x^{2} + e x\right)} \sqrt{d f}}{d e}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log((4*f^2*x^6 - 4*d*f*x^4 + 4*e*f*x^3 + e^2 + 4*(2*f*x^5 + e*x^2)*sqrt(-d*f))/(4*f^2*x^6 + 4*d*f*x^4 + 4*e*f*x^3 + e^2))/(d*f), -1/2*(sqrt(d*f)*arctan(sqrt(d*f)*x/d) - sqrt(d*f)*arctan((2*f*x^4 + 2*d*x^2 + e*x)*sqrt(d*f)/(d*e)))/(d*f)]","B",0
537,1,155,0,0.424483," ","integrate(x*(-2*f*x^3+2*e)/(4*f^2*x^6-4*d*f*x^4+4*e*f*x^3+e^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(\frac{4 \, f^{2} x^{6} + 4 \, d f x^{4} + 4 \, e f x^{3} + e^{2} + 4 \, {\left(2 \, f x^{5} + e x^{2}\right)} \sqrt{d f}}{4 \, f^{2} x^{6} - 4 \, d f x^{4} + 4 \, e f x^{3} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{\sqrt{-d f} x}{d}\right) - \sqrt{-d f} \arctan\left(\frac{{\left(2 \, f x^{4} - 2 \, d x^{2} + e x\right)} \sqrt{-d f}}{d e}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log((4*f^2*x^6 + 4*d*f*x^4 + 4*e*f*x^3 + e^2 + 4*(2*f*x^5 + e*x^2)*sqrt(d*f))/(4*f^2*x^6 - 4*d*f*x^4 + 4*e*f*x^3 + e^2))/(d*f), -1/2*(sqrt(-d*f)*arctan(sqrt(-d*f)*x/d) - sqrt(-d*f)*arctan((2*f*x^4 - 2*d*x^2 + e*x)*sqrt(-d*f)/(d*e)))/(d*f)]","B",0
538,1,155,0,0.409454," ","integrate(x^2/(4*d*f*x^6+4*f^2*x^6+4*e*f*x^3+e^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(\frac{4 \, {\left(d^{2} f + 2 \, d f^{2} + f^{3}\right)} x^{6} + 4 \, {\left(d e f + e f^{2}\right)} x^{3} - d e^{2} + e^{2} f - 2 \, {\left(2 \, {\left(d e + e f\right)} x^{3} + e^{2}\right)} \sqrt{-d f}}{4 \, {\left(d f + f^{2}\right)} x^{6} + 4 \, e f x^{3} + e^{2}}\right)}{12 \, d e f}, \frac{\sqrt{d f} \arctan\left(\frac{{\left(2 \, {\left(d + f\right)} x^{3} + e\right)} \sqrt{d f}}{d e}\right)}{6 \, d e f}\right]"," ",0,"[-1/12*sqrt(-d*f)*log((4*(d^2*f + 2*d*f^2 + f^3)*x^6 + 4*(d*e*f + e*f^2)*x^3 - d*e^2 + e^2*f - 2*(2*(d*e + e*f)*x^3 + e^2)*sqrt(-d*f))/(4*(d*f + f^2)*x^6 + 4*e*f*x^3 + e^2))/(d*e*f), 1/6*sqrt(d*f)*arctan((2*(d + f)*x^3 + e)*sqrt(d*f)/(d*e))/(d*e*f)]","A",0
539,1,168,0,0.411332," ","integrate(x^2/(-4*d*f*x^6+4*f^2*x^6+4*e*f*x^3+e^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(-\frac{4 \, {\left(d^{2} f - 2 \, d f^{2} + f^{3}\right)} x^{6} - 4 \, {\left(d e f - e f^{2}\right)} x^{3} + d e^{2} + e^{2} f + 2 \, {\left(2 \, {\left(d e - e f\right)} x^{3} - e^{2}\right)} \sqrt{d f}}{4 \, {\left(d f - f^{2}\right)} x^{6} - 4 \, e f x^{3} - e^{2}}\right)}{12 \, d e f}, \frac{\sqrt{-d f} \arctan\left(-\frac{{\left(2 \, {\left(d - f\right)} x^{3} - e\right)} \sqrt{-d f}}{d e}\right)}{6 \, d e f}\right]"," ",0,"[1/12*sqrt(d*f)*log(-(4*(d^2*f - 2*d*f^2 + f^3)*x^6 - 4*(d*e*f - e*f^2)*x^3 + d*e^2 + e^2*f + 2*(2*(d*e - e*f)*x^3 - e^2)*sqrt(d*f))/(4*(d*f - f^2)*x^6 - 4*e*f*x^3 - e^2))/(d*e*f), 1/6*sqrt(-d*f)*arctan(-(2*(d - f)*x^3 - e)*sqrt(-d*f)/(d*e))/(d*e*f)]","A",0
540,1,146,0,0.448967," ","integrate(x^m*(e*(1+m)+2*f*(-2+m)*x^3)/(e^2+4*e*f*x^3+4*f^2*x^6+4*d*f*x^(2+2*m)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(-\frac{4 \, f^{2} x^{6} - 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{3} + 4 \, {\left(2 \, f x^{4} + e x\right)} \sqrt{-d f} x^{m} + e^{2}}{4 \, f^{2} x^{6} + 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{3} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{{\left(2 \, f x^{3} + e\right)} \sqrt{d f}}{2 \, d f x x^{m}}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log(-(4*f^2*x^6 - 4*d*f*x^2*x^(2*m) + 4*e*f*x^3 + 4*(2*f*x^4 + e*x)*sqrt(-d*f)*x^m + e^2)/(4*f^2*x^6 + 4*d*f*x^2*x^(2*m) + 4*e*f*x^3 + e^2))/(d*f), -1/2*sqrt(d*f)*arctan(1/2*(2*f*x^3 + e)*sqrt(d*f)/(d*f*x*x^m))/(d*f)]","A",0
541,1,146,0,0.516944," ","integrate(x^m*(e*(1+m)+2*f*(-2+m)*x^3)/(e^2+4*e*f*x^3+4*f^2*x^6-4*d*f*x^(2+2*m)),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(-\frac{4 \, f^{2} x^{6} + 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{3} + 4 \, {\left(2 \, f x^{4} + e x\right)} \sqrt{d f} x^{m} + e^{2}}{4 \, f^{2} x^{6} - 4 \, d f x^{2} x^{2 \, m} + 4 \, e f x^{3} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{{\left(2 \, f x^{3} + e\right)} \sqrt{-d f}}{2 \, d f x x^{m}}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log(-(4*f^2*x^6 + 4*d*f*x^2*x^(2*m) + 4*e*f*x^3 + 4*(2*f*x^4 + e*x)*sqrt(d*f)*x^m + e^2)/(4*f^2*x^6 - 4*d*f*x^2*x^(2*m) + 4*e*f*x^3 + e^2))/(d*f), -1/2*sqrt(-d*f)*arctan(1/2*(2*f*x^3 + e)*sqrt(-d*f)/(d*f*x*x^m))/(d*f)]","A",0
542,1,165,0,1.110515," ","integrate(x^m*(e*(1+m)+2*f*(1+m-n)*x^n)/(e^2+4*d*f*x^(2+2*m)+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-d f} \log\left(-\frac{4 \, d f x^{2} x^{2 \, m} - 4 \, \sqrt{-d f} e x x^{m} - 4 \, f^{2} x^{2 \, n} - e^{2} - 4 \, {\left(2 \, \sqrt{-d f} f x x^{m} + e f\right)} x^{n}}{4 \, d f x^{2} x^{2 \, m} + 4 \, f^{2} x^{2 \, n} + 4 \, e f x^{n} + e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{d f} \arctan\left(\frac{2 \, \sqrt{d f} f x^{n} + \sqrt{d f} e}{2 \, d f x x^{m}}\right)}{2 \, d f}\right]"," ",0,"[-1/4*sqrt(-d*f)*log(-(4*d*f*x^2*x^(2*m) - 4*sqrt(-d*f)*e*x*x^m - 4*f^2*x^(2*n) - e^2 - 4*(2*sqrt(-d*f)*f*x*x^m + e*f)*x^n)/(4*d*f*x^2*x^(2*m) + 4*f^2*x^(2*n) + 4*e*f*x^n + e^2))/(d*f), -1/2*sqrt(d*f)*arctan(1/2*(2*sqrt(d*f)*f*x^n + sqrt(d*f)*e)/(d*f*x*x^m))/(d*f)]","A",0
543,1,165,0,0.433162," ","integrate(x^m*(e*(1+m)+2*f*(1+m-n)*x^n)/(e^2-4*d*f*x^(2+2*m)+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""fricas"")","\left[\frac{\sqrt{d f} \log\left(-\frac{4 \, d f x^{2} x^{2 \, m} + 4 \, \sqrt{d f} e x x^{m} + 4 \, f^{2} x^{2 \, n} + e^{2} + 4 \, {\left(2 \, \sqrt{d f} f x x^{m} + e f\right)} x^{n}}{4 \, d f x^{2} x^{2 \, m} - 4 \, f^{2} x^{2 \, n} - 4 \, e f x^{n} - e^{2}}\right)}{4 \, d f}, -\frac{\sqrt{-d f} \arctan\left(\frac{2 \, \sqrt{-d f} f x^{n} + \sqrt{-d f} e}{2 \, d f x x^{m}}\right)}{2 \, d f}\right]"," ",0,"[1/4*sqrt(d*f)*log(-(4*d*f*x^2*x^(2*m) + 4*sqrt(d*f)*e*x*x^m + 4*f^2*x^(2*n) + e^2 + 4*(2*sqrt(d*f)*f*x*x^m + e*f)*x^n)/(4*d*f*x^2*x^(2*m) - 4*f^2*x^(2*n) - 4*e*f*x^n - e^2))/(d*f), -1/2*sqrt(-d*f)*arctan(1/2*(2*sqrt(-d*f)*f*x^n + sqrt(-d*f)*e)/(d*f*x*x^m))/(d*f)]","A",0
544,1,233,0,0.610596," ","integrate(x^5/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{4} x^{4} - 6 \, {\left(a b c^{4} - b c^{2} d^{2}\right)} x^{2} + 6 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) + 3 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - 3 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - 4 \, {\left(b c^{3} d x^{2} - 5 \, a c^{3} d + 3 \, c d^{3}\right)} \sqrt{b x^{2} + a}}{12 \, b^{3} c^{5}}"," ",0,"1/12*(3*b^2*c^4*x^4 - 6*(a*b*c^4 - b*c^2*d^2)*x^2 + 6*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(b*c^2*x^2 + a*c^2 - d^2) + 3*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - 3*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - 4*(b*c^3*d*x^2 - 5*a*c^3*d + 3*c*d^3)*sqrt(b*x^2 + a))/(b^3*c^5)","A",0
545,1,161,0,0.671014," ","integrate(x^3/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, b c^{2} x^{2} - 4 \, \sqrt{b x^{2} + a} c d - 2 \, {\left(a c^{2} - d^{2}\right)} \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) - {\left(a c^{2} - d^{2}\right)} \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) + {\left(a c^{2} - d^{2}\right)} \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right)}{4 \, b^{2} c^{3}}"," ",0,"1/4*(2*b*c^2*x^2 - 4*sqrt(b*x^2 + a)*c*d - 2*(a*c^2 - d^2)*log(b*c^2*x^2 + a*c^2 - d^2) - (a*c^2 - d^2)*log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) + (a*c^2 - d^2)*log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2))/(b^2*c^3)","B",0
546,1,105,0,0.657638," ","integrate(x/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) + \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right)}{4 \, b c}"," ",0,"1/4*(2*log(b*c^2*x^2 + a*c^2 - d^2) + log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2))/(b*c)","B",0
547,1,316,0,0.875493," ","integrate(1/x/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{2 \, a c \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) - 4 \, a c \log\left(x\right) + a c \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - a c \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) + 2 \, \sqrt{a} d \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{4 \, {\left(a^{2} c^{2} - a d^{2}\right)}}, -\frac{2 \, a c \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) - 4 \, a c \log\left(x\right) + a c \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - a c \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) + 4 \, \sqrt{-a} d \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right)}{4 \, {\left(a^{2} c^{2} - a d^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*c*log(b*c^2*x^2 + a*c^2 - d^2) - 4*a*c*log(x) + a*c*log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - a*c*log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) + 2*sqrt(a)*d*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a^2*c^2 - a*d^2), -1/4*(2*a*c*log(b*c^2*x^2 + a*c^2 - d^2) - 4*a*c*log(x) + a*c*log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - a*c*log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) + 4*sqrt(-a)*d*arctan(sqrt(-a)/sqrt(b*x^2 + a)))/(a^2*c^2 - a*d^2)]","A",0
548,1,530,0,1.796169," ","integrate(1/x^3/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b c^{3} x^{2} \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) - 4 \, a^{2} b c^{3} x^{2} \log\left(x\right) + a^{2} b c^{3} x^{2} \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - a^{2} b c^{3} x^{2} \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - 2 \, a^{3} c^{3} + 2 \, a^{2} c d^{2} - {\left(3 \, a b c^{2} d - b d^{3}\right)} \sqrt{a} x^{2} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(a^{2} c^{2} d - a d^{3}\right)} \sqrt{b x^{2} + a}}{4 \, {\left(a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4}\right)} x^{2}}, \frac{2 \, a^{2} b c^{3} x^{2} \log\left(b c^{2} x^{2} + a c^{2} - d^{2}\right) - 4 \, a^{2} b c^{3} x^{2} \log\left(x\right) + a^{2} b c^{3} x^{2} \log\left(-\frac{b c^{2} x^{2} + a c^{2} + 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - a^{2} b c^{3} x^{2} \log\left(-\frac{b c^{2} x^{2} + a c^{2} - 2 \, \sqrt{b x^{2} + a} c d + d^{2}}{x^{2}}\right) - 2 \, a^{3} c^{3} + 2 \, a^{2} c d^{2} + 2 \, {\left(3 \, a b c^{2} d - b d^{3}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 2 \, {\left(a^{2} c^{2} d - a d^{3}\right)} \sqrt{b x^{2} + a}}{4 \, {\left(a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4}\right)} x^{2}}\right]"," ",0,"[1/4*(2*a^2*b*c^3*x^2*log(b*c^2*x^2 + a*c^2 - d^2) - 4*a^2*b*c^3*x^2*log(x) + a^2*b*c^3*x^2*log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - a^2*b*c^3*x^2*log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - 2*a^3*c^3 + 2*a^2*c*d^2 - (3*a*b*c^2*d - b*d^3)*sqrt(a)*x^2*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(a^2*c^2*d - a*d^3)*sqrt(b*x^2 + a))/((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4)*x^2), 1/4*(2*a^2*b*c^3*x^2*log(b*c^2*x^2 + a*c^2 - d^2) - 4*a^2*b*c^3*x^2*log(x) + a^2*b*c^3*x^2*log(-(b*c^2*x^2 + a*c^2 + 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - a^2*b*c^3*x^2*log(-(b*c^2*x^2 + a*c^2 - 2*sqrt(b*x^2 + a)*c*d + d^2)/x^2) - 2*a^3*c^3 + 2*a^2*c*d^2 + 2*(3*a*b*c^2*d - b*d^3)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 2*(a^2*c^2*d - a*d^3)*sqrt(b*x^2 + a))/((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4)*x^2)]","A",0
549,1,1168,0,0.988146," ","integrate(x^2/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\left[\frac{4 \, b c x + 2 \, \sqrt{b} d \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + b \sqrt{-\frac{a c^{2} - d^{2}}{b}} \log\left(\frac{a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4} + {\left(a^{2} b^{2} c^{4} - 8 \, a b^{2} c^{2} d^{2} + 8 \, b^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{3} b c^{4} - 5 \, a^{2} b c^{2} d^{2} + 4 \, a b d^{4}\right)} x^{2} - 4 \, {\left({\left(a b^{2} c^{2} d - 2 \, b^{2} d^{3}\right)} x^{3} + {\left(a^{2} b c^{2} d - a b d^{3}\right)} x\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{a c^{2} - d^{2}}{b}}}{b^{2} c^{4} x^{4} + a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4} + 2 \, {\left(a b c^{4} - b c^{2} d^{2}\right)} x^{2}}\right) + 2 \, b \sqrt{-\frac{a c^{2} - d^{2}}{b}} \log\left(\frac{b c^{2} x^{2} - 2 \, b c x \sqrt{-\frac{a c^{2} - d^{2}}{b}} - a c^{2} + d^{2}}{b c^{2} x^{2} + a c^{2} - d^{2}}\right)}{4 \, b^{2} c^{2}}, \frac{4 \, b c x + 4 \, \sqrt{-b} d \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + b \sqrt{-\frac{a c^{2} - d^{2}}{b}} \log\left(\frac{a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4} + {\left(a^{2} b^{2} c^{4} - 8 \, a b^{2} c^{2} d^{2} + 8 \, b^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{3} b c^{4} - 5 \, a^{2} b c^{2} d^{2} + 4 \, a b d^{4}\right)} x^{2} - 4 \, {\left({\left(a b^{2} c^{2} d - 2 \, b^{2} d^{3}\right)} x^{3} + {\left(a^{2} b c^{2} d - a b d^{3}\right)} x\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{a c^{2} - d^{2}}{b}}}{b^{2} c^{4} x^{4} + a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4} + 2 \, {\left(a b c^{4} - b c^{2} d^{2}\right)} x^{2}}\right) + 2 \, b \sqrt{-\frac{a c^{2} - d^{2}}{b}} \log\left(\frac{b c^{2} x^{2} - 2 \, b c x \sqrt{-\frac{a c^{2} - d^{2}}{b}} - a c^{2} + d^{2}}{b c^{2} x^{2} + a c^{2} - d^{2}}\right)}{4 \, b^{2} c^{2}}, \frac{2 \, b c x + 2 \, b \sqrt{\frac{a c^{2} - d^{2}}{b}} \arctan\left(-\frac{b c x \sqrt{\frac{a c^{2} - d^{2}}{b}}}{a c^{2} - d^{2}}\right) - b \sqrt{\frac{a c^{2} - d^{2}}{b}} \arctan\left(\frac{{\left(a^{2} c^{2} - a d^{2} + {\left(a b c^{2} - 2 \, b d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{a c^{2} - d^{2}}{b}}}{2 \, {\left({\left(a b c^{2} d - b d^{3}\right)} x^{3} + {\left(a^{2} c^{2} d - a d^{3}\right)} x\right)}}\right) + \sqrt{b} d \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, b^{2} c^{2}}, \frac{2 \, b c x + 2 \, b \sqrt{\frac{a c^{2} - d^{2}}{b}} \arctan\left(-\frac{b c x \sqrt{\frac{a c^{2} - d^{2}}{b}}}{a c^{2} - d^{2}}\right) + 2 \, \sqrt{-b} d \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - b \sqrt{\frac{a c^{2} - d^{2}}{b}} \arctan\left(\frac{{\left(a^{2} c^{2} - a d^{2} + {\left(a b c^{2} - 2 \, b d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{a c^{2} - d^{2}}{b}}}{2 \, {\left({\left(a b c^{2} d - b d^{3}\right)} x^{3} + {\left(a^{2} c^{2} d - a d^{3}\right)} x\right)}}\right)}{2 \, b^{2} c^{2}}\right]"," ",0,"[1/4*(4*b*c*x + 2*sqrt(b)*d*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + b*sqrt(-(a*c^2 - d^2)/b)*log((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4 + (a^2*b^2*c^4 - 8*a*b^2*c^2*d^2 + 8*b^2*d^4)*x^4 + 2*(a^3*b*c^4 - 5*a^2*b*c^2*d^2 + 4*a*b*d^4)*x^2 - 4*((a*b^2*c^2*d - 2*b^2*d^3)*x^3 + (a^2*b*c^2*d - a*b*d^3)*x)*sqrt(b*x^2 + a)*sqrt(-(a*c^2 - d^2)/b))/(b^2*c^4*x^4 + a^2*c^4 - 2*a*c^2*d^2 + d^4 + 2*(a*b*c^4 - b*c^2*d^2)*x^2)) + 2*b*sqrt(-(a*c^2 - d^2)/b)*log((b*c^2*x^2 - 2*b*c*x*sqrt(-(a*c^2 - d^2)/b) - a*c^2 + d^2)/(b*c^2*x^2 + a*c^2 - d^2)))/(b^2*c^2), 1/4*(4*b*c*x + 4*sqrt(-b)*d*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + b*sqrt(-(a*c^2 - d^2)/b)*log((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4 + (a^2*b^2*c^4 - 8*a*b^2*c^2*d^2 + 8*b^2*d^4)*x^4 + 2*(a^3*b*c^4 - 5*a^2*b*c^2*d^2 + 4*a*b*d^4)*x^2 - 4*((a*b^2*c^2*d - 2*b^2*d^3)*x^3 + (a^2*b*c^2*d - a*b*d^3)*x)*sqrt(b*x^2 + a)*sqrt(-(a*c^2 - d^2)/b))/(b^2*c^4*x^4 + a^2*c^4 - 2*a*c^2*d^2 + d^4 + 2*(a*b*c^4 - b*c^2*d^2)*x^2)) + 2*b*sqrt(-(a*c^2 - d^2)/b)*log((b*c^2*x^2 - 2*b*c*x*sqrt(-(a*c^2 - d^2)/b) - a*c^2 + d^2)/(b*c^2*x^2 + a*c^2 - d^2)))/(b^2*c^2), 1/2*(2*b*c*x + 2*b*sqrt((a*c^2 - d^2)/b)*arctan(-b*c*x*sqrt((a*c^2 - d^2)/b)/(a*c^2 - d^2)) - b*sqrt((a*c^2 - d^2)/b)*arctan(1/2*(a^2*c^2 - a*d^2 + (a*b*c^2 - 2*b*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt((a*c^2 - d^2)/b)/((a*b*c^2*d - b*d^3)*x^3 + (a^2*c^2*d - a*d^3)*x)) + sqrt(b)*d*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/(b^2*c^2), 1/2*(2*b*c*x + 2*b*sqrt((a*c^2 - d^2)/b)*arctan(-b*c*x*sqrt((a*c^2 - d^2)/b)/(a*c^2 - d^2)) + 2*sqrt(-b)*d*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - b*sqrt((a*c^2 - d^2)/b)*arctan(1/2*(a^2*c^2 - a*d^2 + (a*b*c^2 - 2*b*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt((a*c^2 - d^2)/b)/((a*b*c^2*d - b*d^3)*x^3 + (a^2*c^2*d - a*d^3)*x)))/(b^2*c^2)]","A",0
550,1,510,0,0.653006," ","integrate(1/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c^{2} + b d^{2}} \log\left(\frac{a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4} + {\left(a^{2} b^{2} c^{4} - 8 \, a b^{2} c^{2} d^{2} + 8 \, b^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{3} b c^{4} - 5 \, a^{2} b c^{2} d^{2} + 4 \, a b d^{4}\right)} x^{2} - 4 \, \sqrt{-a b c^{2} + b d^{2}} {\left({\left(a b c^{2} d - 2 \, b d^{3}\right)} x^{3} + {\left(a^{2} c^{2} d - a d^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{b^{2} c^{4} x^{4} + a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4} + 2 \, {\left(a b c^{4} - b c^{2} d^{2}\right)} x^{2}}\right) + 2 \, \sqrt{-a b c^{2} + b d^{2}} \log\left(\frac{b c^{2} x^{2} - a c^{2} - 2 \, \sqrt{-a b c^{2} + b d^{2}} c x + d^{2}}{b c^{2} x^{2} + a c^{2} - d^{2}}\right)}{4 \, {\left(a b c^{2} - b d^{2}\right)}}, -\frac{2 \, \sqrt{a b c^{2} - b d^{2}} \arctan\left(-\frac{\sqrt{a b c^{2} - b d^{2}} c x}{a c^{2} - d^{2}}\right) - \sqrt{a b c^{2} - b d^{2}} \arctan\left(\frac{{\left(a^{2} c^{2} - a d^{2} + {\left(a b c^{2} - 2 \, b d^{2}\right)} x^{2}\right)} \sqrt{a b c^{2} - b d^{2}} \sqrt{b x^{2} + a}}{2 \, {\left({\left(a b^{2} c^{2} d - b^{2} d^{3}\right)} x^{3} + {\left(a^{2} b c^{2} d - a b d^{3}\right)} x\right)}}\right)}{2 \, {\left(a b c^{2} - b d^{2}\right)}}\right]"," ",0,"[-1/4*(sqrt(-a*b*c^2 + b*d^2)*log((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4 + (a^2*b^2*c^4 - 8*a*b^2*c^2*d^2 + 8*b^2*d^4)*x^4 + 2*(a^3*b*c^4 - 5*a^2*b*c^2*d^2 + 4*a*b*d^4)*x^2 - 4*sqrt(-a*b*c^2 + b*d^2)*((a*b*c^2*d - 2*b*d^3)*x^3 + (a^2*c^2*d - a*d^3)*x)*sqrt(b*x^2 + a))/(b^2*c^4*x^4 + a^2*c^4 - 2*a*c^2*d^2 + d^4 + 2*(a*b*c^4 - b*c^2*d^2)*x^2)) + 2*sqrt(-a*b*c^2 + b*d^2)*log((b*c^2*x^2 - a*c^2 - 2*sqrt(-a*b*c^2 + b*d^2)*c*x + d^2)/(b*c^2*x^2 + a*c^2 - d^2)))/(a*b*c^2 - b*d^2), -1/2*(2*sqrt(a*b*c^2 - b*d^2)*arctan(-sqrt(a*b*c^2 - b*d^2)*c*x/(a*c^2 - d^2)) - sqrt(a*b*c^2 - b*d^2)*arctan(1/2*(a^2*c^2 - a*d^2 + (a*b*c^2 - 2*b*d^2)*x^2)*sqrt(a*b*c^2 - b*d^2)*sqrt(b*x^2 + a)/((a*b^2*c^2*d - b^2*d^3)*x^3 + (a^2*b*c^2*d - a*b*d^3)*x)))/(a*b*c^2 - b*d^2)]","B",0
551,1,581,0,0.745418," ","integrate(1/x^2/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{a c^{2} x \sqrt{-\frac{b}{a c^{2} - d^{2}}} \log\left(\frac{a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4} + {\left(a^{2} b^{2} c^{4} - 8 \, a b^{2} c^{2} d^{2} + 8 \, b^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{3} b c^{4} - 5 \, a^{2} b c^{2} d^{2} + 4 \, a b d^{4}\right)} x^{2} + 4 \, {\left({\left(a^{2} b c^{4} d - 3 \, a b c^{2} d^{3} + 2 \, b d^{5}\right)} x^{3} + {\left(a^{3} c^{4} d - 2 \, a^{2} c^{2} d^{3} + a d^{5}\right)} x\right)} \sqrt{b x^{2} + a} \sqrt{-\frac{b}{a c^{2} - d^{2}}}}{b^{2} c^{4} x^{4} + a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4} + 2 \, {\left(a b c^{4} - b c^{2} d^{2}\right)} x^{2}}\right) + 2 \, a c^{2} x \sqrt{-\frac{b}{a c^{2} - d^{2}}} \log\left(\frac{b c^{2} x^{2} - a c^{2} + 2 \, {\left(a c^{3} - c d^{2}\right)} x \sqrt{-\frac{b}{a c^{2} - d^{2}}} + d^{2}}{b c^{2} x^{2} + a c^{2} - d^{2}}\right) + 4 \, a c - 4 \, \sqrt{b x^{2} + a} d}{4 \, {\left(a^{2} c^{2} - a d^{2}\right)} x}, -\frac{2 \, a c^{2} x \sqrt{\frac{b}{a c^{2} - d^{2}}} \arctan\left(c x \sqrt{\frac{b}{a c^{2} - d^{2}}}\right) - a c^{2} x \sqrt{\frac{b}{a c^{2} - d^{2}}} \arctan\left(-\frac{{\left(a^{2} c^{2} - a d^{2} + {\left(a b c^{2} - 2 \, b d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{\frac{b}{a c^{2} - d^{2}}}}{2 \, {\left(b^{2} d x^{3} + a b d x\right)}}\right) + 2 \, a c - 2 \, \sqrt{b x^{2} + a} d}{2 \, {\left(a^{2} c^{2} - a d^{2}\right)} x}\right]"," ",0,"[-1/4*(a*c^2*x*sqrt(-b/(a*c^2 - d^2))*log((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4 + (a^2*b^2*c^4 - 8*a*b^2*c^2*d^2 + 8*b^2*d^4)*x^4 + 2*(a^3*b*c^4 - 5*a^2*b*c^2*d^2 + 4*a*b*d^4)*x^2 + 4*((a^2*b*c^4*d - 3*a*b*c^2*d^3 + 2*b*d^5)*x^3 + (a^3*c^4*d - 2*a^2*c^2*d^3 + a*d^5)*x)*sqrt(b*x^2 + a)*sqrt(-b/(a*c^2 - d^2)))/(b^2*c^4*x^4 + a^2*c^4 - 2*a*c^2*d^2 + d^4 + 2*(a*b*c^4 - b*c^2*d^2)*x^2)) + 2*a*c^2*x*sqrt(-b/(a*c^2 - d^2))*log((b*c^2*x^2 - a*c^2 + 2*(a*c^3 - c*d^2)*x*sqrt(-b/(a*c^2 - d^2)) + d^2)/(b*c^2*x^2 + a*c^2 - d^2)) + 4*a*c - 4*sqrt(b*x^2 + a)*d)/((a^2*c^2 - a*d^2)*x), -1/2*(2*a*c^2*x*sqrt(b/(a*c^2 - d^2))*arctan(c*x*sqrt(b/(a*c^2 - d^2))) - a*c^2*x*sqrt(b/(a*c^2 - d^2))*arctan(-1/2*(a^2*c^2 - a*d^2 + (a*b*c^2 - 2*b*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(b/(a*c^2 - d^2))/(b^2*d*x^3 + a*b*d*x)) + 2*a*c - 2*sqrt(b*x^2 + a)*d)/((a^2*c^2 - a*d^2)*x)]","A",0
552,1,191,0,0.539711," ","integrate(x^8/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{4} x^{6} - 6 \, {\left(a b c^{4} - b c^{2} d^{2}\right)} x^{3} + 6 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) + 6 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left(\sqrt{b x^{3} + a} c + d\right) - 6 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left(\sqrt{b x^{3} + a} c - d\right) - 4 \, {\left(b c^{3} d x^{3} - 5 \, a c^{3} d + 3 \, c d^{3}\right)} \sqrt{b x^{3} + a}}{18 \, b^{3} c^{5}}"," ",0,"1/18*(3*b^2*c^4*x^6 - 6*(a*b*c^4 - b*c^2*d^2)*x^3 + 6*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(b*c^2*x^3 + a*c^2 - d^2) + 6*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(sqrt(b*x^3 + a)*c + d) - 6*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(sqrt(b*x^3 + a)*c - d) - 4*(b*c^3*d*x^3 - 5*a*c^3*d + 3*c*d^3)*sqrt(b*x^3 + a))/(b^3*c^5)","A",0
553,1,118,0,0.620866," ","integrate(x^5/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\frac{b c^{2} x^{3} - 2 \, \sqrt{b x^{3} + a} c d - {\left(a c^{2} - d^{2}\right)} \log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) - {\left(a c^{2} - d^{2}\right)} \log\left(\sqrt{b x^{3} + a} c + d\right) + {\left(a c^{2} - d^{2}\right)} \log\left(\sqrt{b x^{3} + a} c - d\right)}{3 \, b^{2} c^{3}}"," ",0,"1/3*(b*c^2*x^3 - 2*sqrt(b*x^3 + a)*c*d - (a*c^2 - d^2)*log(b*c^2*x^3 + a*c^2 - d^2) - (a*c^2 - d^2)*log(sqrt(b*x^3 + a)*c + d) + (a*c^2 - d^2)*log(sqrt(b*x^3 + a)*c - d))/(b^2*c^3)","A",0
554,1,61,0,0.719104," ","integrate(x^2/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\frac{\log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) + \log\left(\sqrt{b x^{3} + a} c + d\right) - \log\left(\sqrt{b x^{3} + a} c - d\right)}{3 \, b c}"," ",0,"1/3*(log(b*c^2*x^3 + a*c^2 - d^2) + log(sqrt(b*x^3 + a)*c + d) - log(sqrt(b*x^3 + a)*c - d))/(b*c)","B",0
555,1,232,0,0.925966," ","integrate(1/x/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{a c \log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) + a c \log\left(\sqrt{b x^{3} + a} c + d\right) - a c \log\left(\sqrt{b x^{3} + a} c - d\right) - 3 \, a c \log\left(x\right) - \sqrt{a} d \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right)}{3 \, {\left(a^{2} c^{2} - a d^{2}\right)}}, -\frac{a c \log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) + a c \log\left(\sqrt{b x^{3} + a} c + d\right) - a c \log\left(\sqrt{b x^{3} + a} c - d\right) - 3 \, a c \log\left(x\right) + 2 \, \sqrt{-a} d \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right)}{3 \, {\left(a^{2} c^{2} - a d^{2}\right)}}\right]"," ",0,"[-1/3*(a*c*log(b*c^2*x^3 + a*c^2 - d^2) + a*c*log(sqrt(b*x^3 + a)*c + d) - a*c*log(sqrt(b*x^3 + a)*c - d) - 3*a*c*log(x) - sqrt(a)*d*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3))/(a^2*c^2 - a*d^2), -1/3*(a*c*log(b*c^2*x^3 + a*c^2 - d^2) + a*c*log(sqrt(b*x^3 + a)*c + d) - a*c*log(sqrt(b*x^3 + a)*c - d) - 3*a*c*log(x) + 2*sqrt(-a)*d*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a))/(a^2*c^2 - a*d^2)]","A",0
556,1,445,0,0.797884," ","integrate(1/x^4/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b c^{3} x^{3} \log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) + 2 \, a^{2} b c^{3} x^{3} \log\left(\sqrt{b x^{3} + a} c + d\right) - 2 \, a^{2} b c^{3} x^{3} \log\left(\sqrt{b x^{3} + a} c - d\right) - 6 \, a^{2} b c^{3} x^{3} \log\left(x\right) - 2 \, a^{3} c^{3} - {\left(3 \, a b c^{2} d - b d^{3}\right)} \sqrt{a} x^{3} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, a^{2} c d^{2} + 2 \, {\left(a^{2} c^{2} d - a d^{3}\right)} \sqrt{b x^{3} + a}}{6 \, {\left(a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4}\right)} x^{3}}, \frac{a^{2} b c^{3} x^{3} \log\left(b c^{2} x^{3} + a c^{2} - d^{2}\right) + a^{2} b c^{3} x^{3} \log\left(\sqrt{b x^{3} + a} c + d\right) - a^{2} b c^{3} x^{3} \log\left(\sqrt{b x^{3} + a} c - d\right) - 3 \, a^{2} b c^{3} x^{3} \log\left(x\right) - a^{3} c^{3} + {\left(3 \, a b c^{2} d - b d^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + a^{2} c d^{2} + {\left(a^{2} c^{2} d - a d^{3}\right)} \sqrt{b x^{3} + a}}{3 \, {\left(a^{4} c^{4} - 2 \, a^{3} c^{2} d^{2} + a^{2} d^{4}\right)} x^{3}}\right]"," ",0,"[1/6*(2*a^2*b*c^3*x^3*log(b*c^2*x^3 + a*c^2 - d^2) + 2*a^2*b*c^3*x^3*log(sqrt(b*x^3 + a)*c + d) - 2*a^2*b*c^3*x^3*log(sqrt(b*x^3 + a)*c - d) - 6*a^2*b*c^3*x^3*log(x) - 2*a^3*c^3 - (3*a*b*c^2*d - b*d^3)*sqrt(a)*x^3*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*a^2*c*d^2 + 2*(a^2*c^2*d - a*d^3)*sqrt(b*x^3 + a))/((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4)*x^3), 1/3*(a^2*b*c^3*x^3*log(b*c^2*x^3 + a*c^2 - d^2) + a^2*b*c^3*x^3*log(sqrt(b*x^3 + a)*c + d) - a^2*b*c^3*x^3*log(sqrt(b*x^3 + a)*c - d) - 3*a^2*b*c^3*x^3*log(x) - a^3*c^3 + (3*a*b*c^2*d - b*d^3)*sqrt(-a)*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + a^2*c*d^2 + (a^2*c^2*d - a*d^3)*sqrt(b*x^3 + a))/((a^4*c^4 - 2*a^3*c^2*d^2 + a^2*d^4)*x^3)]","A",0
557,-1,0,0,0.000000," ","integrate(x^3/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate(x/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,-1,0,0,0.000000," ","integrate(1/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
560,-1,0,0,0.000000," ","integrate(1/x^2/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate(1/x^3/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,0,0,0,1.068318," ","integrate(1/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b c x^{n} + a c - \sqrt{b x^{n} + a} d}{b^{2} c^{2} x^{2 \, n} + a^{2} c^{2} - a d^{2} + {\left(2 \, a b c^{2} - b d^{2}\right)} x^{n}}, x\right)"," ",0,"integral((b*c*x^n + a*c - sqrt(b*x^n + a)*d)/(b^2*c^2*x^(2*n) + a^2*c^2 - a*d^2 + (2*a*b*c^2 - b*d^2)*x^n), x)","F",0
563,0,0,0,1.020019," ","integrate(x^m/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b c x^{m} x^{n} + a c x^{m} - \sqrt{b x^{n} + a} d x^{m}}{b^{2} c^{2} x^{2 \, n} + a^{2} c^{2} - a d^{2} + {\left(2 \, a b c^{2} - b d^{2}\right)} x^{n}}, x\right)"," ",0,"integral((b*c*x^m*x^n + a*c*x^m - sqrt(b*x^n + a)*d*x^m)/(b^2*c^2*x^(2*n) + a^2*c^2 - a*d^2 + (2*a*b*c^2 - b*d^2)*x^n), x)","F",0
564,1,25,0,0.695997," ","integrate(x^(-1+n)/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, \log\left(\sqrt{b x^{n} + a} c + d\right)}{b c n}"," ",0,"2*log(sqrt(b*x^n + a)*c + d)/(b*c*n)","A",0
565,1,6,0,0.551981," ","integrate(1/(4*x^(3/2)+x^(1/2)),x, algorithm=""fricas"")","\arctan\left(2 \, \sqrt{x}\right)"," ",0,"arctan(2*sqrt(x))","A",0
566,1,21,0,0.683563," ","integrate(1/(-x^(5/2)+x^(1/2)),x, algorithm=""fricas"")","\arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{x} - 1\right)"," ",0,"arctan(sqrt(x)) + 1/2*log(sqrt(x) + 1) - 1/2*log(sqrt(x) - 1)","B",0
567,1,19,0,0.478027," ","integrate(1/(-x^(1/4)+x^(1/2)),x, algorithm=""fricas"")","2 \, \sqrt{x} + 4 \, x^{\frac{1}{4}} + 4 \, \log\left(x^{\frac{1}{4}} - 1\right)"," ",0,"2*sqrt(x) + 4*x^(1/4) + 4*log(x^(1/4) - 1)","A",0
568,1,24,0,0.706999," ","integrate(1/(x^(1/3)+x^(1/2)),x, algorithm=""fricas"")","2 \, \sqrt{x} - 3 \, x^{\frac{1}{3}} + 6 \, x^{\frac{1}{6}} - 6 \, \log\left(x^{\frac{1}{6}} + 1\right)"," ",0,"2*sqrt(x) - 3*x^(1/3) + 6*x^(1/6) - 6*log(x^(1/6) + 1)","A",0
569,1,19,0,0.575093," ","integrate(1/(x^(1/4)+x^(1/2)),x, algorithm=""fricas"")","2 \, \sqrt{x} - 4 \, x^{\frac{1}{4}} + 4 \, \log\left(x^{\frac{1}{4}} + 1\right)"," ",0,"2*sqrt(x) - 4*x^(1/4) + 4*log(x^(1/4) + 1)","A",0
570,1,14,0,0.688782," ","integrate(1/(-x^(1/3)+x^(2/3)),x, algorithm=""fricas"")","3 \, x^{\frac{1}{3}} + 3 \, \log\left(x^{\frac{1}{3}} - 1\right)"," ",0,"3*x^(1/3) + 3*log(x^(1/3) - 1)","A",0
571,1,47,0,0.636679," ","integrate(1/(1/x^(1/4)+x^(1/2)),x, algorithm=""fricas"")","-\frac{4}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{\frac{1}{4}} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, \sqrt{x} - \frac{2}{3} \, \log\left(\sqrt{x} - x^{\frac{1}{4}} + 1\right) + \frac{4}{3} \, \log\left(x^{\frac{1}{4}} + 1\right)"," ",0,"-4/3*sqrt(3)*arctan(2/3*sqrt(3)*x^(1/4) - 1/3*sqrt(3)) + 2*sqrt(x) - 2/3*log(sqrt(x) - x^(1/4) + 1) + 4/3*log(x^(1/4) + 1)","A",0
572,1,49,0,0.614346," ","integrate(1/(x^(1/4)+x^(1/3)),x, algorithm=""fricas"")","\frac{3}{2} \, x^{\frac{2}{3}} - \frac{12}{7} \, x^{\frac{7}{12}} + 2 \, \sqrt{x} - \frac{12}{5} \, x^{\frac{5}{12}} + 3 \, x^{\frac{1}{3}} - 4 \, x^{\frac{1}{4}} + 6 \, x^{\frac{1}{6}} - 12 \, x^{\frac{1}{12}} + 12 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"3/2*x^(2/3) - 12/7*x^(7/12) + 2*sqrt(x) - 12/5*x^(5/12) + 3*x^(1/3) - 4*x^(1/4) + 6*x^(1/6) - 12*x^(1/12) + 12*log(x^(1/12) + 1)","A",0
573,1,76,0,0.792832," ","integrate(1/(1/x^(1/3)+1/x^(1/4)),x, algorithm=""fricas"")","\frac{4}{5} \, {\left(x + 5\right)} x^{\frac{1}{4}} - \frac{6}{7} \, {\left(x + 7\right)} x^{\frac{1}{6}} + \frac{12}{13} \, {\left(x + 13\right)} x^{\frac{1}{12}} - x + \frac{12}{11} \, x^{\frac{11}{12}} - \frac{6}{5} \, x^{\frac{5}{6}} + \frac{4}{3} \, x^{\frac{3}{4}} - \frac{3}{2} \, x^{\frac{2}{3}} + \frac{12}{7} \, x^{\frac{7}{12}} - 2 \, \sqrt{x} + \frac{12}{5} \, x^{\frac{5}{12}} - 3 \, x^{\frac{1}{3}} - 12 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"4/5*(x + 5)*x^(1/4) - 6/7*(x + 7)*x^(1/6) + 12/13*(x + 13)*x^(1/12) - x + 12/11*x^(11/12) - 6/5*x^(5/6) + 4/3*x^(3/4) - 3/2*x^(2/3) + 12/7*x^(7/12) - 2*sqrt(x) + 12/5*x^(5/12) - 3*x^(1/3) - 12*log(x^(1/12) + 1)","A",0
574,1,638,0,2.677811," ","integrate(1/(-1/x^(1/3)+x^(1/2)),x, algorithm=""fricas"")","\frac{1}{10} \, {\left(3 \, \sqrt{5} - \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} - 3\right)} \log\left(\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 3 \, \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} {\left(\sqrt{5} - 1\right)} + 72 \, x^{\frac{1}{6}} + 36\right) + \frac{1}{10} \, {\left(3 \, \sqrt{5} + \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} - 3\right)} \log\left(\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} - 3 \, \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} {\left(\sqrt{5} - 1\right)} + 72 \, x^{\frac{1}{6}} + 36\right) - \frac{3}{10} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(-\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + 36 \, x^{\frac{1}{6}}\right) + \frac{3}{10} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(-\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 36 \, x^{\frac{1}{6}}\right) + 2 \, \sqrt{x} + \frac{6}{5} \, \log\left(x^{\frac{1}{6}} - 1\right)"," ",0,"1/10*(3*sqrt(5) - sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) - 3)*log(9/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 3*sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90)*(sqrt(5) - 1) + 72*x^(1/6) + 36) + 1/10*(3*sqrt(5) + sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) - 3)*log(9/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 - 3*sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90)*(sqrt(5) - 1) + 72*x^(1/6) + 36) - 3/10*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(-9/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 36*x^(1/6)) + 3/10*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(-9/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 36*x^(1/6)) + 2*sqrt(x) + 6/5*log(x^(1/6) - 1)","B",0
575,1,6,0,0.636774," ","integrate(x^(1/2)/(x^2+x),x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{x}\right)"," ",0,"2*arctan(sqrt(x))","A",0
576,1,15,0,0.903937," ","integrate(x/(x+4*x^(1/2)),x, algorithm=""fricas"")","x - 8 \, \sqrt{x} + 32 \, \log\left(\sqrt{x} + 4\right)"," ",0,"x - 8*sqrt(x) + 32*log(sqrt(x) + 4)","A",0
577,1,120,0,0.624523," ","integrate(x^(1/2)/(x^(1/3)+x),x, algorithm=""fricas"")","3 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} x^{\frac{1}{6}} + x^{\frac{1}{3}} + 1} - \sqrt{2} x^{\frac{1}{6}} - 1\right) + 3 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} x^{\frac{1}{6}} + 4 \, x^{\frac{1}{3}} + 4} - \sqrt{2} x^{\frac{1}{6}} + 1\right) + \frac{3}{4} \, \sqrt{2} \log\left(4 \, \sqrt{2} x^{\frac{1}{6}} + 4 \, x^{\frac{1}{3}} + 4\right) - \frac{3}{4} \, \sqrt{2} \log\left(-4 \, \sqrt{2} x^{\frac{1}{6}} + 4 \, x^{\frac{1}{3}} + 4\right) + 2 \, \sqrt{x}"," ",0,"3*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*x^(1/6) + x^(1/3) + 1) - sqrt(2)*x^(1/6) - 1) + 3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*x^(1/6) + 4*x^(1/3) + 4) - sqrt(2)*x^(1/6) + 1) + 3/4*sqrt(2)*log(4*sqrt(2)*x^(1/6) + 4*x^(1/3) + 4) - 3/4*sqrt(2)*log(-4*sqrt(2)*x^(1/6) + 4*x^(1/3) + 4) + 2*sqrt(x)","A",0
578,1,62,0,0.718879," ","integrate(x^(1/3)/(x^(1/4)+x^(1/2)),x, algorithm=""fricas"")","4 \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{\frac{1}{12}} - \frac{1}{3} \, \sqrt{3}\right) + \frac{6}{5} \, x^{\frac{5}{6}} - \frac{12}{7} \, x^{\frac{7}{12}} + 3 \, x^{\frac{1}{3}} - 12 \, x^{\frac{1}{12}} - 2 \, \log\left(x^{\frac{1}{6}} - x^{\frac{1}{12}} + 1\right) + 4 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"4*sqrt(3)*arctan(2/3*sqrt(3)*x^(1/12) - 1/3*sqrt(3)) + 6/5*x^(5/6) - 12/7*x^(7/12) + 3*x^(1/3) - 12*x^(1/12) - 2*log(x^(1/6) - x^(1/12) + 1) + 4*log(x^(1/12) + 1)","A",0
579,1,71,0,0.571422," ","integrate(x^(1/2)/(x^(1/4)+x^(1/3)),x, algorithm=""fricas"")","\frac{6}{7} \, {\left(x + 7\right)} x^{\frac{1}{6}} - \frac{12}{13} \, {\left(x + 13\right)} x^{\frac{1}{12}} + x - \frac{12}{11} \, x^{\frac{11}{12}} + \frac{6}{5} \, x^{\frac{5}{6}} - \frac{4}{3} \, x^{\frac{3}{4}} + \frac{3}{2} \, x^{\frac{2}{3}} - \frac{12}{7} \, x^{\frac{7}{12}} + 2 \, \sqrt{x} - \frac{12}{5} \, x^{\frac{5}{12}} + 3 \, x^{\frac{1}{3}} - 4 \, x^{\frac{1}{4}} + 12 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"6/7*(x + 7)*x^(1/6) - 12/13*(x + 13)*x^(1/12) + x - 12/11*x^(11/12) + 6/5*x^(5/6) - 4/3*x^(3/4) + 3/2*x^(2/3) - 12/7*x^(7/12) + 2*sqrt(x) - 12/5*x^(5/12) + 3*x^(1/3) - 4*x^(1/4) + 12*log(x^(1/12) + 1)","A",0
580,1,547,0,2.828068," ","integrate(x^(1/2)/(-1/x^(1/3)+x^(1/2)),x, algorithm=""fricas"")","-\frac{3}{10} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(\frac{3}{2} \, \sqrt{2} \sqrt{\sqrt{5} - 5} + \frac{3}{2} \, \sqrt{5} + 6 \, x^{\frac{1}{6}} + \frac{3}{2}\right) + \frac{3}{10} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(-\frac{3}{2} \, \sqrt{2} \sqrt{\sqrt{5} - 5} + \frac{3}{2} \, \sqrt{5} + 6 \, x^{\frac{1}{6}} + \frac{3}{2}\right) + \frac{1}{10} \, {\left(3 \, \sqrt{5} - \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} - 3\right)} \log\left(-3 \, \sqrt{5} + \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} + 12 \, x^{\frac{1}{6}} + 3\right) + \frac{1}{10} \, {\left(3 \, \sqrt{5} + \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} - 3\right)} \log\left(-3 \, \sqrt{5} - \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} + 12 \, x^{\frac{1}{6}} + 3\right) + x + 6 \, x^{\frac{1}{6}} + \frac{6}{5} \, \log\left(x^{\frac{1}{6}} - 1\right)"," ",0,"-3/10*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(3/2*sqrt(2)*sqrt(sqrt(5) - 5) + 3/2*sqrt(5) + 6*x^(1/6) + 3/2) + 3/10*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(-3/2*sqrt(2)*sqrt(sqrt(5) - 5) + 3/2*sqrt(5) + 6*x^(1/6) + 3/2) + 1/10*(3*sqrt(5) - sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) - 3)*log(-3*sqrt(5) + sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) + 12*x^(1/6) + 3) + 1/10*(3*sqrt(5) + sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) - 3)*log(-3*sqrt(5) - sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) + 12*x^(1/6) + 3) + x + 6*x^(1/6) + 6/5*log(x^(1/6) - 1)","B",0
581,1,44,0,0.615443," ","integrate(x^m*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-b x + a} x x^{m} \sqrt{\frac{b x - a}{x}}}{2 \, a m - {\left(2 \, b m + b\right)} x + a}"," ",0,"2*sqrt(-b*x + a)*x*x^m*sqrt((b*x - a)/x)/(2*a*m - (2*b*m + b)*x + a)","A",0
582,1,35,0,0.702406," ","integrate(x^2*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-b x + a} x^{3} \sqrt{\frac{b x - a}{x}}}{5 \, {\left(b x - a\right)}}"," ",0,"-2/5*sqrt(-b*x + a)*x^3*sqrt((b*x - a)/x)/(b*x - a)","A",0
583,1,35,0,0.561671," ","integrate(x*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-b x + a} x^{2} \sqrt{\frac{b x - a}{x}}}{3 \, {\left(b x - a\right)}}"," ",0,"-2/3*sqrt(-b*x + a)*x^2*sqrt((b*x - a)/x)/(b*x - a)","A",0
584,1,33,0,0.769736," ","integrate((b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-b x + a} x \sqrt{\frac{b x - a}{x}}}{b x - a}"," ",0,"-2*sqrt(-b*x + a)*x*sqrt((b*x - a)/x)/(b*x - a)","A",0
585,1,32,0,0.629437," ","integrate((b-a/x)^(1/2)/x/(-b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-b x + a} \sqrt{\frac{b x - a}{x}}}{b x - a}"," ",0,"2*sqrt(-b*x + a)*sqrt((b*x - a)/x)/(b*x - a)","A",0
586,1,35,0,0.718120," ","integrate((b-a/x)^(1/2)/x^2/(-b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-b x + a} \sqrt{\frac{b x - a}{x}}}{3 \, {\left(b x^{2} - a x\right)}}"," ",0,"2/3*sqrt(-b*x + a)*sqrt((b*x - a)/x)/(b*x^2 - a*x)","A",0
587,0,0,0,0.869650," ","integrate((a+b/x)^m*(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{n} \left(\frac{a x + b}{x}\right)^{m}, x\right)"," ",0,"integral((d*x + c)^n*((a*x + b)/x)^m, x)","F",0
588,0,0,0,0.666998," ","integrate((a+b/x)^m*(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(\frac{a x + b}{x}\right)^{m}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*((a*x + b)/x)^m, x)","F",0
589,0,0,0,0.590782," ","integrate((a+b/x)^m*(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)} \left(\frac{a x + b}{x}\right)^{m}, x\right)"," ",0,"integral((d*x + c)*((a*x + b)/x)^m, x)","F",0
590,0,0,0,0.633890," ","integrate((a+b/x)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x + b}{x}\right)^{m}, x\right)"," ",0,"integral(((a*x + b)/x)^m, x)","F",0
591,0,0,0,0.680715," ","integrate((a+b/x)^m/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{m}}{d x + c}, x\right)"," ",0,"integral(((a*x + b)/x)^m/(d*x + c), x)","F",0
592,0,0,0,0.534033," ","integrate((a+b/x)^m/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{m}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(((a*x + b)/x)^m/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
593,0,0,0,0.645886," ","integrate((a+b/x)^m/(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{m}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}, x\right)"," ",0,"integral(((a*x + b)/x)^m/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x)","F",0
594,0,0,0,0.663510," ","integrate((a+b/x)^m/(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x + b}{x}\right)^{m}}{d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}}, x\right)"," ",0,"integral(((a*x + b)/x)^m/(d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4), x)","F",0
595,1,44,0,0.882435," ","integrate(x^m*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{2} + a} x x^{m} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{b m x^{2} - a m}"," ",0,"-sqrt(-b*x^2 + a)*x*x^m*sqrt((b*x^2 - a)/x^2)/(b*m*x^2 - a*m)","A",0
596,1,41,0,0.548546," ","integrate(x^2*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{2} + a} x^{3} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{2 \, {\left(b x^{2} - a\right)}}"," ",0,"-1/2*sqrt(-b*x^2 + a)*x^3*sqrt((b*x^2 - a)/x^2)/(b*x^2 - a)","A",0
597,1,41,0,0.664976," ","integrate(x*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{2} + a} x^{2} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{b x^{2} - a}"," ",0,"-sqrt(-b*x^2 + a)*x^2*sqrt((b*x^2 - a)/x^2)/(b*x^2 - a)","A",0
598,1,51,0,0.665678," ","integrate((b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-b x^{2} + a} {\left(x^{3} + x\right)} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{b x^{4} - {\left(a + b\right)} x^{2} + a}\right)"," ",0,"-arctan(sqrt(-b*x^2 + a)*(x^3 + x)*sqrt((b*x^2 - a)/x^2)/(b*x^4 - (a + b)*x^2 + a))","B",0
599,1,41,0,0.559008," ","integrate((b-a/x^2)^(1/2)/x/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{2} + a} {\left(x - 1\right)} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{b x^{2} - a}"," ",0,"-sqrt(-b*x^2 + a)*(x - 1)*sqrt((b*x^2 - a)/x^2)/(b*x^2 - a)","A",0
600,1,44,0,0.854875," ","integrate((b-a/x^2)^(1/2)/x^2/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{2} + a} {\left(x^{2} - 1\right)} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{2 \, {\left(b x^{3} - a x\right)}}"," ",0,"-1/2*sqrt(-b*x^2 + a)*(x^2 - 1)*sqrt((b*x^2 - a)/x^2)/(b*x^3 - a*x)","A",0
601,0,0,0,0.771512," ","integrate((d*x+c)^(3/2)/(a+b/x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c x^{2}\right)} \sqrt{d x + c} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}, x\right)"," ",0,"integral((d*x^3 + c*x^2)*sqrt(d*x + c)*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b), x)","F",0
602,1,11,0,0.650823," ","integrate((x^3-1)/(x^4-4*x)^(2/3),x, algorithm=""fricas"")","\frac{3}{4} \, {\left(x^{4} - 4 \, x\right)}^{\frac{1}{3}}"," ",0,"3/4*(x^4 - 4*x)^(1/3)","A",0
603,1,20,0,0.617576," ","integrate((-x^2+2)*(-x^3+6*x)^(1/4),x, algorithm=""fricas"")","-\frac{4}{15} \, {\left(x^{3} - 6 \, x\right)} {\left(-x^{3} + 6 \, x\right)}^{\frac{1}{4}}"," ",0,"-4/15*(x^3 - 6*x)*(-x^3 + 6*x)^(1/4)","A",0
604,1,11,0,0.462510," ","integrate((x^4+1)*(x^5+5*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(x^{5} + 5 \, x\right)}^{\frac{3}{2}}"," ",0,"2/15*(x^5 + 5*x)^(3/2)","A",0
605,1,11,0,0.692120," ","integrate((5*x^4+2)*(x^5+2*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x^{5} + 2 \, x\right)}^{\frac{3}{2}}"," ",0,"2/3*(x^5 + 2*x)^(3/2)","A",0
606,1,11,0,0.692245," ","integrate((3*x^2+x)/(2*x^3+x^2)^(1/2),x, algorithm=""fricas"")","\sqrt{2 \, x^{3} + x^{2}}"," ",0,"sqrt(2*x^3 + x^2)","A",0
607,1,32,0,0.518972," ","integrate((2+(1-5*x)^(1/3))/(3+(1-5*x)^(1/3)),x, algorithm=""fricas"")","x + \frac{3}{10} \, {\left(-5 \, x + 1\right)}^{\frac{2}{3}} - \frac{9}{5} \, {\left(-5 \, x + 1\right)}^{\frac{1}{3}} + \frac{27}{5} \, \log\left({\left(-5 \, x + 1\right)}^{\frac{1}{3}} + 3\right)"," ",0,"x + 3/10*(-5*x + 1)^(2/3) - 9/5*(-5*x + 1)^(1/3) + 27/5*log((-5*x + 1)^(1/3) + 3)","A",0
608,1,15,0,0.581746," ","integrate((1+x^(1/2))/(-1+x^(1/2)),x, algorithm=""fricas"")","x + 4 \, \sqrt{x} + 4 \, \log\left(\sqrt{x} - 1\right)"," ",0,"x + 4*sqrt(x) + 4*log(sqrt(x) - 1)","A",0
609,1,25,0,0.701604," ","integrate((1-(2+3*x)^(1/2))/(1+(2+3*x)^(1/2)),x, algorithm=""fricas"")","-x + \frac{4}{3} \, \sqrt{3 \, x + 2} - \frac{4}{3} \, \log\left(\sqrt{3 \, x + 2} + 1\right)"," ",0,"-x + 4/3*sqrt(3*x + 2) - 4/3*log(sqrt(3*x + 2) + 1)","A",0
610,1,29,0,0.597903," ","integrate((-1+(b*x+a)^(1/2))/(1+(b*x+a)^(1/2)),x, algorithm=""fricas"")","\frac{b x - 4 \, \sqrt{b x + a} + 4 \, \log\left(\sqrt{b x + a} + 1\right)}{b}"," ",0,"(b*x - 4*sqrt(b*x + a) + 4*log(sqrt(b*x + a) + 1))/b","A",0
611,1,10,0,0.692002," ","integrate((a+b*n*x^(-1+n))/(a*x+b*x^n),x, algorithm=""fricas"")","\log\left(a x + b x^{n}\right)"," ",0,"log(a*x + b*x^n)","A",0
612,1,10,0,0.711297," ","integrate((a+b*n*x^(-1+n))/(x^n)/(b+a*x^(1-n)),x, algorithm=""fricas"")","\log\left(a x + b x^{n}\right)"," ",0,"log(a*x + b*x^n)","A",0
613,-1,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(2*a*d+(a*e*n+b*d*m+3*a*e+3*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+4*a*f+4*b*e+4*c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+5*a*g+5*b*f+5*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+6*b*g+6*c*f)*x^4+c*g*(7+2*m+3*n)*x^5),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(a*d+(a*e*n+b*d*m+2*a*e+2*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+3*a*f+3*b*e+3*c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+4*a*g+4*b*f+4*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+5*b*g+5*c*f)*x^4+c*g*(6+2*m+3*n)*x^5),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(b*d+a*e+b*d*m+a*e*n+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+2*a*f+2*b*e+2*c*d)*x+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+3*a*g+3*b*f+3*c*e)*x^2+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+4*b*g+4*c*f)*x^3+c*g*(5+2*m+3*n)*x^4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-a*d+(a*e*n+b*d*m)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+a*f+b*e+c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+2*a*g+2*b*f+2*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+3*b*g+3*c*f)*x^4+c*g*(4+2*m+3*n)*x^5)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x^4+c*g*(3+2*m+3*n)*x^5)/x^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,1,94,0,1.140937," ","integrate(x^3*(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{252 \, b^{2} d^{5} x^{5} + 315 \, {\left(b^{2} c + a^{2}\right)} d^{4} x^{4} + 16 \, {\left(35 \, a b d^{4} x^{4} + 5 \, a b c d^{3} x^{3} - 6 \, a b c^{2} d^{2} x^{2} + 8 \, a b c^{3} d x - 16 \, a b c^{4}\right)} \sqrt{d x + c}}{1260 \, d^{4}}"," ",0,"1/1260*(252*b^2*d^5*x^5 + 315*(b^2*c + a^2)*d^4*x^4 + 16*(35*a*b*d^4*x^4 + 5*a*b*c*d^3*x^3 - 6*a*b*c^2*d^2*x^2 + 8*a*b*c^3*d*x - 16*a*b*c^4)*sqrt(d*x + c))/d^4","A",0
619,1,81,0,1.213069," ","integrate(x^2*(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{105 \, b^{2} d^{4} x^{4} + 140 \, {\left(b^{2} c + a^{2}\right)} d^{3} x^{3} + 16 \, {\left(15 \, a b d^{3} x^{3} + 3 \, a b c d^{2} x^{2} - 4 \, a b c^{2} d x + 8 \, a b c^{3}\right)} \sqrt{d x + c}}{420 \, d^{3}}"," ",0,"1/420*(105*b^2*d^4*x^4 + 140*(b^2*c + a^2)*d^3*x^3 + 16*(15*a*b*d^3*x^3 + 3*a*b*c*d^2*x^2 - 4*a*b*c^2*d*x + 8*a*b*c^3)*sqrt(d*x + c))/d^3","A",0
620,1,67,0,1.255987," ","integrate(x*(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{10 \, b^{2} d^{3} x^{3} + 15 \, {\left(b^{2} c + a^{2}\right)} d^{2} x^{2} + 8 \, {\left(3 \, a b d^{2} x^{2} + a b c d x - 2 \, a b c^{2}\right)} \sqrt{d x + c}}{30 \, d^{2}}"," ",0,"1/30*(10*b^2*d^3*x^3 + 15*(b^2*c + a^2)*d^2*x^2 + 8*(3*a*b*d^2*x^2 + a*b*c*d*x - 2*a*b*c^2)*sqrt(d*x + c))/d^2","A",0
621,1,49,0,0.754666," ","integrate((a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{2} x^{2} + 6 \, {\left(b^{2} c + a^{2}\right)} d x + 8 \, {\left(a b d x + a b c\right)} \sqrt{d x + c}}{6 \, d}"," ",0,"1/6*(3*b^2*d^2*x^2 + 6*(b^2*c + a^2)*d*x + 8*(a*b*d*x + a*b*c)*sqrt(d*x + c))/d","A",0
622,1,118,0,1.003157," ","integrate((a+b*(d*x+c)^(1/2))^2/x,x, algorithm=""fricas"")","\left[b^{2} d x + 2 \, a b \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 4 \, \sqrt{d x + c} a b + {\left(b^{2} c + a^{2}\right)} \log\left(x\right), b^{2} d x + 4 \, a b \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 4 \, \sqrt{d x + c} a b + {\left(b^{2} c + a^{2}\right)} \log\left(x\right)\right]"," ",0,"[b^2*d*x + 2*a*b*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 4*sqrt(d*x + c)*a*b + (b^2*c + a^2)*log(x), b^2*d*x + 4*a*b*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 4*sqrt(d*x + c)*a*b + (b^2*c + a^2)*log(x)]","A",0
623,1,147,0,0.999502," ","integrate((a+b*(d*x+c)^(1/2))^2/x^2,x, algorithm=""fricas"")","\left[\frac{b^{2} c d x \log\left(x\right) + a b \sqrt{c} d x \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - b^{2} c^{2} - 2 \, \sqrt{d x + c} a b c - a^{2} c}{c x}, \frac{b^{2} c d x \log\left(x\right) + 2 \, a b \sqrt{-c} d x \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - b^{2} c^{2} - 2 \, \sqrt{d x + c} a b c - a^{2} c}{c x}\right]"," ",0,"[(b^2*c*d*x*log(x) + a*b*sqrt(c)*d*x*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - b^2*c^2 - 2*sqrt(d*x + c)*a*b*c - a^2*c)/(c*x), (b^2*c*d*x*log(x) + 2*a*b*sqrt(-c)*d*x*arctan(sqrt(d*x + c)*sqrt(-c)/c) - b^2*c^2 - 2*sqrt(d*x + c)*a*b*c - a^2*c)/(c*x)]","A",0
624,1,181,0,0.853657," ","integrate((a+b*(d*x+c)^(1/2))^2/x^3,x, algorithm=""fricas"")","\left[\frac{a b \sqrt{c} d^{2} x^{2} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 4 \, b^{2} c^{2} d x - 2 \, b^{2} c^{3} - 2 \, a^{2} c^{2} - 2 \, {\left(a b c d x + 2 \, a b c^{2}\right)} \sqrt{d x + c}}{4 \, c^{2} x^{2}}, -\frac{a b \sqrt{-c} d^{2} x^{2} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 2 \, b^{2} c^{2} d x + b^{2} c^{3} + a^{2} c^{2} + {\left(a b c d x + 2 \, a b c^{2}\right)} \sqrt{d x + c}}{2 \, c^{2} x^{2}}\right]"," ",0,"[1/4*(a*b*sqrt(c)*d^2*x^2*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 4*b^2*c^2*d*x - 2*b^2*c^3 - 2*a^2*c^2 - 2*(a*b*c*d*x + 2*a*b*c^2)*sqrt(d*x + c))/(c^2*x^2), -1/2*(a*b*sqrt(-c)*d^2*x^2*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 2*b^2*c^2*d*x + b^2*c^3 + a^2*c^2 + (a*b*c*d*x + 2*a*b*c^2)*sqrt(d*x + c))/(c^2*x^2)]","A",0
625,1,286,0,1.164136," ","integrate(x^3*(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(45045 \, b^{8} d^{4} x^{4} - 29568 \, b^{8} c^{4} + 72960 \, a^{2} b^{6} c^{3} - 96128 \, a^{4} b^{4} c^{2} + 59904 \, a^{6} b^{2} c - 14336 \, a^{8} + 231 \, {\left(15 \, b^{8} c - 14 \, a^{2} b^{6}\right)} d^{3} x^{3} - 28 \, {\left(165 \, b^{8} c^{2} - 291 \, a^{2} b^{6} c + 140 \, a^{4} b^{4}\right)} d^{2} x^{2} + 32 \, {\left(231 \, b^{8} c^{3} - 555 \, a^{2} b^{6} c^{2} + 520 \, a^{4} b^{4} c - 168 \, a^{6} b^{2}\right)} d x + {\left(3003 \, a b^{7} d^{3} x^{3} - 27648 \, a b^{7} c^{3} + 41472 \, a^{3} b^{5} c^{2} - 28160 \, a^{5} b^{3} c + 7168 \, a^{7} b - 3528 \, {\left(2 \, a b^{7} c - a^{3} b^{5}\right)} d^{2} x^{2} + 32 \, {\left(417 \, a b^{7} c^{2} - 417 \, a^{3} b^{5} c + 140 \, a^{5} b^{3}\right)} d x\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{765765 \, b^{8} d^{4}}"," ",0,"4/765765*(45045*b^8*d^4*x^4 - 29568*b^8*c^4 + 72960*a^2*b^6*c^3 - 96128*a^4*b^4*c^2 + 59904*a^6*b^2*c - 14336*a^8 + 231*(15*b^8*c - 14*a^2*b^6)*d^3*x^3 - 28*(165*b^8*c^2 - 291*a^2*b^6*c + 140*a^4*b^4)*d^2*x^2 + 32*(231*b^8*c^3 - 555*a^2*b^6*c^2 + 520*a^4*b^4*c - 168*a^6*b^2)*d*x + (3003*a*b^7*d^3*x^3 - 27648*a*b^7*c^3 + 41472*a^3*b^5*c^2 - 28160*a^5*b^3*c + 7168*a^7*b - 3528*(2*a*b^7*c - a^3*b^5)*d^2*x^2 + 32*(417*a*b^7*c^2 - 417*a^3*b^5*c + 140*a^5*b^3)*d*x)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a)/(b^8*d^4)","A",0
626,1,184,0,1.014063," ","integrate(x^2*(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3465 \, b^{6} d^{3} x^{3} + 2464 \, b^{6} c^{3} - 4640 \, a^{2} b^{4} c^{2} + 4096 \, a^{4} b^{2} c - 1280 \, a^{6} + 35 \, {\left(11 \, b^{6} c - 10 \, a^{2} b^{4}\right)} d^{2} x^{2} - 8 \, {\left(77 \, b^{6} c^{2} - 127 \, a^{2} b^{4} c + 60 \, a^{4} b^{2}\right)} d x + {\left(315 \, a b^{5} d^{2} x^{2} + 1888 \, a b^{5} c^{2} - 1888 \, a^{3} b^{3} c + 640 \, a^{5} b - 400 \, {\left(2 \, a b^{5} c - a^{3} b^{3}\right)} d x\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{45045 \, b^{6} d^{3}}"," ",0,"4/45045*(3465*b^6*d^3*x^3 + 2464*b^6*c^3 - 4640*a^2*b^4*c^2 + 4096*a^4*b^2*c - 1280*a^6 + 35*(11*b^6*c - 10*a^2*b^4)*d^2*x^2 - 8*(77*b^6*c^2 - 127*a^2*b^4*c + 60*a^4*b^2)*d*x + (315*a*b^5*d^2*x^2 + 1888*a*b^5*c^2 - 1888*a^3*b^3*c + 640*a^5*b - 400*(2*a*b^5*c - a^3*b^3)*d*x)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a)/(b^6*d^3)","A",0
627,1,103,0,0.912248," ","integrate(x*(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(35 \, b^{4} d^{2} x^{2} - 28 \, b^{4} c^{2} + 36 \, a^{2} b^{2} c - 16 \, a^{4} + {\left(7 \, b^{4} c - 6 \, a^{2} b^{2}\right)} d x + {\left(5 \, a b^{3} d x - 16 \, a b^{3} c + 8 \, a^{3} b\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{315 \, b^{4} d^{2}}"," ",0,"4/315*(35*b^4*d^2*x^2 - 28*b^4*c^2 + 36*a^2*b^2*c - 16*a^4 + (7*b^4*c - 6*a^2*b^2)*d*x + (5*a*b^3*d*x - 16*a*b^3*c + 8*a^3*b)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a)/(b^4*d^2)","A",0
628,1,50,0,1.017017," ","integrate((a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, b^{2} d x + 3 \, b^{2} c + \sqrt{d x + c} a b - 2 \, a^{2}\right)} \sqrt{\sqrt{d x + c} b + a}}{15 \, b^{2} d}"," ",0,"4/15*(3*b^2*d*x + 3*b^2*c + sqrt(d*x + c)*a*b - 2*a^2)*sqrt(sqrt(d*x + c)*b + a)/(b^2*d)","A",0
629,1,194,0,0.956772," ","integrate((a+b*(d*x+c)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","-\sqrt{a + \sqrt{b^{2} c}} \log\left(2 \, \sqrt{\sqrt{d x + c} b + a} + 2 \, \sqrt{a + \sqrt{b^{2} c}}\right) + \sqrt{a + \sqrt{b^{2} c}} \log\left(2 \, \sqrt{\sqrt{d x + c} b + a} - 2 \, \sqrt{a + \sqrt{b^{2} c}}\right) - \sqrt{a - \sqrt{b^{2} c}} \log\left(2 \, \sqrt{\sqrt{d x + c} b + a} + 2 \, \sqrt{a - \sqrt{b^{2} c}}\right) + \sqrt{a - \sqrt{b^{2} c}} \log\left(2 \, \sqrt{\sqrt{d x + c} b + a} - 2 \, \sqrt{a - \sqrt{b^{2} c}}\right) + 4 \, \sqrt{\sqrt{d x + c} b + a}"," ",0,"-sqrt(a + sqrt(b^2*c))*log(2*sqrt(sqrt(d*x + c)*b + a) + 2*sqrt(a + sqrt(b^2*c))) + sqrt(a + sqrt(b^2*c))*log(2*sqrt(sqrt(d*x + c)*b + a) - 2*sqrt(a + sqrt(b^2*c))) - sqrt(a - sqrt(b^2*c))*log(2*sqrt(sqrt(d*x + c)*b + a) + 2*sqrt(a - sqrt(b^2*c))) + sqrt(a - sqrt(b^2*c))*log(2*sqrt(sqrt(d*x + c)*b + a) - 2*sqrt(a - sqrt(b^2*c))) + 4*sqrt(sqrt(d*x + c)*b + a)","B",0
630,1,1003,0,1.076987," ","integrate((a+b*(d*x+c)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{x \sqrt{-\frac{a b^{2} d^{2} + \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}} \log\left(\sqrt{\sqrt{d x + c} b + a} b^{4} d^{3} + {\left(b^{4} c d^{2} - \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(a b^{2} c^{2} - a^{3} c\right)}\right)} \sqrt{-\frac{a b^{2} d^{2} + \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}}\right) - x \sqrt{-\frac{a b^{2} d^{2} + \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}} \log\left(\sqrt{\sqrt{d x + c} b + a} b^{4} d^{3} - {\left(b^{4} c d^{2} - \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(a b^{2} c^{2} - a^{3} c\right)}\right)} \sqrt{-\frac{a b^{2} d^{2} + \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}}\right) + x \sqrt{-\frac{a b^{2} d^{2} - \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}} \log\left(\sqrt{\sqrt{d x + c} b + a} b^{4} d^{3} + {\left(b^{4} c d^{2} + \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(a b^{2} c^{2} - a^{3} c\right)}\right)} \sqrt{-\frac{a b^{2} d^{2} - \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}}\right) - x \sqrt{-\frac{a b^{2} d^{2} - \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}} \log\left(\sqrt{\sqrt{d x + c} b + a} b^{4} d^{3} - {\left(b^{4} c d^{2} + \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(a b^{2} c^{2} - a^{3} c\right)}\right)} \sqrt{-\frac{a b^{2} d^{2} - \sqrt{\frac{b^{6} d^{4}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}} {\left(b^{2} c^{2} - a^{2} c\right)}}{b^{2} c^{2} - a^{2} c}}\right) + 4 \, \sqrt{\sqrt{d x + c} b + a}}{4 \, x}"," ",0,"-1/4*(x*sqrt(-(a*b^2*d^2 + sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))*log(sqrt(sqrt(d*x + c)*b + a)*b^4*d^3 + (b^4*c*d^2 - sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(a*b^2*c^2 - a^3*c))*sqrt(-(a*b^2*d^2 + sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))) - x*sqrt(-(a*b^2*d^2 + sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))*log(sqrt(sqrt(d*x + c)*b + a)*b^4*d^3 - (b^4*c*d^2 - sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(a*b^2*c^2 - a^3*c))*sqrt(-(a*b^2*d^2 + sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))) + x*sqrt(-(a*b^2*d^2 - sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))*log(sqrt(sqrt(d*x + c)*b + a)*b^4*d^3 + (b^4*c*d^2 + sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(a*b^2*c^2 - a^3*c))*sqrt(-(a*b^2*d^2 - sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))) - x*sqrt(-(a*b^2*d^2 - sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))*log(sqrt(sqrt(d*x + c)*b + a)*b^4*d^3 - (b^4*c*d^2 + sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(a*b^2*c^2 - a^3*c))*sqrt(-(a*b^2*d^2 - sqrt(b^6*d^4/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c))*(b^2*c^2 - a^2*c))/(b^2*c^2 - a^2*c))) + 4*sqrt(sqrt(d*x + c)*b + a))/x","B",0
631,1,2856,0,1.314122," ","integrate((a+b*(d*x+c)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","\frac{{\left(b^{2} c^{2} - a^{2} c\right)} x^{2} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} + {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}} \log\left({\left(81 \, b^{10} c^{2} - 81 \, a^{2} b^{8} c + 20 \, a^{4} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} + {\left({\left(27 \, b^{10} c^{4} - 24 \, a^{2} b^{8} c^{3} + 5 \, a^{4} b^{6} c^{2}\right)} d^{4} - 2 \, {\left(2 \, a b^{8} c^{7} - 7 \, a^{3} b^{6} c^{6} + 9 \, a^{5} b^{4} c^{5} - 5 \, a^{7} b^{2} c^{4} + a^{9} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}\right)} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} + {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}}\right) - {\left(b^{2} c^{2} - a^{2} c\right)} x^{2} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} + {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}} \log\left({\left(81 \, b^{10} c^{2} - 81 \, a^{2} b^{8} c + 20 \, a^{4} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} - {\left({\left(27 \, b^{10} c^{4} - 24 \, a^{2} b^{8} c^{3} + 5 \, a^{4} b^{6} c^{2}\right)} d^{4} - 2 \, {\left(2 \, a b^{8} c^{7} - 7 \, a^{3} b^{6} c^{6} + 9 \, a^{5} b^{4} c^{5} - 5 \, a^{7} b^{2} c^{4} + a^{9} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}\right)} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} + {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}}\right) + {\left(b^{2} c^{2} - a^{2} c\right)} x^{2} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} - {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}} \log\left({\left(81 \, b^{10} c^{2} - 81 \, a^{2} b^{8} c + 20 \, a^{4} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} + {\left({\left(27 \, b^{10} c^{4} - 24 \, a^{2} b^{8} c^{3} + 5 \, a^{4} b^{6} c^{2}\right)} d^{4} + 2 \, {\left(2 \, a b^{8} c^{7} - 7 \, a^{3} b^{6} c^{6} + 9 \, a^{5} b^{4} c^{5} - 5 \, a^{7} b^{2} c^{4} + a^{9} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}\right)} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} - {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}}\right) - {\left(b^{2} c^{2} - a^{2} c\right)} x^{2} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} - {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}} \log\left({\left(81 \, b^{10} c^{2} - 81 \, a^{2} b^{8} c + 20 \, a^{4} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} - {\left({\left(27 \, b^{10} c^{4} - 24 \, a^{2} b^{8} c^{3} + 5 \, a^{4} b^{6} c^{2}\right)} d^{4} + 2 \, {\left(2 \, a b^{8} c^{7} - 7 \, a^{3} b^{6} c^{6} + 9 \, a^{5} b^{4} c^{5} - 5 \, a^{7} b^{2} c^{4} + a^{9} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}\right)} \sqrt{-\frac{{\left(15 \, a b^{6} c^{2} - 15 \, a^{3} b^{4} c + 4 \, a^{5} b^{2}\right)} d^{4} - {\left(b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}\right)} \sqrt{\frac{{\left(81 \, b^{14} c^{2} - 90 \, a^{2} b^{12} c + 25 \, a^{4} b^{10}\right)} d^{8}}{b^{12} c^{9} - 6 \, a^{2} b^{10} c^{8} + 15 \, a^{4} b^{8} c^{7} - 20 \, a^{6} b^{6} c^{6} + 15 \, a^{8} b^{4} c^{5} - 6 \, a^{10} b^{2} c^{4} + a^{12} c^{3}}}}{b^{6} c^{6} - 3 \, a^{2} b^{4} c^{5} + 3 \, a^{4} b^{2} c^{4} - a^{6} c^{3}}}\right) - 4 \, {\left(b^{2} c d x - \sqrt{d x + c} a b d x + 4 \, b^{2} c^{2} - 4 \, a^{2} c\right)} \sqrt{\sqrt{d x + c} b + a}}{32 \, {\left(b^{2} c^{2} - a^{2} c\right)} x^{2}}"," ",0,"1/32*((b^2*c^2 - a^2*c)*x^2*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 + (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))*log((81*b^10*c^2 - 81*a^2*b^8*c + 20*a^4*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 + ((27*b^10*c^4 - 24*a^2*b^8*c^3 + 5*a^4*b^6*c^2)*d^4 - 2*(2*a*b^8*c^7 - 7*a^3*b^6*c^6 + 9*a^5*b^4*c^5 - 5*a^7*b^2*c^4 + a^9*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 + (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))) - (b^2*c^2 - a^2*c)*x^2*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 + (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))*log((81*b^10*c^2 - 81*a^2*b^8*c + 20*a^4*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 - ((27*b^10*c^4 - 24*a^2*b^8*c^3 + 5*a^4*b^6*c^2)*d^4 - 2*(2*a*b^8*c^7 - 7*a^3*b^6*c^6 + 9*a^5*b^4*c^5 - 5*a^7*b^2*c^4 + a^9*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 + (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))) + (b^2*c^2 - a^2*c)*x^2*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 - (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))*log((81*b^10*c^2 - 81*a^2*b^8*c + 20*a^4*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 + ((27*b^10*c^4 - 24*a^2*b^8*c^3 + 5*a^4*b^6*c^2)*d^4 + 2*(2*a*b^8*c^7 - 7*a^3*b^6*c^6 + 9*a^5*b^4*c^5 - 5*a^7*b^2*c^4 + a^9*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 - (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))) - (b^2*c^2 - a^2*c)*x^2*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 - (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))*log((81*b^10*c^2 - 81*a^2*b^8*c + 20*a^4*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 - ((27*b^10*c^4 - 24*a^2*b^8*c^3 + 5*a^4*b^6*c^2)*d^4 + 2*(2*a*b^8*c^7 - 7*a^3*b^6*c^6 + 9*a^5*b^4*c^5 - 5*a^7*b^2*c^4 + a^9*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))*sqrt(-((15*a*b^6*c^2 - 15*a^3*b^4*c + 4*a^5*b^2)*d^4 - (b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3)*sqrt((81*b^14*c^2 - 90*a^2*b^12*c + 25*a^4*b^10)*d^8/(b^12*c^9 - 6*a^2*b^10*c^8 + 15*a^4*b^8*c^7 - 20*a^6*b^6*c^6 + 15*a^8*b^4*c^5 - 6*a^10*b^2*c^4 + a^12*c^3)))/(b^6*c^6 - 3*a^2*b^4*c^5 + 3*a^4*b^2*c^4 - a^6*c^3))) - 4*(b^2*c*d*x - sqrt(d*x + c)*a*b*d*x + 4*b^2*c^2 - 4*a^2*c)*sqrt(sqrt(d*x + c)*b + a))/((b^2*c^2 - a^2*c)*x^2)","B",0
632,1,228,0,0.869668," ","integrate(x^3/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{70 \, a b^{6} d^{3} x^{3} - 105 \, {\left(a b^{6} c - a^{3} b^{4}\right)} d^{2} x^{2} + 210 \, {\left(a b^{6} c^{2} - 2 \, a^{3} b^{4} c + a^{5} b^{2}\right)} d x - 420 \, {\left(a b^{6} c^{3} - 3 \, a^{3} b^{4} c^{2} + 3 \, a^{5} b^{2} c - a^{7}\right)} \log\left(\sqrt{d x + c} b + a\right) - 4 \, {\left(15 \, b^{7} d^{3} x^{3} - 48 \, b^{7} c^{3} + 231 \, a^{2} b^{5} c^{2} - 280 \, a^{4} b^{3} c + 105 \, a^{6} b - 3 \, {\left(6 \, b^{7} c - 7 \, a^{2} b^{5}\right)} d^{2} x^{2} + {\left(24 \, b^{7} c^{2} - 63 \, a^{2} b^{5} c + 35 \, a^{4} b^{3}\right)} d x\right)} \sqrt{d x + c}}{210 \, b^{8} d^{4}}"," ",0,"-1/210*(70*a*b^6*d^3*x^3 - 105*(a*b^6*c - a^3*b^4)*d^2*x^2 + 210*(a*b^6*c^2 - 2*a^3*b^4*c + a^5*b^2)*d*x - 420*(a*b^6*c^3 - 3*a^3*b^4*c^2 + 3*a^5*b^2*c - a^7)*log(sqrt(d*x + c)*b + a) - 4*(15*b^7*d^3*x^3 - 48*b^7*c^3 + 231*a^2*b^5*c^2 - 280*a^4*b^3*c + 105*a^6*b - 3*(6*b^7*c - 7*a^2*b^5)*d^2*x^2 + (24*b^7*c^2 - 63*a^2*b^5*c + 35*a^4*b^3)*d*x)*sqrt(d*x + c))/(b^8*d^4)","A",0
633,1,138,0,0.833619," ","integrate(x^2/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{15 \, a b^{4} d^{2} x^{2} - 30 \, {\left(a b^{4} c - a^{3} b^{2}\right)} d x + 60 \, {\left(a b^{4} c^{2} - 2 \, a^{3} b^{2} c + a^{5}\right)} \log\left(\sqrt{d x + c} b + a\right) - 4 \, {\left(3 \, b^{5} d^{2} x^{2} + 8 \, b^{5} c^{2} - 25 \, a^{2} b^{3} c + 15 \, a^{4} b - {\left(4 \, b^{5} c - 5 \, a^{2} b^{3}\right)} d x\right)} \sqrt{d x + c}}{30 \, b^{6} d^{3}}"," ",0,"-1/30*(15*a*b^4*d^2*x^2 - 30*(a*b^4*c - a^3*b^2)*d*x + 60*(a*b^4*c^2 - 2*a^3*b^2*c + a^5)*log(sqrt(d*x + c)*b + a) - 4*(3*b^5*d^2*x^2 + 8*b^5*c^2 - 25*a^2*b^3*c + 15*a^4*b - (4*b^5*c - 5*a^2*b^3)*d*x)*sqrt(d*x + c))/(b^6*d^3)","A",0
634,1,71,0,0.922216," ","integrate(x/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{3 \, a b^{2} d x - 6 \, {\left(a b^{2} c - a^{3}\right)} \log\left(\sqrt{d x + c} b + a\right) - 2 \, {\left(b^{3} d x - 2 \, b^{3} c + 3 \, a^{2} b\right)} \sqrt{d x + c}}{3 \, b^{4} d^{2}}"," ",0,"-1/3*(3*a*b^2*d*x - 6*(a*b^2*c - a^3)*log(sqrt(d*x + c)*b + a) - 2*(b^3*d*x - 2*b^3*c + 3*a^2*b)*sqrt(d*x + c))/(b^4*d^2)","A",0
635,1,33,0,0.811597," ","integrate(1/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a \log\left(\sqrt{d x + c} b + a\right) - \sqrt{d x + c} b\right)}}{b^{2} d}"," ",0,"-2*(a*log(sqrt(d*x + c)*b + a) - sqrt(d*x + c)*b)/(b^2*d)","A",0
636,1,125,0,0.649879," ","integrate(1/x/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, a \log\left(\sqrt{d x + c} b + a\right) - a \log\left(x\right)}{b^{2} c - a^{2}}, \frac{2 \, b \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 2 \, a \log\left(\sqrt{d x + c} b + a\right) - a \log\left(x\right)}{b^{2} c - a^{2}}\right]"," ",0,"[(b*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*a*log(sqrt(d*x + c)*b + a) - a*log(x))/(b^2*c - a^2), (2*b*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 2*a*log(sqrt(d*x + c)*b + a) - a*log(x))/(b^2*c - a^2)]","A",0
637,1,283,0,0.857388," ","integrate(1/x^2/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","\left[-\frac{4 \, a b^{2} c d x \log\left(\sqrt{d x + c} b + a\right) - 2 \, a b^{2} c d x \log\left(x\right) - 2 \, a b^{2} c^{2} - {\left(b^{3} c + a^{2} b\right)} \sqrt{c} d x \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, a^{3} c + 2 \, {\left(b^{3} c^{2} - a^{2} b c\right)} \sqrt{d x + c}}{2 \, {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x}, -\frac{2 \, a b^{2} c d x \log\left(\sqrt{d x + c} b + a\right) - a b^{2} c d x \log\left(x\right) - a b^{2} c^{2} + {\left(b^{3} c + a^{2} b\right)} \sqrt{-c} d x \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + a^{3} c + {\left(b^{3} c^{2} - a^{2} b c\right)} \sqrt{d x + c}}{{\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x}\right]"," ",0,"[-1/2*(4*a*b^2*c*d*x*log(sqrt(d*x + c)*b + a) - 2*a*b^2*c*d*x*log(x) - 2*a*b^2*c^2 - (b^3*c + a^2*b)*sqrt(c)*d*x*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*a^3*c + 2*(b^3*c^2 - a^2*b*c)*sqrt(d*x + c))/((b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x), -(2*a*b^2*c*d*x*log(sqrt(d*x + c)*b + a) - a*b^2*c*d*x*log(x) - a*b^2*c^2 + (b^3*c + a^2*b)*sqrt(-c)*d*x*arctan(sqrt(d*x + c)*sqrt(-c)/c) + a^3*c + (b^3*c^2 - a^2*b*c)*sqrt(d*x + c))/((b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x)]","A",0
638,1,534,0,2.148301," ","integrate(1/x^3/(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","\left[\frac{16 \, a b^{4} c^{2} d^{2} x^{2} \log\left(\sqrt{d x + c} b + a\right) - 8 \, a b^{4} c^{2} d^{2} x^{2} \log\left(x\right) + 4 \, a b^{4} c^{4} - 8 \, a^{3} b^{2} c^{3} + 4 \, a^{5} c^{2} + {\left(3 \, b^{5} c^{2} + 6 \, a^{2} b^{3} c - a^{4} b\right)} \sqrt{c} d^{2} x^{2} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 8 \, {\left(a b^{4} c^{3} - a^{3} b^{2} c^{2}\right)} d x - 2 \, {\left(2 \, b^{5} c^{4} - 4 \, a^{2} b^{3} c^{3} + 2 \, a^{4} b c^{2} - {\left(3 \, b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} - a^{4} b c\right)} d x\right)} \sqrt{d x + c}}{8 \, {\left(b^{6} c^{5} - 3 \, a^{2} b^{4} c^{4} + 3 \, a^{4} b^{2} c^{3} - a^{6} c^{2}\right)} x^{2}}, \frac{8 \, a b^{4} c^{2} d^{2} x^{2} \log\left(\sqrt{d x + c} b + a\right) - 4 \, a b^{4} c^{2} d^{2} x^{2} \log\left(x\right) + 2 \, a b^{4} c^{4} - 4 \, a^{3} b^{2} c^{3} + 2 \, a^{5} c^{2} + {\left(3 \, b^{5} c^{2} + 6 \, a^{2} b^{3} c - a^{4} b\right)} \sqrt{-c} d^{2} x^{2} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - 4 \, {\left(a b^{4} c^{3} - a^{3} b^{2} c^{2}\right)} d x - {\left(2 \, b^{5} c^{4} - 4 \, a^{2} b^{3} c^{3} + 2 \, a^{4} b c^{2} - {\left(3 \, b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} - a^{4} b c\right)} d x\right)} \sqrt{d x + c}}{4 \, {\left(b^{6} c^{5} - 3 \, a^{2} b^{4} c^{4} + 3 \, a^{4} b^{2} c^{3} - a^{6} c^{2}\right)} x^{2}}\right]"," ",0,"[1/8*(16*a*b^4*c^2*d^2*x^2*log(sqrt(d*x + c)*b + a) - 8*a*b^4*c^2*d^2*x^2*log(x) + 4*a*b^4*c^4 - 8*a^3*b^2*c^3 + 4*a^5*c^2 + (3*b^5*c^2 + 6*a^2*b^3*c - a^4*b)*sqrt(c)*d^2*x^2*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 8*(a*b^4*c^3 - a^3*b^2*c^2)*d*x - 2*(2*b^5*c^4 - 4*a^2*b^3*c^3 + 2*a^4*b*c^2 - (3*b^5*c^3 - 2*a^2*b^3*c^2 - a^4*b*c)*d*x)*sqrt(d*x + c))/((b^6*c^5 - 3*a^2*b^4*c^4 + 3*a^4*b^2*c^3 - a^6*c^2)*x^2), 1/4*(8*a*b^4*c^2*d^2*x^2*log(sqrt(d*x + c)*b + a) - 4*a*b^4*c^2*d^2*x^2*log(x) + 2*a*b^4*c^4 - 4*a^3*b^2*c^3 + 2*a^5*c^2 + (3*b^5*c^2 + 6*a^2*b^3*c - a^4*b)*sqrt(-c)*d^2*x^2*arctan(sqrt(d*x + c)*sqrt(-c)/c) - 4*(a*b^4*c^3 - a^3*b^2*c^2)*d*x - (2*b^5*c^4 - 4*a^2*b^3*c^3 + 2*a^4*b*c^2 - (3*b^5*c^3 - 2*a^2*b^3*c^2 - a^4*b*c)*d*x)*sqrt(d*x + c))/((b^6*c^5 - 3*a^2*b^4*c^4 + 3*a^4*b^2*c^3 - a^6*c^2)*x^2)]","A",0
639,1,392,0,0.927053," ","integrate(x^3/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{10 \, b^{8} d^{4} x^{4} + 55 \, b^{8} c^{4} - 220 \, a^{2} b^{6} c^{3} + 195 \, a^{4} b^{4} c^{2} + 30 \, a^{6} b^{2} c - 60 \, a^{8} - 5 \, {\left(b^{8} c - 7 \, a^{2} b^{6}\right)} d^{3} x^{3} + 15 \, {\left(b^{8} c^{2} - 8 \, a^{2} b^{6} c + 7 \, a^{4} b^{4}\right)} d^{2} x^{2} + 5 \, {\left(17 \, b^{8} c^{3} - 87 \, a^{2} b^{6} c^{2} + 96 \, a^{4} b^{4} c - 30 \, a^{6} b^{2}\right)} d x - 60 \, {\left(b^{8} c^{4} - 10 \, a^{2} b^{6} c^{3} + 24 \, a^{4} b^{4} c^{2} - 22 \, a^{6} b^{2} c + 7 \, a^{8} + {\left(b^{8} c^{3} - 9 \, a^{2} b^{6} c^{2} + 15 \, a^{4} b^{4} c - 7 \, a^{6} b^{2}\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) - 4 \, {\left(6 \, a b^{7} d^{3} x^{3} + 81 \, a b^{7} c^{3} - 271 \, a^{3} b^{5} c^{2} + 295 \, a^{5} b^{3} c - 105 \, a^{7} b - 2 \, {\left(6 \, a b^{7} c - 7 \, a^{3} b^{5}\right)} d^{2} x^{2} + 2 \, {\left(24 \, a b^{7} c^{2} - 61 \, a^{3} b^{5} c + 35 \, a^{5} b^{3}\right)} d x\right)} \sqrt{d x + c}}{30 \, {\left(b^{10} d^{5} x + {\left(b^{10} c - a^{2} b^{8}\right)} d^{4}\right)}}"," ",0,"1/30*(10*b^8*d^4*x^4 + 55*b^8*c^4 - 220*a^2*b^6*c^3 + 195*a^4*b^4*c^2 + 30*a^6*b^2*c - 60*a^8 - 5*(b^8*c - 7*a^2*b^6)*d^3*x^3 + 15*(b^8*c^2 - 8*a^2*b^6*c + 7*a^4*b^4)*d^2*x^2 + 5*(17*b^8*c^3 - 87*a^2*b^6*c^2 + 96*a^4*b^4*c - 30*a^6*b^2)*d*x - 60*(b^8*c^4 - 10*a^2*b^6*c^3 + 24*a^4*b^4*c^2 - 22*a^6*b^2*c + 7*a^8 + (b^8*c^3 - 9*a^2*b^6*c^2 + 15*a^4*b^4*c - 7*a^6*b^2)*d*x)*log(sqrt(d*x + c)*b + a) - 4*(6*a*b^7*d^3*x^3 + 81*a*b^7*c^3 - 271*a^3*b^5*c^2 + 295*a^5*b^3*c - 105*a^7*b - 2*(6*a*b^7*c - 7*a^3*b^5)*d^2*x^2 + 2*(24*a*b^7*c^2 - 61*a^3*b^5*c + 35*a^5*b^3)*d*x)*sqrt(d*x + c))/(b^10*d^5*x + (b^10*c - a^2*b^8)*d^4)","A",0
640,1,269,0,0.842817," ","integrate(x^2/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{3 \, b^{6} d^{3} x^{3} - 9 \, b^{6} c^{3} + 15 \, a^{2} b^{4} c^{2} + 6 \, a^{4} b^{2} c - 12 \, a^{6} - 3 \, {\left(b^{6} c - 5 \, a^{2} b^{4}\right)} d^{2} x^{2} - 3 \, {\left(5 \, b^{6} c^{2} - 14 \, a^{2} b^{4} c + 6 \, a^{4} b^{2}\right)} d x + 12 \, {\left(b^{6} c^{3} - 7 \, a^{2} b^{4} c^{2} + 11 \, a^{4} b^{2} c - 5 \, a^{6} + {\left(b^{6} c^{2} - 6 \, a^{2} b^{4} c + 5 \, a^{4} b^{2}\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) - 4 \, {\left(2 \, a b^{5} d^{2} x^{2} - 13 \, a b^{5} c^{2} + 28 \, a^{3} b^{3} c - 15 \, a^{5} b - 2 \, {\left(4 \, a b^{5} c - 5 \, a^{3} b^{3}\right)} d x\right)} \sqrt{d x + c}}{6 \, {\left(b^{8} d^{4} x + {\left(b^{8} c - a^{2} b^{6}\right)} d^{3}\right)}}"," ",0,"1/6*(3*b^6*d^3*x^3 - 9*b^6*c^3 + 15*a^2*b^4*c^2 + 6*a^4*b^2*c - 12*a^6 - 3*(b^6*c - 5*a^2*b^4)*d^2*x^2 - 3*(5*b^6*c^2 - 14*a^2*b^4*c + 6*a^4*b^2)*d*x + 12*(b^6*c^3 - 7*a^2*b^4*c^2 + 11*a^4*b^2*c - 5*a^6 + (b^6*c^2 - 6*a^2*b^4*c + 5*a^4*b^2)*d*x)*log(sqrt(d*x + c)*b + a) - 4*(2*a*b^5*d^2*x^2 - 13*a*b^5*c^2 + 28*a^3*b^3*c - 15*a^5*b - 2*(4*a*b^5*c - 5*a^3*b^3)*d*x)*sqrt(d*x + c))/(b^8*d^4*x + (b^8*c - a^2*b^6)*d^3)","A",0
641,1,163,0,0.964810," ","integrate(x/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{b^{4} d^{2} x^{2} + b^{4} c^{2} + a^{2} b^{2} c - 2 \, a^{4} + {\left(2 \, b^{4} c - a^{2} b^{2}\right)} d x - 2 \, {\left(b^{4} c^{2} - 4 \, a^{2} b^{2} c + 3 \, a^{4} + {\left(b^{4} c - 3 \, a^{2} b^{2}\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) - 2 \, {\left(2 \, a b^{3} d x + 3 \, a b^{3} c - 3 \, a^{3} b\right)} \sqrt{d x + c}}{b^{6} d^{3} x + {\left(b^{6} c - a^{2} b^{4}\right)} d^{2}}"," ",0,"(b^4*d^2*x^2 + b^4*c^2 + a^2*b^2*c - 2*a^4 + (2*b^4*c - a^2*b^2)*d*x - 2*(b^4*c^2 - 4*a^2*b^2*c + 3*a^4 + (b^4*c - 3*a^2*b^2)*d*x)*log(sqrt(d*x + c)*b + a) - 2*(2*a*b^3*d*x + 3*a*b^3*c - 3*a^3*b)*sqrt(d*x + c))/(b^6*d^3*x + (b^6*c - a^2*b^4)*d^2)","A",0
642,1,75,0,0.824593," ","integrate(1/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{d x + c} a b - a^{2} + {\left(b^{2} d x + b^{2} c - a^{2}\right)} \log\left(\sqrt{d x + c} b + a\right)\right)}}{b^{4} d^{2} x + {\left(b^{4} c - a^{2} b^{2}\right)} d}"," ",0,"2*(sqrt(d*x + c)*a*b - a^2 + (b^2*d*x + b^2*c - a^2)*log(sqrt(d*x + c)*b + a))/(b^4*d^2*x + (b^4*c - a^2*b^2)*d)","A",0
643,1,444,0,1.043075," ","integrate(1/x/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b^{2} c - 2 \, a^{4} + 2 \, {\left(a b^{3} d x + a b^{3} c - a^{3} b\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(b^{4} c^{2} - a^{4} + {\left(b^{4} c + a^{2} b^{2}\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) + {\left(b^{4} c^{2} - a^{4} + {\left(b^{4} c + a^{2} b^{2}\right)} d x\right)} \log\left(x\right) - 2 \, {\left(a b^{3} c - a^{3} b\right)} \sqrt{d x + c}}{b^{6} c^{3} - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{4} b^{2} c - a^{6} + {\left(b^{6} c^{2} - 2 \, a^{2} b^{4} c + a^{4} b^{2}\right)} d x}, \frac{2 \, a^{2} b^{2} c - 2 \, a^{4} - 4 \, {\left(a b^{3} d x + a b^{3} c - a^{3} b\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - 2 \, {\left(b^{4} c^{2} - a^{4} + {\left(b^{4} c + a^{2} b^{2}\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) + {\left(b^{4} c^{2} - a^{4} + {\left(b^{4} c + a^{2} b^{2}\right)} d x\right)} \log\left(x\right) - 2 \, {\left(a b^{3} c - a^{3} b\right)} \sqrt{d x + c}}{b^{6} c^{3} - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{4} b^{2} c - a^{6} + {\left(b^{6} c^{2} - 2 \, a^{2} b^{4} c + a^{4} b^{2}\right)} d x}\right]"," ",0,"[(2*a^2*b^2*c - 2*a^4 + 2*(a*b^3*d*x + a*b^3*c - a^3*b)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(b^4*c^2 - a^4 + (b^4*c + a^2*b^2)*d*x)*log(sqrt(d*x + c)*b + a) + (b^4*c^2 - a^4 + (b^4*c + a^2*b^2)*d*x)*log(x) - 2*(a*b^3*c - a^3*b)*sqrt(d*x + c))/(b^6*c^3 - 3*a^2*b^4*c^2 + 3*a^4*b^2*c - a^6 + (b^6*c^2 - 2*a^2*b^4*c + a^4*b^2)*d*x), (2*a^2*b^2*c - 2*a^4 - 4*(a*b^3*d*x + a*b^3*c - a^3*b)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - 2*(b^4*c^2 - a^4 + (b^4*c + a^2*b^2)*d*x)*log(sqrt(d*x + c)*b + a) + (b^4*c^2 - a^4 + (b^4*c + a^2*b^2)*d*x)*log(x) - 2*(a*b^3*c - a^3*b)*sqrt(d*x + c))/(b^6*c^3 - 3*a^2*b^4*c^2 + 3*a^4*b^2*c - a^6 + (b^6*c^2 - 2*a^2*b^4*c + a^4*b^2)*d*x)]","A",0
644,1,854,0,1.630254," ","integrate(1/x^2/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\left[-\frac{b^{6} c^{4} - a^{2} b^{4} c^{3} - a^{4} b^{2} c^{2} + a^{6} c + {\left(b^{6} c^{3} + 2 \, a^{2} b^{4} c^{2} - 3 \, a^{4} b^{2} c\right)} d x - {\left({\left(3 \, a b^{5} c + a^{3} b^{3}\right)} d^{2} x^{2} + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} c - a^{5} b\right)} d x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left({\left(b^{6} c^{2} + 3 \, a^{2} b^{4} c\right)} d^{2} x^{2} + {\left(b^{6} c^{3} + 2 \, a^{2} b^{4} c^{2} - 3 \, a^{4} b^{2} c\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) + {\left({\left(b^{6} c^{2} + 3 \, a^{2} b^{4} c\right)} d^{2} x^{2} + {\left(b^{6} c^{3} + 2 \, a^{2} b^{4} c^{2} - 3 \, a^{4} b^{2} c\right)} d x\right)} \log\left(x\right) - 2 \, {\left(a b^{5} c^{3} - 2 \, a^{3} b^{3} c^{2} + a^{5} b c + 2 \, {\left(a b^{5} c^{2} - a^{3} b^{3} c\right)} d x\right)} \sqrt{d x + c}}{{\left(b^{8} c^{4} - 3 \, a^{2} b^{6} c^{3} + 3 \, a^{4} b^{4} c^{2} - a^{6} b^{2} c\right)} d x^{2} + {\left(b^{8} c^{5} - 4 \, a^{2} b^{6} c^{4} + 6 \, a^{4} b^{4} c^{3} - 4 \, a^{6} b^{2} c^{2} + a^{8} c\right)} x}, -\frac{b^{6} c^{4} - a^{2} b^{4} c^{3} - a^{4} b^{2} c^{2} + a^{6} c + {\left(b^{6} c^{3} + 2 \, a^{2} b^{4} c^{2} - 3 \, a^{4} b^{2} c\right)} d x - 2 \, {\left({\left(3 \, a b^{5} c + a^{3} b^{3}\right)} d^{2} x^{2} + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} c - a^{5} b\right)} d x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - 2 \, {\left({\left(b^{6} c^{2} + 3 \, a^{2} b^{4} c\right)} d^{2} x^{2} + {\left(b^{6} c^{3} + 2 \, a^{2} b^{4} c^{2} - 3 \, a^{4} b^{2} c\right)} d x\right)} \log\left(\sqrt{d x + c} b + a\right) + {\left({\left(b^{6} c^{2} + 3 \, a^{2} b^{4} c\right)} d^{2} x^{2} + {\left(b^{6} c^{3} + 2 \, a^{2} b^{4} c^{2} - 3 \, a^{4} b^{2} c\right)} d x\right)} \log\left(x\right) - 2 \, {\left(a b^{5} c^{3} - 2 \, a^{3} b^{3} c^{2} + a^{5} b c + 2 \, {\left(a b^{5} c^{2} - a^{3} b^{3} c\right)} d x\right)} \sqrt{d x + c}}{{\left(b^{8} c^{4} - 3 \, a^{2} b^{6} c^{3} + 3 \, a^{4} b^{4} c^{2} - a^{6} b^{2} c\right)} d x^{2} + {\left(b^{8} c^{5} - 4 \, a^{2} b^{6} c^{4} + 6 \, a^{4} b^{4} c^{3} - 4 \, a^{6} b^{2} c^{2} + a^{8} c\right)} x}\right]"," ",0,"[-(b^6*c^4 - a^2*b^4*c^3 - a^4*b^2*c^2 + a^6*c + (b^6*c^3 + 2*a^2*b^4*c^2 - 3*a^4*b^2*c)*d*x - ((3*a*b^5*c + a^3*b^3)*d^2*x^2 + (3*a*b^5*c^2 - 2*a^3*b^3*c - a^5*b)*d*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*((b^6*c^2 + 3*a^2*b^4*c)*d^2*x^2 + (b^6*c^3 + 2*a^2*b^4*c^2 - 3*a^4*b^2*c)*d*x)*log(sqrt(d*x + c)*b + a) + ((b^6*c^2 + 3*a^2*b^4*c)*d^2*x^2 + (b^6*c^3 + 2*a^2*b^4*c^2 - 3*a^4*b^2*c)*d*x)*log(x) - 2*(a*b^5*c^3 - 2*a^3*b^3*c^2 + a^5*b*c + 2*(a*b^5*c^2 - a^3*b^3*c)*d*x)*sqrt(d*x + c))/((b^8*c^4 - 3*a^2*b^6*c^3 + 3*a^4*b^4*c^2 - a^6*b^2*c)*d*x^2 + (b^8*c^5 - 4*a^2*b^6*c^4 + 6*a^4*b^4*c^3 - 4*a^6*b^2*c^2 + a^8*c)*x), -(b^6*c^4 - a^2*b^4*c^3 - a^4*b^2*c^2 + a^6*c + (b^6*c^3 + 2*a^2*b^4*c^2 - 3*a^4*b^2*c)*d*x - 2*((3*a*b^5*c + a^3*b^3)*d^2*x^2 + (3*a*b^5*c^2 - 2*a^3*b^3*c - a^5*b)*d*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - 2*((b^6*c^2 + 3*a^2*b^4*c)*d^2*x^2 + (b^6*c^3 + 2*a^2*b^4*c^2 - 3*a^4*b^2*c)*d*x)*log(sqrt(d*x + c)*b + a) + ((b^6*c^2 + 3*a^2*b^4*c)*d^2*x^2 + (b^6*c^3 + 2*a^2*b^4*c^2 - 3*a^4*b^2*c)*d*x)*log(x) - 2*(a*b^5*c^3 - 2*a^3*b^3*c^2 + a^5*b*c + 2*(a*b^5*c^2 - a^3*b^3*c)*d*x)*sqrt(d*x + c))/((b^8*c^4 - 3*a^2*b^6*c^3 + 3*a^4*b^4*c^2 - a^6*b^2*c)*d*x^2 + (b^8*c^5 - 4*a^2*b^6*c^4 + 6*a^4*b^4*c^3 - 4*a^6*b^2*c^2 + a^8*c)*x)]","B",0
645,1,1252,0,3.958538," ","integrate(1/x^3/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, b^{8} c^{6} - 4 \, a^{2} b^{6} c^{5} + 4 \, a^{6} b^{2} c^{3} - 2 \, a^{8} c^{2} - 4 \, {\left(b^{8} c^{4} + 4 \, a^{2} b^{6} c^{3} - 5 \, a^{4} b^{4} c^{2}\right)} d^{2} x^{2} - 2 \, {\left(b^{8} c^{5} + 3 \, a^{2} b^{6} c^{4} - 9 \, a^{4} b^{4} c^{3} + 5 \, a^{6} b^{2} c^{2}\right)} d x - {\left({\left(15 \, a b^{7} c^{2} + 10 \, a^{3} b^{5} c - a^{5} b^{3}\right)} d^{3} x^{3} + {\left(15 \, a b^{7} c^{3} - 5 \, a^{3} b^{5} c^{2} - 11 \, a^{5} b^{3} c + a^{7} b\right)} d^{2} x^{2}\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 8 \, {\left({\left(b^{8} c^{3} + 5 \, a^{2} b^{6} c^{2}\right)} d^{3} x^{3} + {\left(b^{8} c^{4} + 4 \, a^{2} b^{6} c^{3} - 5 \, a^{4} b^{4} c^{2}\right)} d^{2} x^{2}\right)} \log\left(\sqrt{d x + c} b + a\right) - 4 \, {\left({\left(b^{8} c^{3} + 5 \, a^{2} b^{6} c^{2}\right)} d^{3} x^{3} + {\left(b^{8} c^{4} + 4 \, a^{2} b^{6} c^{3} - 5 \, a^{4} b^{4} c^{2}\right)} d^{2} x^{2}\right)} \log\left(x\right) - 2 \, {\left(2 \, a b^{7} c^{5} - 6 \, a^{3} b^{5} c^{4} + 6 \, a^{5} b^{3} c^{3} - 2 \, a^{7} b c^{2} - {\left(11 \, a b^{7} c^{3} - 10 \, a^{3} b^{5} c^{2} - a^{5} b^{3} c\right)} d^{2} x^{2} - {\left(5 \, a b^{7} c^{4} - 9 \, a^{3} b^{5} c^{3} + 3 \, a^{5} b^{3} c^{2} + a^{7} b c\right)} d x\right)} \sqrt{d x + c}}{4 \, {\left({\left(b^{10} c^{6} - 4 \, a^{2} b^{8} c^{5} + 6 \, a^{4} b^{6} c^{4} - 4 \, a^{6} b^{4} c^{3} + a^{8} b^{2} c^{2}\right)} d x^{3} + {\left(b^{10} c^{7} - 5 \, a^{2} b^{8} c^{6} + 10 \, a^{4} b^{6} c^{5} - 10 \, a^{6} b^{4} c^{4} + 5 \, a^{8} b^{2} c^{3} - a^{10} c^{2}\right)} x^{2}\right)}}, -\frac{b^{8} c^{6} - 2 \, a^{2} b^{6} c^{5} + 2 \, a^{6} b^{2} c^{3} - a^{8} c^{2} - 2 \, {\left(b^{8} c^{4} + 4 \, a^{2} b^{6} c^{3} - 5 \, a^{4} b^{4} c^{2}\right)} d^{2} x^{2} - {\left(b^{8} c^{5} + 3 \, a^{2} b^{6} c^{4} - 9 \, a^{4} b^{4} c^{3} + 5 \, a^{6} b^{2} c^{2}\right)} d x + {\left({\left(15 \, a b^{7} c^{2} + 10 \, a^{3} b^{5} c - a^{5} b^{3}\right)} d^{3} x^{3} + {\left(15 \, a b^{7} c^{3} - 5 \, a^{3} b^{5} c^{2} - 11 \, a^{5} b^{3} c + a^{7} b\right)} d^{2} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 4 \, {\left({\left(b^{8} c^{3} + 5 \, a^{2} b^{6} c^{2}\right)} d^{3} x^{3} + {\left(b^{8} c^{4} + 4 \, a^{2} b^{6} c^{3} - 5 \, a^{4} b^{4} c^{2}\right)} d^{2} x^{2}\right)} \log\left(\sqrt{d x + c} b + a\right) - 2 \, {\left({\left(b^{8} c^{3} + 5 \, a^{2} b^{6} c^{2}\right)} d^{3} x^{3} + {\left(b^{8} c^{4} + 4 \, a^{2} b^{6} c^{3} - 5 \, a^{4} b^{4} c^{2}\right)} d^{2} x^{2}\right)} \log\left(x\right) - {\left(2 \, a b^{7} c^{5} - 6 \, a^{3} b^{5} c^{4} + 6 \, a^{5} b^{3} c^{3} - 2 \, a^{7} b c^{2} - {\left(11 \, a b^{7} c^{3} - 10 \, a^{3} b^{5} c^{2} - a^{5} b^{3} c\right)} d^{2} x^{2} - {\left(5 \, a b^{7} c^{4} - 9 \, a^{3} b^{5} c^{3} + 3 \, a^{5} b^{3} c^{2} + a^{7} b c\right)} d x\right)} \sqrt{d x + c}}{2 \, {\left({\left(b^{10} c^{6} - 4 \, a^{2} b^{8} c^{5} + 6 \, a^{4} b^{6} c^{4} - 4 \, a^{6} b^{4} c^{3} + a^{8} b^{2} c^{2}\right)} d x^{3} + {\left(b^{10} c^{7} - 5 \, a^{2} b^{8} c^{6} + 10 \, a^{4} b^{6} c^{5} - 10 \, a^{6} b^{4} c^{4} + 5 \, a^{8} b^{2} c^{3} - a^{10} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*b^8*c^6 - 4*a^2*b^6*c^5 + 4*a^6*b^2*c^3 - 2*a^8*c^2 - 4*(b^8*c^4 + 4*a^2*b^6*c^3 - 5*a^4*b^4*c^2)*d^2*x^2 - 2*(b^8*c^5 + 3*a^2*b^6*c^4 - 9*a^4*b^4*c^3 + 5*a^6*b^2*c^2)*d*x - ((15*a*b^7*c^2 + 10*a^3*b^5*c - a^5*b^3)*d^3*x^3 + (15*a*b^7*c^3 - 5*a^3*b^5*c^2 - 11*a^5*b^3*c + a^7*b)*d^2*x^2)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 8*((b^8*c^3 + 5*a^2*b^6*c^2)*d^3*x^3 + (b^8*c^4 + 4*a^2*b^6*c^3 - 5*a^4*b^4*c^2)*d^2*x^2)*log(sqrt(d*x + c)*b + a) - 4*((b^8*c^3 + 5*a^2*b^6*c^2)*d^3*x^3 + (b^8*c^4 + 4*a^2*b^6*c^3 - 5*a^4*b^4*c^2)*d^2*x^2)*log(x) - 2*(2*a*b^7*c^5 - 6*a^3*b^5*c^4 + 6*a^5*b^3*c^3 - 2*a^7*b*c^2 - (11*a*b^7*c^3 - 10*a^3*b^5*c^2 - a^5*b^3*c)*d^2*x^2 - (5*a*b^7*c^4 - 9*a^3*b^5*c^3 + 3*a^5*b^3*c^2 + a^7*b*c)*d*x)*sqrt(d*x + c))/((b^10*c^6 - 4*a^2*b^8*c^5 + 6*a^4*b^6*c^4 - 4*a^6*b^4*c^3 + a^8*b^2*c^2)*d*x^3 + (b^10*c^7 - 5*a^2*b^8*c^6 + 10*a^4*b^6*c^5 - 10*a^6*b^4*c^4 + 5*a^8*b^2*c^3 - a^10*c^2)*x^2), -1/2*(b^8*c^6 - 2*a^2*b^6*c^5 + 2*a^6*b^2*c^3 - a^8*c^2 - 2*(b^8*c^4 + 4*a^2*b^6*c^3 - 5*a^4*b^4*c^2)*d^2*x^2 - (b^8*c^5 + 3*a^2*b^6*c^4 - 9*a^4*b^4*c^3 + 5*a^6*b^2*c^2)*d*x + ((15*a*b^7*c^2 + 10*a^3*b^5*c - a^5*b^3)*d^3*x^3 + (15*a*b^7*c^3 - 5*a^3*b^5*c^2 - 11*a^5*b^3*c + a^7*b)*d^2*x^2)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 4*((b^8*c^3 + 5*a^2*b^6*c^2)*d^3*x^3 + (b^8*c^4 + 4*a^2*b^6*c^3 - 5*a^4*b^4*c^2)*d^2*x^2)*log(sqrt(d*x + c)*b + a) - 2*((b^8*c^3 + 5*a^2*b^6*c^2)*d^3*x^3 + (b^8*c^4 + 4*a^2*b^6*c^3 - 5*a^4*b^4*c^2)*d^2*x^2)*log(x) - (2*a*b^7*c^5 - 6*a^3*b^5*c^4 + 6*a^5*b^3*c^3 - 2*a^7*b*c^2 - (11*a*b^7*c^3 - 10*a^3*b^5*c^2 - a^5*b^3*c)*d^2*x^2 - (5*a*b^7*c^4 - 9*a^3*b^5*c^3 + 3*a^5*b^3*c^2 + a^7*b*c)*d*x)*sqrt(d*x + c))/((b^10*c^6 - 4*a^2*b^8*c^5 + 6*a^4*b^6*c^4 - 4*a^6*b^4*c^3 + a^8*b^2*c^2)*d*x^3 + (b^10*c^7 - 5*a^2*b^8*c^6 + 10*a^4*b^6*c^5 - 10*a^6*b^4*c^4 + 5*a^8*b^2*c^3 - a^10*c^2)*x^2)]","B",0
646,1,231,0,1.061242," ","integrate(x^3/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(3234 \, a b^{6} d^{3} x^{3} - 17280 \, a b^{6} c^{3} + 46976 \, a^{3} b^{4} c^{2} - 44544 \, a^{5} b^{2} c + 14336 \, a^{7} - 28 \, {\left(141 \, a b^{6} c - 140 \, a^{3} b^{4}\right)} d^{2} x^{2} + 64 \, {\left(87 \, a b^{6} c^{2} - 170 \, a^{3} b^{4} c + 84 \, a^{5} b^{2}\right)} d x - {\left(3003 \, b^{7} d^{3} x^{3} - 4992 \, b^{7} c^{3} + 18816 \, a^{2} b^{5} c^{2} - 20480 \, a^{4} b^{3} c + 7168 \, a^{6} b - 252 \, {\left(13 \, b^{7} c - 14 \, a^{2} b^{5}\right)} d^{2} x^{2} + 32 \, {\left(117 \, b^{7} c^{2} - 267 \, a^{2} b^{5} c + 140 \, a^{4} b^{3}\right)} d x\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{45045 \, b^{8} d^{4}}"," ",0,"-4/45045*(3234*a*b^6*d^3*x^3 - 17280*a*b^6*c^3 + 46976*a^3*b^4*c^2 - 44544*a^5*b^2*c + 14336*a^7 - 28*(141*a*b^6*c - 140*a^3*b^4)*d^2*x^2 + 64*(87*a*b^6*c^2 - 170*a^3*b^4*c + 84*a^5*b^2)*d*x - (3003*b^7*d^3*x^3 - 4992*b^7*c^3 + 18816*a^2*b^5*c^2 - 20480*a^4*b^3*c + 7168*a^6*b - 252*(13*b^7*c - 14*a^2*b^5)*d^2*x^2 + 32*(117*b^7*c^2 - 267*a^2*b^5*c + 140*a^4*b^3)*d*x)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a)/(b^8*d^4)","A",0
647,1,140,0,1.013078," ","integrate(x^2/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(350 \, a b^{4} d^{2} x^{2} + 1472 \, a b^{4} c^{2} - 2688 \, a^{3} b^{2} c + 1280 \, a^{5} - 8 \, {\left(61 \, a b^{4} c - 60 \, a^{3} b^{2}\right)} d x - {\left(315 \, b^{5} d^{2} x^{2} + 480 \, b^{5} c^{2} - 1184 \, a^{2} b^{3} c + 640 \, a^{4} b - 40 \, {\left(9 \, b^{5} c - 10 \, a^{2} b^{3}\right)} d x\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{3465 \, b^{6} d^{3}}"," ",0,"-4/3465*(350*a*b^4*d^2*x^2 + 1472*a*b^4*c^2 - 2688*a^3*b^2*c + 1280*a^5 - 8*(61*a*b^4*c - 60*a^3*b^2)*d*x - (315*b^5*d^2*x^2 + 480*b^5*c^2 - 1184*a^2*b^3*c + 640*a^4*b - 40*(9*b^5*c - 10*a^2*b^3)*d*x)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a)/(b^6*d^3)","A",0
648,1,71,0,1.024460," ","integrate(x/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(18 \, a b^{2} d x - 52 \, a b^{2} c + 48 \, a^{3} - {\left(15 \, b^{3} d x - 20 \, b^{3} c + 24 \, a^{2} b\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{105 \, b^{4} d^{2}}"," ",0,"-4/105*(18*a*b^2*d*x - 52*a*b^2*c + 48*a^3 - (15*b^3*d*x - 20*b^3*c + 24*a^2*b)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a)/(b^4*d^2)","A",0
649,1,34,0,1.023522," ","integrate(1/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{\sqrt{d x + c} b + a} {\left(\sqrt{d x + c} b - 2 \, a\right)}}{3 \, b^{2} d}"," ",0,"4/3*sqrt(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b - 2*a)/(b^2*d)","A",0
650,1,743,0,1.112070," ","integrate(1/x/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\sqrt{-\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} + a}{b^{2} c - a^{2}}} \log\left(4 \, {\left({\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} - a\right)} \sqrt{-\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} + a}{b^{2} c - a^{2}}} + 4 \, \sqrt{\sqrt{d x + c} b + a}\right) - \sqrt{-\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} + a}{b^{2} c - a^{2}}} \log\left(-4 \, {\left({\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} - a\right)} \sqrt{-\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} + a}{b^{2} c - a^{2}}} + 4 \, \sqrt{\sqrt{d x + c} b + a}\right) - \sqrt{\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} - a}{b^{2} c - a^{2}}} \log\left(4 \, {\left({\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} + a\right)} \sqrt{\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} - a}{b^{2} c - a^{2}}} + 4 \, \sqrt{\sqrt{d x + c} b + a}\right) + \sqrt{\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} - a}{b^{2} c - a^{2}}} \log\left(-4 \, {\left({\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} + a\right)} \sqrt{\frac{{\left(b^{2} c - a^{2}\right)} \sqrt{\frac{b^{2} c}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}}} - a}{b^{2} c - a^{2}}} + 4 \, \sqrt{\sqrt{d x + c} b + a}\right)"," ",0,"sqrt(-((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) + a)/(b^2*c - a^2))*log(4*((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) - a)*sqrt(-((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) + a)/(b^2*c - a^2)) + 4*sqrt(sqrt(d*x + c)*b + a)) - sqrt(-((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) + a)/(b^2*c - a^2))*log(-4*((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) - a)*sqrt(-((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) + a)/(b^2*c - a^2)) + 4*sqrt(sqrt(d*x + c)*b + a)) - sqrt(((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) - a)/(b^2*c - a^2))*log(4*((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) + a)*sqrt(((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) - a)/(b^2*c - a^2)) + 4*sqrt(sqrt(d*x + c)*b + a)) + sqrt(((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) - a)/(b^2*c - a^2))*log(-4*((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) + a)*sqrt(((b^2*c - a^2)*sqrt(b^2*c/(b^4*c^2 - 2*a^2*b^2*c + a^4)) - a)/(b^2*c - a^2)) + 4*sqrt(sqrt(d*x + c)*b + a))","B",0
651,1,2493,0,1.173597," ","integrate(1/x^2/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{{\left(b^{2} c - a^{2}\right)} x \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} + {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}} \log\left({\left(b^{6} c + 3 \, a^{2} b^{4}\right)} \sqrt{\sqrt{d x + c} b + a} d^{3} + {\left(2 \, {\left(a b^{6} c^{2} + 3 \, a^{3} b^{4} c\right)} d^{2} - {\left(b^{8} c^{5} - 2 \, a^{2} b^{6} c^{4} + 2 \, a^{6} b^{2} c^{2} - a^{8} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}\right)} \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} + {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}}\right) - {\left(b^{2} c - a^{2}\right)} x \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} + {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}} \log\left({\left(b^{6} c + 3 \, a^{2} b^{4}\right)} \sqrt{\sqrt{d x + c} b + a} d^{3} - {\left(2 \, {\left(a b^{6} c^{2} + 3 \, a^{3} b^{4} c\right)} d^{2} - {\left(b^{8} c^{5} - 2 \, a^{2} b^{6} c^{4} + 2 \, a^{6} b^{2} c^{2} - a^{8} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}\right)} \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} + {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}}\right) + {\left(b^{2} c - a^{2}\right)} x \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} - {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}} \log\left({\left(b^{6} c + 3 \, a^{2} b^{4}\right)} \sqrt{\sqrt{d x + c} b + a} d^{3} + {\left(2 \, {\left(a b^{6} c^{2} + 3 \, a^{3} b^{4} c\right)} d^{2} + {\left(b^{8} c^{5} - 2 \, a^{2} b^{6} c^{4} + 2 \, a^{6} b^{2} c^{2} - a^{8} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}\right)} \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} - {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}}\right) - {\left(b^{2} c - a^{2}\right)} x \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} - {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}} \log\left({\left(b^{6} c + 3 \, a^{2} b^{4}\right)} \sqrt{\sqrt{d x + c} b + a} d^{3} - {\left(2 \, {\left(a b^{6} c^{2} + 3 \, a^{3} b^{4} c\right)} d^{2} + {\left(b^{8} c^{5} - 2 \, a^{2} b^{6} c^{4} + 2 \, a^{6} b^{2} c^{2} - a^{8} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}\right)} \sqrt{-\frac{{\left(3 \, a b^{4} c + a^{3} b^{2}\right)} d^{2} - {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{\frac{{\left(b^{10} c^{2} + 6 \, a^{2} b^{8} c + 9 \, a^{4} b^{6}\right)} d^{4}}{b^{12} c^{7} - 6 \, a^{2} b^{10} c^{6} + 15 \, a^{4} b^{8} c^{5} - 20 \, a^{6} b^{6} c^{4} + 15 \, a^{8} b^{4} c^{3} - 6 \, a^{10} b^{2} c^{2} + a^{12} c}}}{b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c}}\right) - 4 \, \sqrt{\sqrt{d x + c} b + a} {\left(\sqrt{d x + c} b - a\right)}}{4 \, {\left(b^{2} c - a^{2}\right)} x}"," ",0,"1/4*((b^2*c - a^2)*x*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 + (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))*log((b^6*c + 3*a^2*b^4)*sqrt(sqrt(d*x + c)*b + a)*d^3 + (2*(a*b^6*c^2 + 3*a^3*b^4*c)*d^2 - (b^8*c^5 - 2*a^2*b^6*c^4 + 2*a^6*b^2*c^2 - a^8*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 + (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))) - (b^2*c - a^2)*x*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 + (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))*log((b^6*c + 3*a^2*b^4)*sqrt(sqrt(d*x + c)*b + a)*d^3 - (2*(a*b^6*c^2 + 3*a^3*b^4*c)*d^2 - (b^8*c^5 - 2*a^2*b^6*c^4 + 2*a^6*b^2*c^2 - a^8*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 + (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))) + (b^2*c - a^2)*x*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 - (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))*log((b^6*c + 3*a^2*b^4)*sqrt(sqrt(d*x + c)*b + a)*d^3 + (2*(a*b^6*c^2 + 3*a^3*b^4*c)*d^2 + (b^8*c^5 - 2*a^2*b^6*c^4 + 2*a^6*b^2*c^2 - a^8*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 - (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))) - (b^2*c - a^2)*x*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 - (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))*log((b^6*c + 3*a^2*b^4)*sqrt(sqrt(d*x + c)*b + a)*d^3 - (2*(a*b^6*c^2 + 3*a^3*b^4*c)*d^2 + (b^8*c^5 - 2*a^2*b^6*c^4 + 2*a^6*b^2*c^2 - a^8*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))*sqrt(-((3*a*b^4*c + a^3*b^2)*d^2 - (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt((b^10*c^2 + 6*a^2*b^8*c + 9*a^4*b^6)*d^4/(b^12*c^7 - 6*a^2*b^10*c^6 + 15*a^4*b^8*c^5 - 20*a^6*b^6*c^4 + 15*a^8*b^4*c^3 - 6*a^10*b^2*c^2 + a^12*c)))/(b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c))) - 4*sqrt(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b - a))/((b^2*c - a^2)*x)","B",0
652,1,4390,0,2.414688," ","integrate(1/x^3/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x^{2} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} + {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}} \log\left({\left(625 \, b^{12} c^{3} + 3750 \, a^{2} b^{10} c^{2} - 1491 \, a^{4} b^{8} c + 140 \, a^{6} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} + {\left({\left(325 \, a b^{12} c^{5} + 1977 \, a^{3} b^{10} c^{4} - 609 \, a^{5} b^{8} c^{3} + 35 \, a^{7} b^{6} c^{2}\right)} d^{4} - {\left(5 \, b^{14} c^{10} - 16 \, a^{2} b^{12} c^{9} + 3 \, a^{4} b^{10} c^{8} + 50 \, a^{6} b^{8} c^{7} - 85 \, a^{8} b^{6} c^{6} + 60 \, a^{10} b^{4} c^{5} - 19 \, a^{12} b^{2} c^{4} + 2 \, a^{14} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}\right)} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} + {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}}\right) - {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x^{2} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} + {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}} \log\left({\left(625 \, b^{12} c^{3} + 3750 \, a^{2} b^{10} c^{2} - 1491 \, a^{4} b^{8} c + 140 \, a^{6} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} - {\left({\left(325 \, a b^{12} c^{5} + 1977 \, a^{3} b^{10} c^{4} - 609 \, a^{5} b^{8} c^{3} + 35 \, a^{7} b^{6} c^{2}\right)} d^{4} - {\left(5 \, b^{14} c^{10} - 16 \, a^{2} b^{12} c^{9} + 3 \, a^{4} b^{10} c^{8} + 50 \, a^{6} b^{8} c^{7} - 85 \, a^{8} b^{6} c^{6} + 60 \, a^{10} b^{4} c^{5} - 19 \, a^{12} b^{2} c^{4} + 2 \, a^{14} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}\right)} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} + {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}}\right) + {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x^{2} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} - {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}} \log\left({\left(625 \, b^{12} c^{3} + 3750 \, a^{2} b^{10} c^{2} - 1491 \, a^{4} b^{8} c + 140 \, a^{6} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} + {\left({\left(325 \, a b^{12} c^{5} + 1977 \, a^{3} b^{10} c^{4} - 609 \, a^{5} b^{8} c^{3} + 35 \, a^{7} b^{6} c^{2}\right)} d^{4} + {\left(5 \, b^{14} c^{10} - 16 \, a^{2} b^{12} c^{9} + 3 \, a^{4} b^{10} c^{8} + 50 \, a^{6} b^{8} c^{7} - 85 \, a^{8} b^{6} c^{6} + 60 \, a^{10} b^{4} c^{5} - 19 \, a^{12} b^{2} c^{4} + 2 \, a^{14} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}\right)} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} - {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}}\right) - {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x^{2} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} - {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}} \log\left({\left(625 \, b^{12} c^{3} + 3750 \, a^{2} b^{10} c^{2} - 1491 \, a^{4} b^{8} c + 140 \, a^{6} b^{6}\right)} \sqrt{\sqrt{d x + c} b + a} d^{6} - {\left({\left(325 \, a b^{12} c^{5} + 1977 \, a^{3} b^{10} c^{4} - 609 \, a^{5} b^{8} c^{3} + 35 \, a^{7} b^{6} c^{2}\right)} d^{4} + {\left(5 \, b^{14} c^{10} - 16 \, a^{2} b^{12} c^{9} + 3 \, a^{4} b^{10} c^{8} + 50 \, a^{6} b^{8} c^{7} - 85 \, a^{8} b^{6} c^{6} + 60 \, a^{10} b^{4} c^{5} - 19 \, a^{12} b^{2} c^{4} + 2 \, a^{14} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}\right)} \sqrt{-\frac{{\left(105 \, a b^{8} c^{3} + 70 \, a^{3} b^{6} c^{2} - 35 \, a^{5} b^{4} c + 4 \, a^{7} b^{2}\right)} d^{4} - {\left(b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}\right)} \sqrt{\frac{{\left(625 \, b^{18} c^{4} + 7700 \, a^{2} b^{16} c^{3} + 21966 \, a^{4} b^{14} c^{2} - 10780 \, a^{6} b^{12} c + 1225 \, a^{8} b^{10}\right)} d^{8}}{b^{20} c^{13} - 10 \, a^{2} b^{18} c^{12} + 45 \, a^{4} b^{16} c^{11} - 120 \, a^{6} b^{14} c^{10} + 210 \, a^{8} b^{12} c^{9} - 252 \, a^{10} b^{10} c^{8} + 210 \, a^{12} b^{8} c^{7} - 120 \, a^{14} b^{6} c^{6} + 45 \, a^{16} b^{4} c^{5} - 10 \, a^{18} b^{2} c^{4} + a^{20} c^{3}}}}{b^{10} c^{8} - 5 \, a^{2} b^{8} c^{7} + 10 \, a^{4} b^{6} c^{6} - 10 \, a^{6} b^{4} c^{5} + 5 \, a^{8} b^{2} c^{4} - a^{10} c^{3}}}\right) + 4 \, {\left(6 \, a b^{2} c d x - 4 \, a b^{2} c^{2} + 4 \, a^{3} c + {\left(4 \, b^{3} c^{2} - 4 \, a^{2} b c - {\left(5 \, b^{3} c + a^{2} b\right)} d x\right)} \sqrt{d x + c}\right)} \sqrt{\sqrt{d x + c} b + a}}{32 \, {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} x^{2}}"," ",0,"-1/32*((b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x^2*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 + (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))*log((625*b^12*c^3 + 3750*a^2*b^10*c^2 - 1491*a^4*b^8*c + 140*a^6*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 + ((325*a*b^12*c^5 + 1977*a^3*b^10*c^4 - 609*a^5*b^8*c^3 + 35*a^7*b^6*c^2)*d^4 - (5*b^14*c^10 - 16*a^2*b^12*c^9 + 3*a^4*b^10*c^8 + 50*a^6*b^8*c^7 - 85*a^8*b^6*c^6 + 60*a^10*b^4*c^5 - 19*a^12*b^2*c^4 + 2*a^14*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 + (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))) - (b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x^2*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 + (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))*log((625*b^12*c^3 + 3750*a^2*b^10*c^2 - 1491*a^4*b^8*c + 140*a^6*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 - ((325*a*b^12*c^5 + 1977*a^3*b^10*c^4 - 609*a^5*b^8*c^3 + 35*a^7*b^6*c^2)*d^4 - (5*b^14*c^10 - 16*a^2*b^12*c^9 + 3*a^4*b^10*c^8 + 50*a^6*b^8*c^7 - 85*a^8*b^6*c^6 + 60*a^10*b^4*c^5 - 19*a^12*b^2*c^4 + 2*a^14*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 + (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))) + (b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x^2*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 - (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))*log((625*b^12*c^3 + 3750*a^2*b^10*c^2 - 1491*a^4*b^8*c + 140*a^6*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 + ((325*a*b^12*c^5 + 1977*a^3*b^10*c^4 - 609*a^5*b^8*c^3 + 35*a^7*b^6*c^2)*d^4 + (5*b^14*c^10 - 16*a^2*b^12*c^9 + 3*a^4*b^10*c^8 + 50*a^6*b^8*c^7 - 85*a^8*b^6*c^6 + 60*a^10*b^4*c^5 - 19*a^12*b^2*c^4 + 2*a^14*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 - (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))) - (b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x^2*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 - (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))*log((625*b^12*c^3 + 3750*a^2*b^10*c^2 - 1491*a^4*b^8*c + 140*a^6*b^6)*sqrt(sqrt(d*x + c)*b + a)*d^6 - ((325*a*b^12*c^5 + 1977*a^3*b^10*c^4 - 609*a^5*b^8*c^3 + 35*a^7*b^6*c^2)*d^4 + (5*b^14*c^10 - 16*a^2*b^12*c^9 + 3*a^4*b^10*c^8 + 50*a^6*b^8*c^7 - 85*a^8*b^6*c^6 + 60*a^10*b^4*c^5 - 19*a^12*b^2*c^4 + 2*a^14*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))*sqrt(-((105*a*b^8*c^3 + 70*a^3*b^6*c^2 - 35*a^5*b^4*c + 4*a^7*b^2)*d^4 - (b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3)*sqrt((625*b^18*c^4 + 7700*a^2*b^16*c^3 + 21966*a^4*b^14*c^2 - 10780*a^6*b^12*c + 1225*a^8*b^10)*d^8/(b^20*c^13 - 10*a^2*b^18*c^12 + 45*a^4*b^16*c^11 - 120*a^6*b^14*c^10 + 210*a^8*b^12*c^9 - 252*a^10*b^10*c^8 + 210*a^12*b^8*c^7 - 120*a^14*b^6*c^6 + 45*a^16*b^4*c^5 - 10*a^18*b^2*c^4 + a^20*c^3)))/(b^10*c^8 - 5*a^2*b^8*c^7 + 10*a^4*b^6*c^6 - 10*a^6*b^4*c^5 + 5*a^8*b^2*c^4 - a^10*c^3))) + 4*(6*a*b^2*c*d*x - 4*a*b^2*c^2 + 4*a^3*c + (4*b^3*c^2 - 4*a^2*b*c - (5*b^3*c + a^2*b)*d*x)*sqrt(d*x + c))*sqrt(sqrt(d*x + c)*b + a))/((b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*x^2)","B",0
653,1,1416,0,1.325764," ","integrate(x^3*(a+b*(d*x+c)^(1/2))^p,x, algorithm=""fricas"")","-\frac{2 \, {\left(5040 \, b^{8} c^{4} - 20160 \, a^{2} b^{6} c^{3} + 30240 \, a^{4} b^{4} c^{2} - 20160 \, a^{6} b^{2} c + 5040 \, a^{8} + 48 \, {\left(b^{8} c^{4} + 6 \, a^{2} b^{6} c^{3} + a^{4} b^{4} c^{2}\right)} p^{4} - {\left(b^{8} d^{4} p^{7} + 28 \, b^{8} d^{4} p^{6} + 322 \, b^{8} d^{4} p^{5} + 1960 \, b^{8} d^{4} p^{4} + 6769 \, b^{8} d^{4} p^{3} + 13132 \, b^{8} d^{4} p^{2} + 13068 \, b^{8} d^{4} p + 5040 \, b^{8} d^{4}\right)} x^{4} + 384 \, {\left(2 \, b^{8} c^{4} + 7 \, a^{2} b^{6} c^{3} - 3 \, a^{4} b^{4} c^{2}\right)} p^{3} - {\left(b^{8} c d^{3} p^{7} + {\left(22 \, b^{8} c - 7 \, a^{2} b^{6}\right)} d^{3} p^{6} + 5 \, {\left(38 \, b^{8} c - 21 \, a^{2} b^{6}\right)} d^{3} p^{5} + 5 \, {\left(164 \, b^{8} c - 119 \, a^{2} b^{6}\right)} d^{3} p^{4} + {\left(1849 \, b^{8} c - 1575 \, a^{2} b^{6}\right)} d^{3} p^{3} + 2 \, {\left(1019 \, b^{8} c - 959 \, a^{2} b^{6}\right)} d^{3} p^{2} + 840 \, {\left(b^{8} c - a^{2} b^{6}\right)} d^{3} p\right)} x^{3} + 48 \, {\left(86 \, b^{8} c^{4} + 81 \, a^{2} b^{6} c^{3} - 124 \, a^{4} b^{4} c^{2} + 45 \, a^{6} b^{2} c\right)} p^{2} + 6 \, {\left(18 \, b^{8} c^{2} d^{2} p^{5} + {\left(b^{8} c^{2} + a^{2} b^{6} c\right)} d^{2} p^{6} + {\left(118 \, b^{8} c^{2} - 95 \, a^{2} b^{6} c + 35 \, a^{4} b^{4}\right)} d^{2} p^{4} + 6 \, {\left(58 \, b^{8} c^{2} - 80 \, a^{2} b^{6} c + 35 \, a^{4} b^{4}\right)} d^{2} p^{3} + {\left(457 \, b^{8} c^{2} - 806 \, a^{2} b^{6} c + 385 \, a^{4} b^{4}\right)} d^{2} p^{2} + 210 \, {\left(b^{8} c^{2} - 2 \, a^{2} b^{6} c + a^{4} b^{4}\right)} d^{2} p\right)} x^{2} + 192 \, {\left(44 \, b^{8} c^{4} - 71 \, a^{2} b^{6} c^{3} + 54 \, a^{4} b^{4} c^{2} - 15 \, a^{6} b^{2} c\right)} p - 24 \, {\left({\left(b^{8} c^{3} + 3 \, a^{2} b^{6} c^{2}\right)} d p^{5} + 2 \, {\left(8 \, b^{8} c^{3} + 9 \, a^{2} b^{6} c^{2} - 5 \, a^{4} b^{4} c\right)} d p^{4} + {\left(86 \, b^{8} c^{3} - 57 \, a^{2} b^{6} c^{2} + 15 \, a^{4} b^{4} c\right)} d p^{3} + {\left(176 \, b^{8} c^{3} - 387 \, a^{2} b^{6} c^{2} + 340 \, a^{4} b^{4} c - 105 \, a^{6} b^{2}\right)} d p^{2} + 105 \, {\left(b^{8} c^{3} - 3 \, a^{2} b^{6} c^{2} + 3 \, a^{4} b^{4} c - a^{6} b^{2}\right)} d p\right)} x + {\left(192 \, {\left(a b^{7} c^{3} + a^{3} b^{5} c^{2}\right)} p^{4} + 96 \, {\left(27 \, a b^{7} c^{3} + 2 \, a^{3} b^{5} c^{2} - 5 \, a^{5} b^{3} c\right)} p^{3} - {\left(a b^{7} d^{3} p^{7} + 21 \, a b^{7} d^{3} p^{6} + 175 \, a b^{7} d^{3} p^{5} + 735 \, a b^{7} d^{3} p^{4} + 1624 \, a b^{7} d^{3} p^{3} + 1764 \, a b^{7} d^{3} p^{2} + 720 \, a b^{7} d^{3} p\right)} x^{3} + 192 \, {\left(56 \, a b^{7} c^{3} - 49 \, a^{3} b^{5} c^{2} + 15 \, a^{5} b^{3} c\right)} p^{2} + 6 \, {\left(2 \, a b^{7} c d^{2} p^{6} + {\left(33 \, a b^{7} c - 7 \, a^{3} b^{5}\right)} d^{2} p^{5} + 10 \, {\left(20 \, a b^{7} c - 7 \, a^{3} b^{5}\right)} d^{2} p^{4} + 5 \, {\left(111 \, a b^{7} c - 49 \, a^{3} b^{5}\right)} d^{2} p^{3} + 2 \, {\left(349 \, a b^{7} c - 175 \, a^{3} b^{5}\right)} d^{2} p^{2} + 24 \, {\left(13 \, a b^{7} c - 7 \, a^{3} b^{5}\right)} d^{2} p\right)} x^{2} + 48 \, {\left(279 \, a b^{7} c^{3} - 511 \, a^{3} b^{5} c^{2} + 385 \, a^{5} b^{3} c - 105 \, a^{7} b\right)} p - 24 \, {\left({\left(3 \, a b^{7} c^{2} + a^{3} b^{5} c\right)} d p^{5} + 2 \, {\left(21 \, a b^{7} c^{2} - 5 \, a^{3} b^{5} c\right)} d p^{4} + {\left(192 \, a b^{7} c^{2} - 135 \, a^{3} b^{5} c + 35 \, a^{5} b^{3}\right)} d p^{3} + {\left(327 \, a b^{7} c^{2} - 320 \, a^{3} b^{5} c + 105 \, a^{5} b^{3}\right)} d p^{2} + 2 \, {\left(87 \, a b^{7} c^{2} - 98 \, a^{3} b^{5} c + 35 \, a^{5} b^{3}\right)} d p\right)} x\right)} \sqrt{d x + c}\right)} {\left(\sqrt{d x + c} b + a\right)}^{p}}{b^{8} d^{4} p^{8} + 36 \, b^{8} d^{4} p^{7} + 546 \, b^{8} d^{4} p^{6} + 4536 \, b^{8} d^{4} p^{5} + 22449 \, b^{8} d^{4} p^{4} + 67284 \, b^{8} d^{4} p^{3} + 118124 \, b^{8} d^{4} p^{2} + 109584 \, b^{8} d^{4} p + 40320 \, b^{8} d^{4}}"," ",0,"-2*(5040*b^8*c^4 - 20160*a^2*b^6*c^3 + 30240*a^4*b^4*c^2 - 20160*a^6*b^2*c + 5040*a^8 + 48*(b^8*c^4 + 6*a^2*b^6*c^3 + a^4*b^4*c^2)*p^4 - (b^8*d^4*p^7 + 28*b^8*d^4*p^6 + 322*b^8*d^4*p^5 + 1960*b^8*d^4*p^4 + 6769*b^8*d^4*p^3 + 13132*b^8*d^4*p^2 + 13068*b^8*d^4*p + 5040*b^8*d^4)*x^4 + 384*(2*b^8*c^4 + 7*a^2*b^6*c^3 - 3*a^4*b^4*c^2)*p^3 - (b^8*c*d^3*p^7 + (22*b^8*c - 7*a^2*b^6)*d^3*p^6 + 5*(38*b^8*c - 21*a^2*b^6)*d^3*p^5 + 5*(164*b^8*c - 119*a^2*b^6)*d^3*p^4 + (1849*b^8*c - 1575*a^2*b^6)*d^3*p^3 + 2*(1019*b^8*c - 959*a^2*b^6)*d^3*p^2 + 840*(b^8*c - a^2*b^6)*d^3*p)*x^3 + 48*(86*b^8*c^4 + 81*a^2*b^6*c^3 - 124*a^4*b^4*c^2 + 45*a^6*b^2*c)*p^2 + 6*(18*b^8*c^2*d^2*p^5 + (b^8*c^2 + a^2*b^6*c)*d^2*p^6 + (118*b^8*c^2 - 95*a^2*b^6*c + 35*a^4*b^4)*d^2*p^4 + 6*(58*b^8*c^2 - 80*a^2*b^6*c + 35*a^4*b^4)*d^2*p^3 + (457*b^8*c^2 - 806*a^2*b^6*c + 385*a^4*b^4)*d^2*p^2 + 210*(b^8*c^2 - 2*a^2*b^6*c + a^4*b^4)*d^2*p)*x^2 + 192*(44*b^8*c^4 - 71*a^2*b^6*c^3 + 54*a^4*b^4*c^2 - 15*a^6*b^2*c)*p - 24*((b^8*c^3 + 3*a^2*b^6*c^2)*d*p^5 + 2*(8*b^8*c^3 + 9*a^2*b^6*c^2 - 5*a^4*b^4*c)*d*p^4 + (86*b^8*c^3 - 57*a^2*b^6*c^2 + 15*a^4*b^4*c)*d*p^3 + (176*b^8*c^3 - 387*a^2*b^6*c^2 + 340*a^4*b^4*c - 105*a^6*b^2)*d*p^2 + 105*(b^8*c^3 - 3*a^2*b^6*c^2 + 3*a^4*b^4*c - a^6*b^2)*d*p)*x + (192*(a*b^7*c^3 + a^3*b^5*c^2)*p^4 + 96*(27*a*b^7*c^3 + 2*a^3*b^5*c^2 - 5*a^5*b^3*c)*p^3 - (a*b^7*d^3*p^7 + 21*a*b^7*d^3*p^6 + 175*a*b^7*d^3*p^5 + 735*a*b^7*d^3*p^4 + 1624*a*b^7*d^3*p^3 + 1764*a*b^7*d^3*p^2 + 720*a*b^7*d^3*p)*x^3 + 192*(56*a*b^7*c^3 - 49*a^3*b^5*c^2 + 15*a^5*b^3*c)*p^2 + 6*(2*a*b^7*c*d^2*p^6 + (33*a*b^7*c - 7*a^3*b^5)*d^2*p^5 + 10*(20*a*b^7*c - 7*a^3*b^5)*d^2*p^4 + 5*(111*a*b^7*c - 49*a^3*b^5)*d^2*p^3 + 2*(349*a*b^7*c - 175*a^3*b^5)*d^2*p^2 + 24*(13*a*b^7*c - 7*a^3*b^5)*d^2*p)*x^2 + 48*(279*a*b^7*c^3 - 511*a^3*b^5*c^2 + 385*a^5*b^3*c - 105*a^7*b)*p - 24*((3*a*b^7*c^2 + a^3*b^5*c)*d*p^5 + 2*(21*a*b^7*c^2 - 5*a^3*b^5*c)*d*p^4 + (192*a*b^7*c^2 - 135*a^3*b^5*c + 35*a^5*b^3)*d*p^3 + (327*a*b^7*c^2 - 320*a^3*b^5*c + 105*a^5*b^3)*d*p^2 + 2*(87*a*b^7*c^2 - 98*a^3*b^5*c + 35*a^5*b^3)*d*p)*x)*sqrt(d*x + c))*(sqrt(d*x + c)*b + a)^p/(b^8*d^4*p^8 + 36*b^8*d^4*p^7 + 546*b^8*d^4*p^6 + 4536*b^8*d^4*p^5 + 22449*b^8*d^4*p^4 + 67284*b^8*d^4*p^3 + 118124*b^8*d^4*p^2 + 109584*b^8*d^4*p + 40320*b^8*d^4)","B",0
654,1,712,0,1.169521," ","integrate(x^2*(a+b*(d*x+c)^(1/2))^p,x, algorithm=""fricas"")","\frac{2 \, {\left(120 \, b^{6} c^{3} - 360 \, a^{2} b^{4} c^{2} + 360 \, a^{4} b^{2} c - 120 \, a^{6} + 8 \, {\left(b^{6} c^{3} + 3 \, a^{2} b^{4} c^{2}\right)} p^{3} + {\left(b^{6} d^{3} p^{5} + 15 \, b^{6} d^{3} p^{4} + 85 \, b^{6} d^{3} p^{3} + 225 \, b^{6} d^{3} p^{2} + 274 \, b^{6} d^{3} p + 120 \, b^{6} d^{3}\right)} x^{3} + 24 \, {\left(3 \, b^{6} c^{3} + 3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} c\right)} p^{2} + {\left(b^{6} c d^{2} p^{5} + {\left(11 \, b^{6} c - 5 \, a^{2} b^{4}\right)} d^{2} p^{4} + {\left(41 \, b^{6} c - 30 \, a^{2} b^{4}\right)} d^{2} p^{3} + {\left(61 \, b^{6} c - 55 \, a^{2} b^{4}\right)} d^{2} p^{2} + 30 \, {\left(b^{6} c - a^{2} b^{4}\right)} d^{2} p\right)} x^{2} + 8 \, {\left(23 \, b^{6} c^{3} - 24 \, a^{2} b^{4} c^{2} + 9 \, a^{4} b^{2} c\right)} p - 4 \, {\left({\left(b^{6} c^{2} + a^{2} b^{4} c\right)} d p^{4} + 3 \, {\left(3 \, b^{6} c^{2} - a^{2} b^{4} c\right)} d p^{3} + {\left(23 \, b^{6} c^{2} - 34 \, a^{2} b^{4} c + 15 \, a^{4} b^{2}\right)} d p^{2} + 15 \, {\left(b^{6} c^{2} - 2 \, a^{2} b^{4} c + a^{4} b^{2}\right)} d p\right)} x + {\left(8 \, {\left(3 \, a b^{5} c^{2} + a^{3} b^{3} c\right)} p^{3} + 24 \, {\left(7 \, a b^{5} c^{2} - 3 \, a^{3} b^{3} c\right)} p^{2} + {\left(a b^{5} d^{2} p^{5} + 10 \, a b^{5} d^{2} p^{4} + 35 \, a b^{5} d^{2} p^{3} + 50 \, a b^{5} d^{2} p^{2} + 24 \, a b^{5} d^{2} p\right)} x^{2} + 8 \, {\left(33 \, a b^{5} c^{2} - 40 \, a^{3} b^{3} c + 15 \, a^{5} b\right)} p - 4 \, {\left(2 \, a b^{5} c d p^{4} + 5 \, {\left(3 \, a b^{5} c - a^{3} b^{3}\right)} d p^{3} + {\left(31 \, a b^{5} c - 15 \, a^{3} b^{3}\right)} d p^{2} + 2 \, {\left(9 \, a b^{5} c - 5 \, a^{3} b^{3}\right)} d p\right)} x\right)} \sqrt{d x + c}\right)} {\left(\sqrt{d x + c} b + a\right)}^{p}}{b^{6} d^{3} p^{6} + 21 \, b^{6} d^{3} p^{5} + 175 \, b^{6} d^{3} p^{4} + 735 \, b^{6} d^{3} p^{3} + 1624 \, b^{6} d^{3} p^{2} + 1764 \, b^{6} d^{3} p + 720 \, b^{6} d^{3}}"," ",0,"2*(120*b^6*c^3 - 360*a^2*b^4*c^2 + 360*a^4*b^2*c - 120*a^6 + 8*(b^6*c^3 + 3*a^2*b^4*c^2)*p^3 + (b^6*d^3*p^5 + 15*b^6*d^3*p^4 + 85*b^6*d^3*p^3 + 225*b^6*d^3*p^2 + 274*b^6*d^3*p + 120*b^6*d^3)*x^3 + 24*(3*b^6*c^3 + 3*a^2*b^4*c^2 - 2*a^4*b^2*c)*p^2 + (b^6*c*d^2*p^5 + (11*b^6*c - 5*a^2*b^4)*d^2*p^4 + (41*b^6*c - 30*a^2*b^4)*d^2*p^3 + (61*b^6*c - 55*a^2*b^4)*d^2*p^2 + 30*(b^6*c - a^2*b^4)*d^2*p)*x^2 + 8*(23*b^6*c^3 - 24*a^2*b^4*c^2 + 9*a^4*b^2*c)*p - 4*((b^6*c^2 + a^2*b^4*c)*d*p^4 + 3*(3*b^6*c^2 - a^2*b^4*c)*d*p^3 + (23*b^6*c^2 - 34*a^2*b^4*c + 15*a^4*b^2)*d*p^2 + 15*(b^6*c^2 - 2*a^2*b^4*c + a^4*b^2)*d*p)*x + (8*(3*a*b^5*c^2 + a^3*b^3*c)*p^3 + 24*(7*a*b^5*c^2 - 3*a^3*b^3*c)*p^2 + (a*b^5*d^2*p^5 + 10*a*b^5*d^2*p^4 + 35*a*b^5*d^2*p^3 + 50*a*b^5*d^2*p^2 + 24*a*b^5*d^2*p)*x^2 + 8*(33*a*b^5*c^2 - 40*a^3*b^3*c + 15*a^5*b)*p - 4*(2*a*b^5*c*d*p^4 + 5*(3*a*b^5*c - a^3*b^3)*d*p^3 + (31*a*b^5*c - 15*a^3*b^3)*d*p^2 + 2*(9*a*b^5*c - 5*a^3*b^3)*d*p)*x)*sqrt(d*x + c))*(sqrt(d*x + c)*b + a)^p/(b^6*d^3*p^6 + 21*b^6*d^3*p^5 + 175*b^6*d^3*p^4 + 735*b^6*d^3*p^3 + 1624*b^6*d^3*p^2 + 1764*b^6*d^3*p + 720*b^6*d^3)","B",0
655,1,294,0,1.040158," ","integrate(x*(a+b*(d*x+c)^(1/2))^p,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, b^{4} c^{2} - 12 \, a^{2} b^{2} c + 6 \, a^{4} + 2 \, {\left(b^{4} c^{2} + a^{2} b^{2} c\right)} p^{2} - {\left(b^{4} d^{2} p^{3} + 6 \, b^{4} d^{2} p^{2} + 11 \, b^{4} d^{2} p + 6 \, b^{4} d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{2} - a^{2} b^{2} c\right)} p - {\left(b^{4} c d p^{3} + {\left(4 \, b^{4} c - 3 \, a^{2} b^{2}\right)} d p^{2} + 3 \, {\left(b^{4} c - a^{2} b^{2}\right)} d p\right)} x + {\left(4 \, a b^{3} c p^{2} + 2 \, {\left(5 \, a b^{3} c - 3 \, a^{3} b\right)} p - {\left(a b^{3} d p^{3} + 3 \, a b^{3} d p^{2} + 2 \, a b^{3} d p\right)} x\right)} \sqrt{d x + c}\right)} {\left(\sqrt{d x + c} b + a\right)}^{p}}{b^{4} d^{2} p^{4} + 10 \, b^{4} d^{2} p^{3} + 35 \, b^{4} d^{2} p^{2} + 50 \, b^{4} d^{2} p + 24 \, b^{4} d^{2}}"," ",0,"-2*(6*b^4*c^2 - 12*a^2*b^2*c + 6*a^4 + 2*(b^4*c^2 + a^2*b^2*c)*p^2 - (b^4*d^2*p^3 + 6*b^4*d^2*p^2 + 11*b^4*d^2*p + 6*b^4*d^2)*x^2 + 4*(2*b^4*c^2 - a^2*b^2*c)*p - (b^4*c*d*p^3 + (4*b^4*c - 3*a^2*b^2)*d*p^2 + 3*(b^4*c - a^2*b^2)*d*p)*x + (4*a*b^3*c*p^2 + 2*(5*a*b^3*c - 3*a^3*b)*p - (a*b^3*d*p^3 + 3*a*b^3*d*p^2 + 2*a*b^3*d*p)*x)*sqrt(d*x + c))*(sqrt(d*x + c)*b + a)^p/(b^4*d^2*p^4 + 10*b^4*d^2*p^3 + 35*b^4*d^2*p^2 + 50*b^4*d^2*p + 24*b^4*d^2)","B",0
656,1,81,0,0.986127," ","integrate((a+b*(d*x+c)^(1/2))^p,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} c p + \sqrt{d x + c} a b p + b^{2} c - a^{2} + {\left(b^{2} d p + b^{2} d\right)} x\right)} {\left(\sqrt{d x + c} b + a\right)}^{p}}{b^{2} d p^{2} + 3 \, b^{2} d p + 2 \, b^{2} d}"," ",0,"2*(b^2*c*p + sqrt(d*x + c)*a*b*p + b^2*c - a^2 + (b^2*d*p + b^2*d)*x)*(sqrt(d*x + c)*b + a)^p/(b^2*d*p^2 + 3*b^2*d*p + 2*b^2*d)","A",0
657,0,0,0,1.039887," ","integrate((a+b*(d*x+c)^(1/2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\sqrt{d x + c} b + a\right)}^{p}}{x}, x\right)"," ",0,"integral((sqrt(d*x + c)*b + a)^p/x, x)","F",0
658,1,164,0,1.015080," ","integrate((a+b*(c*x)^n)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{5}{2}} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, {\left(11 \, \left(c x\right)^{n} a b + 3 \, \left(c x\right)^{2 \, n} b^{2} + 23 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b + a}}{15 \, n}, \frac{2 \, {\left(15 \, \sqrt{-a} a^{2} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b + a} \sqrt{-a}}{a}\right) + {\left(11 \, \left(c x\right)^{n} a b + 3 \, \left(c x\right)^{2 \, n} b^{2} + 23 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b + a}\right)}}{15 \, n}\right]"," ",0,"[1/15*(15*a^(5/2)*log(((c*x)^n*b - 2*sqrt((c*x)^n*b + a)*sqrt(a) + 2*a)/(c*x)^n) + 2*(11*(c*x)^n*a*b + 3*(c*x)^(2*n)*b^2 + 23*a^2)*sqrt((c*x)^n*b + a))/n, 2/15*(15*sqrt(-a)*a^2*arctan(sqrt((c*x)^n*b + a)*sqrt(-a)/a) + (11*(c*x)^n*a*b + 3*(c*x)^(2*n)*b^2 + 23*a^2)*sqrt((c*x)^n*b + a))/n]","A",0
659,1,130,0,0.970993," ","integrate((a+b*(c*x)^n)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{\frac{3}{2}} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, {\left(\left(c x\right)^{n} b + 4 \, a\right)} \sqrt{\left(c x\right)^{n} b + a}}{3 \, n}, \frac{2 \, {\left(3 \, \sqrt{-a} a \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b + a} \sqrt{-a}}{a}\right) + {\left(\left(c x\right)^{n} b + 4 \, a\right)} \sqrt{\left(c x\right)^{n} b + a}\right)}}{3 \, n}\right]"," ",0,"[1/3*(3*a^(3/2)*log(((c*x)^n*b - 2*sqrt((c*x)^n*b + a)*sqrt(a) + 2*a)/(c*x)^n) + 2*((c*x)^n*b + 4*a)*sqrt((c*x)^n*b + a))/n, 2/3*(3*sqrt(-a)*a*arctan(sqrt((c*x)^n*b + a)*sqrt(-a)/a) + ((c*x)^n*b + 4*a)*sqrt((c*x)^n*b + a))/n]","A",0
660,1,103,0,0.939927," ","integrate((a+b*(c*x)^n)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, \sqrt{\left(c x\right)^{n} b + a}}{n}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b + a} \sqrt{-a}}{a}\right) + \sqrt{\left(c x\right)^{n} b + a}\right)}}{n}\right]"," ",0,"[(sqrt(a)*log(((c*x)^n*b - 2*sqrt((c*x)^n*b + a)*sqrt(a) + 2*a)/(c*x)^n) + 2*sqrt((c*x)^n*b + a))/n, 2*(sqrt(-a)*arctan(sqrt((c*x)^n*b + a)*sqrt(-a)/a) + sqrt((c*x)^n*b + a))/n]","A",0
661,1,78,0,0.716489," ","integrate(1/x/(a+b*(c*x)^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{n}}\right)}{\sqrt{a} n}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b + a} \sqrt{-a}}{a}\right)}{a n}\right]"," ",0,"[log(((c*x)^n*b - 2*sqrt((c*x)^n*b + a)*sqrt(a) + 2*a)/(c*x)^n)/(sqrt(a)*n), 2*sqrt(-a)*arctan(sqrt((c*x)^n*b + a)*sqrt(-a)/a)/(a*n)]","A",0
662,1,164,0,0.889860," ","integrate(1/x/(a+b*(c*x)^n)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(\left(c x\right)^{n} \sqrt{a} b + a^{\frac{3}{2}}\right)} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, \sqrt{\left(c x\right)^{n} b + a} a}{\left(c x\right)^{n} a^{2} b n + a^{3} n}, \frac{2 \, {\left({\left(\left(c x\right)^{n} \sqrt{-a} b + \sqrt{-a} a\right)} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b + a} \sqrt{-a}}{a}\right) + \sqrt{\left(c x\right)^{n} b + a} a\right)}}{\left(c x\right)^{n} a^{2} b n + a^{3} n}\right]"," ",0,"[(((c*x)^n*sqrt(a)*b + a^(3/2))*log(((c*x)^n*b - 2*sqrt((c*x)^n*b + a)*sqrt(a) + 2*a)/(c*x)^n) + 2*sqrt((c*x)^n*b + a)*a)/((c*x)^n*a^2*b*n + a^3*n), 2*(((c*x)^n*sqrt(-a)*b + sqrt(-a)*a)*arctan(sqrt((c*x)^n*b + a)*sqrt(-a)/a) + sqrt((c*x)^n*b + a)*a)/((c*x)^n*a^2*b*n + a^3*n)]","A",0
663,1,262,0,0.925398," ","integrate(1/x/(a+b*(c*x)^n)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, \left(c x\right)^{n} a^{\frac{3}{2}} b + \left(c x\right)^{2 \, n} \sqrt{a} b^{2} + a^{\frac{5}{2}}\right)} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, {\left(3 \, \left(c x\right)^{n} a b + 4 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b + a}}{3 \, {\left(2 \, \left(c x\right)^{n} a^{4} b n + \left(c x\right)^{2 \, n} a^{3} b^{2} n + a^{5} n\right)}}, \frac{2 \, {\left(3 \, {\left(2 \, \left(c x\right)^{n} \sqrt{-a} a b + \left(c x\right)^{2 \, n} \sqrt{-a} b^{2} + \sqrt{-a} a^{2}\right)} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b + a} \sqrt{-a}}{a}\right) + {\left(3 \, \left(c x\right)^{n} a b + 4 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b + a}\right)}}{3 \, {\left(2 \, \left(c x\right)^{n} a^{4} b n + \left(c x\right)^{2 \, n} a^{3} b^{2} n + a^{5} n\right)}}\right]"," ",0,"[1/3*(3*(2*(c*x)^n*a^(3/2)*b + (c*x)^(2*n)*sqrt(a)*b^2 + a^(5/2))*log(((c*x)^n*b - 2*sqrt((c*x)^n*b + a)*sqrt(a) + 2*a)/(c*x)^n) + 2*(3*(c*x)^n*a*b + 4*a^2)*sqrt((c*x)^n*b + a))/(2*(c*x)^n*a^4*b*n + (c*x)^(2*n)*a^3*b^2*n + a^5*n), 2/3*(3*(2*(c*x)^n*sqrt(-a)*a*b + (c*x)^(2*n)*sqrt(-a)*b^2 + sqrt(-a)*a^2)*arctan(sqrt((c*x)^n*b + a)*sqrt(-a)/a) + (3*(c*x)^n*a*b + 4*a^2)*sqrt((c*x)^n*b + a))/(2*(c*x)^n*a^4*b*n + (c*x)^(2*n)*a^3*b^2*n + a^5*n)]","B",0
664,1,169,0,0.925467," ","integrate((-a+b*(c*x)^n)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{-a} a^{2} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b - a} \sqrt{-a} - 2 \, a}{\left(c x\right)^{n}}\right) - 2 \, {\left(11 \, \left(c x\right)^{n} a b - 3 \, \left(c x\right)^{2 \, n} b^{2} - 23 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b - a}}{15 \, n}, -\frac{2 \, {\left(15 \, a^{\frac{5}{2}} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b - a}}{\sqrt{a}}\right) + {\left(11 \, \left(c x\right)^{n} a b - 3 \, \left(c x\right)^{2 \, n} b^{2} - 23 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b - a}\right)}}{15 \, n}\right]"," ",0,"[1/15*(15*sqrt(-a)*a^2*log(((c*x)^n*b - 2*sqrt((c*x)^n*b - a)*sqrt(-a) - 2*a)/(c*x)^n) - 2*(11*(c*x)^n*a*b - 3*(c*x)^(2*n)*b^2 - 23*a^2)*sqrt((c*x)^n*b - a))/n, -2/15*(15*a^(5/2)*arctan(sqrt((c*x)^n*b - a)/sqrt(a)) + (11*(c*x)^n*a*b - 3*(c*x)^(2*n)*b^2 - 23*a^2)*sqrt((c*x)^n*b - a))/n]","A",0
665,1,135,0,0.933748," ","integrate((-a+b*(c*x)^n)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{-a} a \log\left(\frac{\left(c x\right)^{n} b + 2 \, \sqrt{\left(c x\right)^{n} b - a} \sqrt{-a} - 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, \sqrt{\left(c x\right)^{n} b - a} {\left(\left(c x\right)^{n} b - 4 \, a\right)}}{3 \, n}, \frac{2 \, {\left(3 \, a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b - a}}{\sqrt{a}}\right) + \sqrt{\left(c x\right)^{n} b - a} {\left(\left(c x\right)^{n} b - 4 \, a\right)}\right)}}{3 \, n}\right]"," ",0,"[1/3*(3*sqrt(-a)*a*log(((c*x)^n*b + 2*sqrt((c*x)^n*b - a)*sqrt(-a) - 2*a)/(c*x)^n) + 2*sqrt((c*x)^n*b - a)*((c*x)^n*b - 4*a))/n, 2/3*(3*a^(3/2)*arctan(sqrt((c*x)^n*b - a)/sqrt(a)) + sqrt((c*x)^n*b - a)*((c*x)^n*b - 4*a))/n]","A",0
666,1,110,0,0.973067," ","integrate((-a+b*(c*x)^n)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b - a} \sqrt{-a} - 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, \sqrt{\left(c x\right)^{n} b - a}}{n}, -\frac{2 \, {\left(\sqrt{a} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b - a}}{\sqrt{a}}\right) - \sqrt{\left(c x\right)^{n} b - a}\right)}}{n}\right]"," ",0,"[(sqrt(-a)*log(((c*x)^n*b - 2*sqrt((c*x)^n*b - a)*sqrt(-a) - 2*a)/(c*x)^n) + 2*sqrt((c*x)^n*b - a))/n, -2*(sqrt(a)*arctan(sqrt((c*x)^n*b - a)/sqrt(a)) - sqrt((c*x)^n*b - a))/n]","A",0
667,1,80,0,0.654352," ","integrate(1/x/(-a+b*(c*x)^n)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b - a} \sqrt{-a} - 2 \, a}{\left(c x\right)^{n}}\right)}{a n}, \frac{2 \, \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b - a}}{\sqrt{a}}\right)}{\sqrt{a} n}\right]"," ",0,"[-sqrt(-a)*log(((c*x)^n*b - 2*sqrt((c*x)^n*b - a)*sqrt(-a) - 2*a)/(c*x)^n)/(a*n), 2*arctan(sqrt((c*x)^n*b - a)/sqrt(a))/(sqrt(a)*n)]","A",0
668,1,175,0,0.841963," ","integrate(1/x/(-a+b*(c*x)^n)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(\left(c x\right)^{n} \sqrt{-a} b - \sqrt{-a} a\right)} \log\left(\frac{\left(c x\right)^{n} b + 2 \, \sqrt{\left(c x\right)^{n} b - a} \sqrt{-a} - 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, \sqrt{\left(c x\right)^{n} b - a} a}{\left(c x\right)^{n} a^{2} b n - a^{3} n}, -\frac{2 \, {\left({\left(\left(c x\right)^{n} \sqrt{a} b - a^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b - a}}{\sqrt{a}}\right) + \sqrt{\left(c x\right)^{n} b - a} a\right)}}{\left(c x\right)^{n} a^{2} b n - a^{3} n}\right]"," ",0,"[-(((c*x)^n*sqrt(-a)*b - sqrt(-a)*a)*log(((c*x)^n*b + 2*sqrt((c*x)^n*b - a)*sqrt(-a) - 2*a)/(c*x)^n) + 2*sqrt((c*x)^n*b - a)*a)/((c*x)^n*a^2*b*n - a^3*n), -2*(((c*x)^n*sqrt(a)*b - a^(3/2))*arctan(sqrt((c*x)^n*b - a)/sqrt(a)) + sqrt((c*x)^n*b - a)*a)/((c*x)^n*a^2*b*n - a^3*n)]","A",0
669,1,277,0,0.959450," ","integrate(1/x/(-a+b*(c*x)^n)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, \left(c x\right)^{n} \sqrt{-a} a b - \left(c x\right)^{2 \, n} \sqrt{-a} b^{2} - \sqrt{-a} a^{2}\right)} \log\left(\frac{\left(c x\right)^{n} b - 2 \, \sqrt{\left(c x\right)^{n} b - a} \sqrt{-a} - 2 \, a}{\left(c x\right)^{n}}\right) + 2 \, {\left(3 \, \left(c x\right)^{n} a b - 4 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b - a}}{3 \, {\left(2 \, \left(c x\right)^{n} a^{4} b n - \left(c x\right)^{2 \, n} a^{3} b^{2} n - a^{5} n\right)}}, \frac{2 \, {\left(3 \, {\left(2 \, \left(c x\right)^{n} a^{\frac{3}{2}} b - \left(c x\right)^{2 \, n} \sqrt{a} b^{2} - a^{\frac{5}{2}}\right)} \arctan\left(\frac{\sqrt{\left(c x\right)^{n} b - a}}{\sqrt{a}}\right) - {\left(3 \, \left(c x\right)^{n} a b - 4 \, a^{2}\right)} \sqrt{\left(c x\right)^{n} b - a}\right)}}{3 \, {\left(2 \, \left(c x\right)^{n} a^{4} b n - \left(c x\right)^{2 \, n} a^{3} b^{2} n - a^{5} n\right)}}\right]"," ",0,"[-1/3*(3*(2*(c*x)^n*sqrt(-a)*a*b - (c*x)^(2*n)*sqrt(-a)*b^2 - sqrt(-a)*a^2)*log(((c*x)^n*b - 2*sqrt((c*x)^n*b - a)*sqrt(-a) - 2*a)/(c*x)^n) + 2*(3*(c*x)^n*a*b - 4*a^2)*sqrt((c*x)^n*b - a))/(2*(c*x)^n*a^4*b*n - (c*x)^(2*n)*a^3*b^2*n - a^5*n), 2/3*(3*(2*(c*x)^n*a^(3/2)*b - (c*x)^(2*n)*sqrt(a)*b^2 - a^(5/2))*arctan(sqrt((c*x)^n*b - a)/sqrt(a)) - (3*(c*x)^n*a*b - 4*a^2)*sqrt((c*x)^n*b - a))/(2*(c*x)^n*a^4*b*n - (c*x)^(2*n)*a^3*b^2*n - a^5*n)]","A",0
670,1,56,0,0.874099," ","integrate(1/x/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right)}{\sqrt{a}}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right)}{a}\right]"," ",0,"[log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x)/sqrt(a), 2*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a)/a]","A",0
671,1,78,0,0.991164," ","integrate(1/x/(a+b*(c*x)^m)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{\left(c x\right)^{m} b - 2 \, \sqrt{\left(c x\right)^{m} b + a} \sqrt{a} + 2 \, a}{\left(c x\right)^{m}}\right)}{\sqrt{a} m}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{\left(c x\right)^{m} b + a} \sqrt{-a}}{a}\right)}{a m}\right]"," ",0,"[log(((c*x)^m*b - 2*sqrt((c*x)^m*b + a)*sqrt(a) + 2*a)/(c*x)^m)/(sqrt(a)*m), 2*sqrt(-a)*arctan(sqrt((c*x)^m*b + a)*sqrt(-a)/a)/(a*m)]","A",0
672,1,116,0,0.840953," ","integrate(1/x/(a+b*(c*(d*x)^m)^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left({\left(b e^{\left(m n \log\left(d x\right) + n \log\left(c\right)\right)} - 2 \, \sqrt{b e^{\left(m n \log\left(d x\right) + n \log\left(c\right)\right)} + a} \sqrt{a} + 2 \, a\right)} e^{\left(-m n \log\left(d x\right) - n \log\left(c\right)\right)}\right)}{\sqrt{a} m n}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b e^{\left(m n \log\left(d x\right) + n \log\left(c\right)\right)} + a} \sqrt{-a}}{a}\right)}{a m n}\right]"," ",0,"[log((b*e^(m*n*log(d*x) + n*log(c)) - 2*sqrt(b*e^(m*n*log(d*x) + n*log(c)) + a)*sqrt(a) + 2*a)*e^(-m*n*log(d*x) - n*log(c)))/(sqrt(a)*m*n), 2*sqrt(-a)*arctan(sqrt(b*e^(m*n*log(d*x) + n*log(c)) + a)*sqrt(-a)/a)/(a*m*n)]","A",0
673,1,147,0,0.763555," ","integrate(1/x/(a+b*(c*(d*(e*x)^m)^n)^p)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left({\left(b e^{\left(m n p \log\left(e x\right) + n p \log\left(d\right) + p \log\left(c\right)\right)} - 2 \, \sqrt{b e^{\left(m n p \log\left(e x\right) + n p \log\left(d\right) + p \log\left(c\right)\right)} + a} \sqrt{a} + 2 \, a\right)} e^{\left(-m n p \log\left(e x\right) - n p \log\left(d\right) - p \log\left(c\right)\right)}\right)}{\sqrt{a} m n p}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b e^{\left(m n p \log\left(e x\right) + n p \log\left(d\right) + p \log\left(c\right)\right)} + a} \sqrt{-a}}{a}\right)}{a m n p}\right]"," ",0,"[log((b*e^(m*n*p*log(e*x) + n*p*log(d) + p*log(c)) - 2*sqrt(b*e^(m*n*p*log(e*x) + n*p*log(d) + p*log(c)) + a)*sqrt(a) + 2*a)*e^(-m*n*p*log(e*x) - n*p*log(d) - p*log(c)))/(sqrt(a)*m*n*p), 2*sqrt(-a)*arctan(sqrt(b*e^(m*n*p*log(e*x) + n*p*log(d) + p*log(c)) + a)*sqrt(-a)/a)/(a*m*n*p)]","A",0
674,1,182,0,0.719445," ","integrate(1/x/(a+b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left({\left(b e^{\left(m n p q \log\left(f x\right) + n p q \log\left(e\right) + p q \log\left(d\right) + q \log\left(c\right)\right)} - 2 \, \sqrt{b e^{\left(m n p q \log\left(f x\right) + n p q \log\left(e\right) + p q \log\left(d\right) + q \log\left(c\right)\right)} + a} \sqrt{a} + 2 \, a\right)} e^{\left(-m n p q \log\left(f x\right) - n p q \log\left(e\right) - p q \log\left(d\right) - q \log\left(c\right)\right)}\right)}{\sqrt{a} m n p q}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b e^{\left(m n p q \log\left(f x\right) + n p q \log\left(e\right) + p q \log\left(d\right) + q \log\left(c\right)\right)} + a} \sqrt{-a}}{a}\right)}{a m n p q}\right]"," ",0,"[log((b*e^(m*n*p*q*log(f*x) + n*p*q*log(e) + p*q*log(d) + q*log(c)) - 2*sqrt(b*e^(m*n*p*q*log(f*x) + n*p*q*log(e) + p*q*log(d) + q*log(c)) + a)*sqrt(a) + 2*a)*e^(-m*n*p*q*log(f*x) - n*p*q*log(e) - p*q*log(d) - q*log(c)))/(sqrt(a)*m*n*p*q), 2*sqrt(-a)*arctan(sqrt(b*e^(m*n*p*q*log(f*x) + n*p*q*log(e) + p*q*log(d) + q*log(c)) + a)*sqrt(-a)/a)/(a*m*n*p*q)]","A",0
675,1,55,0,0.714560," ","integrate((x^2-1)^3*(-1+1/x^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{48} \, {\left(8 \, x^{6} - 38 \, x^{4} + 87 \, x^{2} + 48\right)} \sqrt{-\frac{x^{2} - 1}{x^{2}}} - \frac{35}{8} \, \arctan\left(\frac{x \sqrt{-\frac{x^{2} - 1}{x^{2}}} - 1}{x}\right)"," ",0,"1/48*(8*x^6 - 38*x^4 + 87*x^2 + 48)*sqrt(-(x^2 - 1)/x^2) - 35/8*arctan((x*sqrt(-(x^2 - 1)/x^2) - 1)/x)","A",0
676,1,50,0,0.589306," ","integrate((x^2-1)^2*(-1+1/x^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{8} \, {\left(2 \, x^{4} - 9 \, x^{2} - 8\right)} \sqrt{-\frac{x^{2} - 1}{x^{2}}} + \frac{15}{4} \, \arctan\left(\frac{x \sqrt{-\frac{x^{2} - 1}{x^{2}}} - 1}{x}\right)"," ",0,"1/8*(2*x^4 - 9*x^2 - 8)*sqrt(-(x^2 - 1)/x^2) + 15/4*arctan((x*sqrt(-(x^2 - 1)/x^2) - 1)/x)","A",0
677,1,43,0,0.582749," ","integrate((x^2-1)*(-1+1/x^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} + 2\right)} \sqrt{-\frac{x^{2} - 1}{x^{2}}} - 3 \, \arctan\left(\frac{x \sqrt{-\frac{x^{2} - 1}{x^{2}}} - 1}{x}\right)"," ",0,"1/2*(x^2 + 2)*sqrt(-(x^2 - 1)/x^2) - 3*arctan((x*sqrt(-(x^2 - 1)/x^2) - 1)/x)","A",0
678,1,12,0,0.577529," ","integrate((-1+1/x^2)^(1/2)/x/(x^2-1),x, algorithm=""fricas"")","\sqrt{-\frac{x^{2} - 1}{x^{2}}}"," ",0,"sqrt(-(x^2 - 1)/x^2)","A",0
679,1,28,0,0.531263," ","integrate((-1+1/x^2)^(1/2)/x/(x^2-1)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, x^{2} - 1\right)} \sqrt{-\frac{x^{2} - 1}{x^{2}}}}{x^{2} - 1}"," ",0,"-(2*x^2 - 1)*sqrt(-(x^2 - 1)/x^2)/(x^2 - 1)","A",0
680,1,38,0,0.543329," ","integrate((-1+1/x^2)^(1/2)/x/(x^2-1)^3,x, algorithm=""fricas"")","\frac{{\left(8 \, x^{4} - 12 \, x^{2} + 3\right)} \sqrt{-\frac{x^{2} - 1}{x^{2}}}}{3 \, {\left(x^{4} - 2 \, x^{2} + 1\right)}}"," ",0,"1/3*(8*x^4 - 12*x^2 + 3)*sqrt(-(x^2 - 1)/x^2)/(x^4 - 2*x^2 + 1)","A",0
681,1,28,0,0.504217," ","integrate(x*(1+1/x^2)^(1/2)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{x^{2} \sqrt{\frac{x^{2} + 1}{x^{2}}} + x^{2} + 1}{x^{2} + 1}"," ",0,"(x^2*sqrt((x^2 + 1)/x^2) + x^2 + 1)/(x^2 + 1)","B",0
682,1,28,0,0.680207," ","integrate(1/x/(x^2+1)/(1+1/x^2)^(1/2),x, algorithm=""fricas"")","\frac{x^{2} \sqrt{\frac{x^{2} + 1}{x^{2}}} + x^{2} + 1}{x^{2} + 1}"," ",0,"(x^2*sqrt((x^2 + 1)/x^2) + x^2 + 1)/(x^2 + 1)","B",0
683,1,67,0,0.575031," ","integrate(x/(a+b*x^2+(b*x^2+a)^(1/2)),x, algorithm=""fricas"")","\frac{2 \, \log\left(b x^{2} + a - 1\right) + \log\left(\frac{b x^{2} + a + 2 \, \sqrt{b x^{2} + a} + 1}{x^{2}}\right) - \log\left(\frac{b x^{2} + a - 2 \, \sqrt{b x^{2} + a} + 1}{x^{2}}\right)}{4 \, b}"," ",0,"1/4*(2*log(b*x^2 + a - 1) + log((b*x^2 + a + 2*sqrt(b*x^2 + a) + 1)/x^2) - log((b*x^2 + a - 2*sqrt(b*x^2 + a) + 1)/x^2))/b","B",0
684,1,32,0,0.806604," ","integrate(x/(x^2-(x^2)^(1/3)),x, algorithm=""fricas"")","-3 \, \log\left(\frac{{\left(x^{2}\right)}^{\frac{1}{3}}}{x}\right) + \frac{3}{4} \, \log\left(-\frac{x^{2} - {\left(x^{2}\right)}^{\frac{1}{3}}}{x^{2}}\right)"," ",0,"-3*log((x^2)^(1/3)/x) + 3/4*log(-(x^2 - (x^2)^(1/3))/x^2)","B",0
685,1,36,0,0.654330," ","integrate(x*(x^2+1)^3*(x^4+2*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{30} \, {\left(3 \, x^{8} + 12 \, x^{6} + 19 \, x^{4} + 14 \, x^{2} + 2\right)} \sqrt{x^{4} + 2 \, x^{2} + 2}"," ",0,"1/30*(3*x^8 + 12*x^6 + 19*x^4 + 14*x^2 + 2)*sqrt(x^4 + 2*x^2 + 2)","A",0
686,1,53,0,0.526595," ","integrate(x^5*(x^9+1)^2*(-x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{2297295} \, {\left(45045 \, x^{24} - 3003 \, x^{21} - 3234 \, x^{18} + 135702 \, x^{15} - 19390 \, x^{12} - 22160 \, x^{9} + 126561 \, x^{6} - 86507 \, x^{3} - 173014\right)} \sqrt{-x^{3} + 1}"," ",0,"2/2297295*(45045*x^24 - 3003*x^21 - 3234*x^18 + 135702*x^15 - 19390*x^12 - 22160*x^9 + 126561*x^6 - 86507*x^3 - 173014)*sqrt(-x^3 + 1)","A",0
687,1,268,0,0.786319," ","integrate(x/(b*x^2+a)^(3/2)+x/(x^2+1)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} x^{2} + a b\right)} \sqrt{a - b} \log\left(\frac{b^{2} x^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} x^{2} - 4 \, {\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{a - b} + 8 \, a^{2} - 8 \, a b + b^{2}}{x^{4} + 2 \, x^{2} + 1}\right) - 4 \, \sqrt{b x^{2} + a} {\left(a - b\right)}}{4 \, {\left(a^{2} b - a b^{2} + {\left(a b^{2} - b^{3}\right)} x^{2}\right)}}, -\frac{{\left(b^{2} x^{2} + a b\right)} \sqrt{-a + b} \arctan\left(-\frac{{\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{-a + b}}{2 \, {\left({\left(a b - b^{2}\right)} x^{2} + a^{2} - a b\right)}}\right) + 2 \, \sqrt{b x^{2} + a} {\left(a - b\right)}}{2 \, {\left(a^{2} b - a b^{2} + {\left(a b^{2} - b^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*((b^2*x^2 + a*b)*sqrt(a - b)*log((b^2*x^4 + 2*(4*a*b - 3*b^2)*x^2 - 4*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(a - b) + 8*a^2 - 8*a*b + b^2)/(x^4 + 2*x^2 + 1)) - 4*sqrt(b*x^2 + a)*(a - b))/(a^2*b - a*b^2 + (a*b^2 - b^3)*x^2), -1/2*((b^2*x^2 + a*b)*sqrt(-a + b)*arctan(-1/2*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(-a + b)/((a*b - b^2)*x^2 + a^2 - a*b)) + 2*sqrt(b*x^2 + a)*(a - b))/(a^2*b - a*b^2 + (a*b^2 - b^3)*x^2)]","B",0
688,1,268,0,0.764090," ","integrate(x*(b*x^2+x^2+a+1)/(x^2+1)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} x^{2} + a b\right)} \sqrt{a - b} \log\left(\frac{b^{2} x^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} x^{2} - 4 \, {\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{a - b} + 8 \, a^{2} - 8 \, a b + b^{2}}{x^{4} + 2 \, x^{2} + 1}\right) - 4 \, \sqrt{b x^{2} + a} {\left(a - b\right)}}{4 \, {\left(a^{2} b - a b^{2} + {\left(a b^{2} - b^{3}\right)} x^{2}\right)}}, -\frac{{\left(b^{2} x^{2} + a b\right)} \sqrt{-a + b} \arctan\left(-\frac{{\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{-a + b}}{2 \, {\left({\left(a b - b^{2}\right)} x^{2} + a^{2} - a b\right)}}\right) + 2 \, \sqrt{b x^{2} + a} {\left(a - b\right)}}{2 \, {\left(a^{2} b - a b^{2} + {\left(a b^{2} - b^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*((b^2*x^2 + a*b)*sqrt(a - b)*log((b^2*x^4 + 2*(4*a*b - 3*b^2)*x^2 - 4*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(a - b) + 8*a^2 - 8*a*b + b^2)/(x^4 + 2*x^2 + 1)) - 4*sqrt(b*x^2 + a)*(a - b))/(a^2*b - a*b^2 + (a*b^2 - b^3)*x^2), -1/2*((b^2*x^2 + a*b)*sqrt(-a + b)*arctan(-1/2*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(-a + b)/((a*b - b^2)*x^2 + a^2 - a*b)) + 2*sqrt(b*x^2 + a)*(a - b))/(a^2*b - a*b^2 + (a*b^2 - b^3)*x^2)]","B",0
689,1,382,0,0.942160," ","integrate(x/(b*x^2+a)^(5/2)+x/(b*x^2+a)^(3/2)+x/(x^2+1)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sqrt{a - b} \log\left(\frac{b^{2} x^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} x^{2} - 4 \, {\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{a - b} + 8 \, a^{2} - 8 \, a b + b^{2}}{x^{4} + 2 \, x^{2} + 1}\right) - 4 \, {\left(3 \, {\left(a b - b^{2}\right)} x^{2} + 3 \, a^{2} - {\left(3 \, a + 1\right)} b + a\right)} \sqrt{b x^{2} + a}}{12 \, {\left({\left(a b^{3} - b^{4}\right)} x^{4} + a^{3} b - a^{2} b^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sqrt{-a + b} \arctan\left(-\frac{{\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{-a + b}}{2 \, {\left({\left(a b - b^{2}\right)} x^{2} + a^{2} - a b\right)}}\right) + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} x^{2} + 3 \, a^{2} - {\left(3 \, a + 1\right)} b + a\right)} \sqrt{b x^{2} + a}}{6 \, {\left({\left(a b^{3} - b^{4}\right)} x^{4} + a^{3} b - a^{2} b^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sqrt(a - b)*log((b^2*x^4 + 2*(4*a*b - 3*b^2)*x^2 - 4*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(a - b) + 8*a^2 - 8*a*b + b^2)/(x^4 + 2*x^2 + 1)) - 4*(3*(a*b - b^2)*x^2 + 3*a^2 - (3*a + 1)*b + a)*sqrt(b*x^2 + a))/((a*b^3 - b^4)*x^4 + a^3*b - a^2*b^2 + 2*(a^2*b^2 - a*b^3)*x^2), -1/6*(3*(b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sqrt(-a + b)*arctan(-1/2*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(-a + b)/((a*b - b^2)*x^2 + a^2 - a*b)) + 2*(3*(a*b - b^2)*x^2 + 3*a^2 - (3*a + 1)*b + a)*sqrt(b*x^2 + a))/((a*b^3 - b^4)*x^4 + a^3*b - a^2*b^2 + 2*(a^2*b^2 - a*b^3)*x^2)]","B",0
690,1,382,0,0.694671," ","integrate(x*(b^2*x^4+b*x^4+2*a*b*x^2+a*x^2+b*x^2+a^2+x^2+a+1)/(x^2+1)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sqrt{a - b} \log\left(\frac{b^{2} x^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} x^{2} - 4 \, {\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{a - b} + 8 \, a^{2} - 8 \, a b + b^{2}}{x^{4} + 2 \, x^{2} + 1}\right) - 4 \, {\left(3 \, {\left(a b - b^{2}\right)} x^{2} + 3 \, a^{2} - {\left(3 \, a + 1\right)} b + a\right)} \sqrt{b x^{2} + a}}{12 \, {\left({\left(a b^{3} - b^{4}\right)} x^{4} + a^{3} b - a^{2} b^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sqrt{-a + b} \arctan\left(-\frac{{\left(b x^{2} + 2 \, a - b\right)} \sqrt{b x^{2} + a} \sqrt{-a + b}}{2 \, {\left({\left(a b - b^{2}\right)} x^{2} + a^{2} - a b\right)}}\right) + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} x^{2} + 3 \, a^{2} - {\left(3 \, a + 1\right)} b + a\right)} \sqrt{b x^{2} + a}}{6 \, {\left({\left(a b^{3} - b^{4}\right)} x^{4} + a^{3} b - a^{2} b^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sqrt(a - b)*log((b^2*x^4 + 2*(4*a*b - 3*b^2)*x^2 - 4*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(a - b) + 8*a^2 - 8*a*b + b^2)/(x^4 + 2*x^2 + 1)) - 4*(3*(a*b - b^2)*x^2 + 3*a^2 - (3*a + 1)*b + a)*sqrt(b*x^2 + a))/((a*b^3 - b^4)*x^4 + a^3*b - a^2*b^2 + 2*(a^2*b^2 - a*b^3)*x^2), -1/6*(3*(b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sqrt(-a + b)*arctan(-1/2*(b*x^2 + 2*a - b)*sqrt(b*x^2 + a)*sqrt(-a + b)/((a*b - b^2)*x^2 + a^2 - a*b)) + 2*(3*(a*b - b^2)*x^2 + 3*a^2 - (3*a + 1)*b + a)*sqrt(b*x^2 + a))/((a*b^3 - b^4)*x^4 + a^3*b - a^2*b^2 + 2*(a^2*b^2 - a*b^3)*x^2)]","B",0
691,1,39,0,1.112108," ","integrate(1/(x+x^(1/2))^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x + \sqrt{x}} + \frac{1}{2} \, \log\left(4 \, \sqrt{x + \sqrt{x}} {\left(2 \, \sqrt{x} + 1\right)} - 8 \, x - 8 \, \sqrt{x} - 1\right)"," ",0,"2*sqrt(x + sqrt(x)) + 1/2*log(4*sqrt(x + sqrt(x))*(2*sqrt(x) + 1) - 8*x - 8*sqrt(x) - 1)","A",0
692,1,49,0,1.895741," ","integrate((x+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(8 \, x + 2 \, \sqrt{x} - 3\right)} \sqrt{x + \sqrt{x}} + \frac{1}{16} \, \log\left(4 \, \sqrt{x + \sqrt{x}} {\left(2 \, \sqrt{x} + 1\right)} + 8 \, x + 8 \, \sqrt{x} + 1\right)"," ",0,"1/12*(8*x + 2*sqrt(x) - 3)*sqrt(x + sqrt(x)) + 1/16*log(4*sqrt(x + sqrt(x))*(2*sqrt(x) + 1) + 8*x + 8*sqrt(x) + 1)","A",0
693,1,16,0,0.631849," ","integrate((-x)^(1/2)*(x+(-x)^(1/2)),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{-x} x^{2} - \frac{1}{2} \, x^{2}"," ",0,"2/5*sqrt(-x)*x^2 - 1/2*x^2","A",0
694,1,86,0,0.738944," ","integrate((5+x^(1/4))/(-6+x),x, algorithm=""fricas"")","-{\left(6^{\frac{1}{4}} - 5\right)} \log\left(2 \cdot 6^{\frac{1}{4}} + 2 \, x^{\frac{1}{4}}\right) + {\left(6^{\frac{1}{4}} + 5\right)} \log\left(-2 \cdot 6^{\frac{1}{4}} + 2 \, x^{\frac{1}{4}}\right) + 4 \cdot 6^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 6^{\frac{3}{4}} \sqrt{\sqrt{6} + \sqrt{x}} - \frac{1}{6} \cdot 6^{\frac{3}{4}} x^{\frac{1}{4}}\right) + 4 \, x^{\frac{1}{4}} + 5 \, \log\left(4 \, \sqrt{6} + 4 \, \sqrt{x}\right)"," ",0,"-(6^(1/4) - 5)*log(2*6^(1/4) + 2*x^(1/4)) + (6^(1/4) + 5)*log(-2*6^(1/4) + 2*x^(1/4)) + 4*6^(1/4)*arctan(1/6*6^(3/4)*sqrt(sqrt(6) + sqrt(x)) - 1/6*6^(3/4)*x^(1/4)) + 4*x^(1/4) + 5*log(4*sqrt(6) + 4*sqrt(x))","B",0
695,1,12,0,1.117937," ","integrate(1/(4-x+(4-x)^(1/2)),x, algorithm=""fricas"")","-2 \, \log\left(\sqrt{-x + 4} + 1\right)"," ",0,"-2*log(sqrt(-x + 4) + 1)","A",0
696,1,63,0,0.970176," ","integrate(1/(1+x-(2+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \log\left(\frac{2 \, x^{2} - \sqrt{5} {\left(x + 3\right)} - {\left(\sqrt{5} {\left(2 \, x + 1\right)} - 5\right)} \sqrt{x + 2} + 7 \, x + 3}{x^{2} + x - 1}\right) + \log\left(x - \sqrt{x + 2} + 1\right)"," ",0,"1/5*sqrt(5)*log((2*x^2 - sqrt(5)*(x + 3) - (sqrt(5)*(2*x + 1) - 5)*sqrt(x + 2) + 7*x + 3)/(x^2 + x - 1)) + log(x - sqrt(x + 2) + 1)","A",0
697,1,32,0,0.613446," ","integrate(1/(4+x+(1+x)^(1/2)),x, algorithm=""fricas"")","-\frac{2}{11} \, \sqrt{11} \arctan\left(\frac{2}{11} \, \sqrt{11} \sqrt{x + 1} + \frac{1}{11} \, \sqrt{11}\right) + \log\left(x + \sqrt{x + 1} + 4\right)"," ",0,"-2/11*sqrt(11)*arctan(2/11*sqrt(11)*sqrt(x + 1) + 1/11*sqrt(11)) + log(x + sqrt(x + 1) + 4)","A",0
698,1,64,0,0.918721," ","integrate(1/(x-(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \log\left(\frac{2 \, x^{2} - \sqrt{5} {\left(x + 2\right)} - {\left(\sqrt{5} {\left(2 \, x - 1\right)} - 5\right)} \sqrt{x + 1} + 3 \, x - 2}{x^{2} - x - 1}\right) + \log\left(x - \sqrt{x + 1}\right)"," ",0,"1/5*sqrt(5)*log((2*x^2 - sqrt(5)*(x + 2) - (sqrt(5)*(2*x - 1) - 5)*sqrt(x + 1) + 3*x - 2)/(x^2 - x - 1)) + log(x - sqrt(x + 1))","A",0
699,1,21,0,0.627265," ","integrate(1/(x-(2+x)^(1/2)),x, algorithm=""fricas"")","\frac{2}{3} \, \log\left(\sqrt{x + 2} + 1\right) + \frac{4}{3} \, \log\left(\sqrt{x + 2} - 2\right)"," ",0,"2/3*log(sqrt(x + 2) + 1) + 4/3*log(sqrt(x + 2) - 2)","A",0
700,1,65,0,0.967075," ","integrate(1/(x-(1-x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \log\left(\frac{2 \, x^{2} + \sqrt{5} {\left(x - 2\right)} - {\left(\sqrt{5} {\left(2 \, x + 1\right)} + 5\right)} \sqrt{-x + 1} - 3 \, x - 2}{x^{2} + x - 1}\right) + \log\left(-x + \sqrt{-x + 1}\right)"," ",0,"1/5*sqrt(5)*log((2*x^2 + sqrt(5)*(x - 2) - (sqrt(5)*(2*x + 1) + 5)*sqrt(-x + 1) - 3*x - 2)/(x^2 + x - 1)) + log(-x + sqrt(-x + 1))","A",0
701,1,51,0,1.281026," ","integrate((1+x+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(8 \, x + 2 \, \sqrt{x} + 5\right)} \sqrt{x + \sqrt{x} + 1} + \frac{3}{16} \, \log\left(4 \, \sqrt{x + \sqrt{x} + 1} {\left(2 \, \sqrt{x} + 1\right)} - 8 \, x - 8 \, \sqrt{x} - 5\right)"," ",0,"1/12*(8*x + 2*sqrt(x) + 5)*sqrt(x + sqrt(x) + 1) + 3/16*log(4*sqrt(x + sqrt(x) + 1)*(2*sqrt(x) + 1) - 8*x - 8*sqrt(x) - 5)","A",0
702,1,61,0,1.466038," ","integrate((1+x+(1+x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(8 \, x + 2 \, \sqrt{x + 1} + 5\right)} \sqrt{x + \sqrt{x + 1} + 1} + \frac{1}{16} \, \log\left(-4 \, \sqrt{x + \sqrt{x + 1} + 1} {\left(2 \, \sqrt{x + 1} + 1\right)} - 8 \, x - 8 \, \sqrt{x + 1} - 9\right)"," ",0,"1/12*(8*x + 2*sqrt(x + 1) + 5)*sqrt(x + sqrt(x + 1) + 1) + 1/16*log(-4*sqrt(x + sqrt(x + 1) + 1)*(2*sqrt(x + 1) + 1) - 8*x - 8*sqrt(x + 1) - 9)","A",0
703,1,59,0,1.523881," ","integrate((x+(-1+x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(8 \, x + 2 \, \sqrt{x - 1} - 3\right)} \sqrt{x + \sqrt{x - 1}} + \frac{3}{16} \, \log\left(-4 \, \sqrt{x + \sqrt{x - 1}} {\left(2 \, \sqrt{x - 1} + 1\right)} + 8 \, x + 8 \, \sqrt{x - 1} - 3\right)"," ",0,"1/12*(8*x + 2*sqrt(x - 1) - 3)*sqrt(x + sqrt(x - 1)) + 3/16*log(-4*sqrt(x + sqrt(x - 1))*(2*sqrt(x - 1) + 1) + 8*x + 8*sqrt(x - 1) - 3)","A",0
704,1,73,0,1.393986," ","integrate((2*x+(-1+2*x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(16 \, x + 2 \, \sqrt{2 \, x - 1} - 3\right)} \sqrt{2 \, x + \sqrt{2 \, x - 1}} + \frac{3}{32} \, \log\left(-4 \, \sqrt{2 \, x + \sqrt{2 \, x - 1}} {\left(2 \, \sqrt{2 \, x - 1} + 1\right)} + 16 \, x + 8 \, \sqrt{2 \, x - 1} - 3\right)"," ",0,"1/24*(16*x + 2*sqrt(2*x - 1) - 3)*sqrt(2*x + sqrt(2*x - 1)) + 3/32*log(-4*sqrt(2*x + sqrt(2*x - 1))*(2*sqrt(2*x - 1) + 1) + 16*x + 8*sqrt(2*x - 1) - 3)","A",0
705,1,101,0,3.103854," ","integrate((3*x+(-7+8*x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{18} \, {\left(12 \, x + \sqrt{8 \, x - 7} - 4\right)} \sqrt{3 \, x + \sqrt{8 \, x - 7}} + \frac{47}{864} \, \sqrt{6} \log\left(-41472 \, x^{2} - 192 \, {\left(144 \, x - 47\right)} \sqrt{8 \, x - 7} + 8 \, {\left(3 \, \sqrt{6} {\left(144 \, x + 17\right)} \sqrt{8 \, x - 7} + 4 \, \sqrt{6} {\left(432 \, x - 299\right)}\right)} \sqrt{3 \, x + \sqrt{8 \, x - 7}} - 9792 \, x + 30047\right)"," ",0,"1/18*(12*x + sqrt(8*x - 7) - 4)*sqrt(3*x + sqrt(8*x - 7)) + 47/864*sqrt(6)*log(-41472*x^2 - 192*(144*x - 47)*sqrt(8*x - 7) + 8*(3*sqrt(6)*(144*x + 17)*sqrt(8*x - 7) + 4*sqrt(6)*(432*x - 299))*sqrt(3*x + sqrt(8*x - 7)) - 9792*x + 30047)","A",0
706,1,47,0,2.119333," ","integrate(1/(x+(1+x)^(1/2))^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x + \sqrt{x + 1}} + \frac{1}{2} \, \log\left(4 \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} + 1\right)} - 8 \, x - 8 \, \sqrt{x + 1} - 5\right)"," ",0,"2*sqrt(x + sqrt(x + 1)) + 1/2*log(4*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) + 1) - 8*x - 8*sqrt(x + 1) - 5)","A",0
707,1,48,0,0.629042," ","integrate((1+x)/(4+x+(-9+6*x)^(1/2)),x, algorithm=""fricas"")","4 \, \sqrt{6} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{6 \, x - 9} + \frac{1}{4} \, \sqrt{6}\right) + x - 2 \, \sqrt{6 \, x - 9} + 3 \, \log\left(x + \sqrt{6 \, x - 9} + 4\right)"," ",0,"4*sqrt(6)*arctan(1/12*sqrt(6)*sqrt(6*x - 9) + 1/4*sqrt(6)) + x - 2*sqrt(6*x - 9) + 3*log(x + sqrt(6*x - 9) + 4)","A",0
708,1,59,0,0.771418," ","integrate((12-x)/(4+x+(-9+6*x)^(1/2)),x, algorithm=""fricas"")","-\frac{21}{2} \, \sqrt{3} \sqrt{2} \arctan\left(\frac{1}{12} \, \sqrt{3} \sqrt{2} \sqrt{6 \, x - 9} + \frac{1}{4} \, \sqrt{3} \sqrt{2}\right) - x + 2 \, \sqrt{6 \, x - 9} + 10 \, \log\left(x + \sqrt{6 \, x - 9} + 4\right)"," ",0,"-21/2*sqrt(3)*sqrt(2)*arctan(1/12*sqrt(3)*sqrt(2)*sqrt(6*x - 9) + 1/4*sqrt(3)*sqrt(2)) - x + 2*sqrt(6*x - 9) + 10*log(x + sqrt(6*x - 9) + 4)","A",0
709,1,23,0,0.731622," ","integrate((x^3-1)/(x^2+1)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, x^{\frac{3}{2}} - \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)}}{2 \, \sqrt{x}}\right)"," ",0,"2/3*x^(3/2) - sqrt(2)*arctan(1/2*sqrt(2)*(x - 1)/sqrt(x))","A",0
710,1,37,0,1.294519," ","integrate(1/2/(-1+x)^(1/2)/(x-(-1+x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(4 \, \sqrt{x - \sqrt{x - 1}} {\left(2 \, \sqrt{x - 1} - 1\right)} + 8 \, x - 8 \, \sqrt{x - 1} - 3\right)"," ",0,"1/2*log(4*sqrt(x - sqrt(x - 1))*(2*sqrt(x - 1) - 1) + 8*x - 8*sqrt(x - 1) - 3)","B",0
711,1,29,0,0.698307," ","integrate((1+x^(7/2))/(-x^2+1),x, algorithm=""fricas"")","-\frac{2}{5} \, {\left(x^{2} + 5\right)} \sqrt{x} + \arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(x + 1\right) - \log\left(\sqrt{x} - 1\right)"," ",0,"-2/5*(x^2 + 5)*sqrt(x) + arctan(sqrt(x)) + 1/2*log(x + 1) - log(sqrt(x) - 1)","A",0
712,1,76,0,0.640949," ","integrate((4+2*x)/((-1+2*x)^(1/3)+(-1+2*x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(2 \, x + 17\right)} \sqrt{2 \, x - 1} - \frac{3}{8} \, {\left(2 \, x + 23\right)} {\left(2 \, x - 1\right)}^{\frac{1}{3}} + \frac{3}{7} \, {\left(2 \, x + 41\right)} {\left(2 \, x - 1\right)}^{\frac{1}{6}} - x + \frac{3}{5} \, {\left(2 \, x - 1\right)}^{\frac{5}{6}} - \frac{3}{4} \, {\left(2 \, x - 1\right)}^{\frac{2}{3}} - 18 \, \log\left({\left(2 \, x - 1\right)}^{\frac{1}{6}} + 1\right)"," ",0,"1/3*(2*x + 17)*sqrt(2*x - 1) - 3/8*(2*x + 23)*(2*x - 1)^(1/3) + 3/7*(2*x + 41)*(2*x - 1)^(1/6) - x + 3/5*(2*x - 1)^(5/6) - 3/4*(2*x - 1)^(2/3) - 18*log((2*x - 1)^(1/6) + 1)","A",0
713,1,35,0,0.996818," ","integrate(1/(2+(1+x^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{8}{105} \, {\left({\left(15 \, \sqrt{x} + 76\right)} \sqrt{\sqrt{x} + 1} - 36 \, \sqrt{x} - 280\right)} \sqrt{\sqrt{\sqrt{x} + 1} + 2}"," ",0,"8/105*((15*sqrt(x) + 76)*sqrt(sqrt(x) + 1) - 36*sqrt(x) - 280)*sqrt(sqrt(sqrt(x) + 1) + 2)","A",0
714,1,39,0,0.652058," ","integrate((2+(4+x^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{8}{315} \, {\left(2 \, {\left(5 \, \sqrt{x} - 32\right)} \sqrt{\sqrt{x} + 4} + 35 \, x + 4 \, \sqrt{x} - 128\right)} \sqrt{\sqrt{\sqrt{x} + 4} + 2}"," ",0,"8/315*(2*(5*sqrt(x) - 32)*sqrt(sqrt(x) + 4) + 35*x + 4*sqrt(x) - 128)*sqrt(sqrt(sqrt(x) + 4) + 2)","A",0
715,1,57,0,0.708632," ","integrate((2-(4+(-9+5*x)^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{8}{1575} \, {\left(2 \, {\left(5 \, \sqrt{5 \, x - 9} - 32\right)} \sqrt{\sqrt{5 \, x - 9} + 4} - 175 \, x - 4 \, \sqrt{5 \, x - 9} + 443\right)} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2}"," ",0,"-8/1575*(2*(5*sqrt(5*x - 9) - 32)*sqrt(sqrt(5*x - 9) + 4) - 175*x - 4*sqrt(5*x - 9) + 443)*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2)","A",0
716,1,35,0,0.909800," ","integrate(1/(2+(1+x^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{8}{105} \, {\left({\left(15 \, \sqrt{x} + 76\right)} \sqrt{\sqrt{x} + 1} - 36 \, \sqrt{x} - 280\right)} \sqrt{\sqrt{\sqrt{x} + 1} + 2}"," ",0,"8/105*((15*sqrt(x) + 76)*sqrt(sqrt(x) + 1) - 36*sqrt(x) - 280)*sqrt(sqrt(sqrt(x) + 1) + 2)","A",0
717,1,76,0,0.829335," ","integrate((1+(1+(1+x^(1/2))^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{16}{765765} \, {\left({\left(231 \, \sqrt{x} - 1304\right)} \sqrt{\sqrt{x} + 1} + {\left({\left(3003 \, \sqrt{x} - 4672\right)} \sqrt{\sqrt{x} + 1} - 3528 \, \sqrt{x} + 8752\right)} \sqrt{\sqrt{\sqrt{x} + 1} + 1} + 45045 \, x + 4613 \, \sqrt{x} - 28152\right)} \sqrt{\sqrt{\sqrt{\sqrt{x} + 1} + 1} + 1}"," ",0,"16/765765*((231*sqrt(x) - 1304)*sqrt(sqrt(x) + 1) + ((3003*sqrt(x) - 4672)*sqrt(sqrt(x) + 1) - 3528*sqrt(x) + 8752)*sqrt(sqrt(sqrt(x) + 1) + 1) + 45045*x + 4613*sqrt(x) - 28152)*sqrt(sqrt(sqrt(sqrt(x) + 1) + 1) + 1)","A",0
718,1,85,0,0.490601," ","integrate((2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{8}{255255} \, {\left({\left(847 \, \sqrt{x} - 1688\right)} \sqrt{2 \, \sqrt{x} - 1} - 2 \, {\left({\left(1001 \, \sqrt{x} + 6800\right)} \sqrt{2 \, \sqrt{x} - 1} - 2352 \, \sqrt{x} - 29712\right)} \sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} - 30030 \, x + 3843 \, \sqrt{x} + 124080\right)} \sqrt{\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2}"," ",0,"-8/255255*((847*sqrt(x) - 1688)*sqrt(2*sqrt(x) - 1) - 2*((1001*sqrt(x) + 6800)*sqrt(2*sqrt(x) - 1) - 2352*sqrt(x) - 29712)*sqrt(sqrt(2*sqrt(x) - 1) + 3) - 30030*x + 3843*sqrt(x) + 124080)*sqrt(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)","A",0
719,1,62,0,0.833592," ","integrate(x*(1+(1+(-1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{8}{255255} \, {\left(15015 \, x^{2} + {\left(77 \, x + 1032\right)} \sqrt{x - 1} + {\left({\left(1001 \, x + 4544\right)} \sqrt{x - 1} - 1176 \, x - 7696\right)} \sqrt{\sqrt{x - 1} + 1} - 1799 \, x - 22088\right)} \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}"," ",0,"8/255255*(15015*x^2 + (77*x + 1032)*sqrt(x - 1) + ((1001*x + 4544)*sqrt(x - 1) - 1176*x - 7696)*sqrt(sqrt(x - 1) + 1) - 1799*x - 22088)*sqrt(sqrt(sqrt(x - 1) + 1) + 1)","A",0
720,1,35,0,1.308645," ","integrate(1/(-1+x)^(1/2)/(x-(-1+x)^(1/2))^(1/2),x, algorithm=""fricas"")","\log\left(4 \, \sqrt{x - \sqrt{x - 1}} {\left(2 \, \sqrt{x - 1} - 1\right)} + 8 \, x - 8 \, \sqrt{x - 1} - 3\right)"," ",0,"log(4*sqrt(x - sqrt(x - 1))*(2*sqrt(x - 1) - 1) + 8*x - 8*sqrt(x - 1) - 3)","B",0
721,1,85,0,1.791526," ","integrate(1/(1+x+(-1+2*x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-8 \, x^{2} - 8 \, {\left(2 \, x + 1\right)} \sqrt{2 \, x - 1} + 2 \, {\left(\sqrt{2} {\left(2 \, x + 3\right)} \sqrt{2 \, x - 1} + \sqrt{2} {\left(6 \, x - 1\right)}\right)} \sqrt{x + \sqrt{2 \, x - 1} + 1} - 24 \, x + 7\right) + 2 \, \sqrt{x + \sqrt{2 \, x - 1} + 1}"," ",0,"1/4*sqrt(2)*log(-8*x^2 - 8*(2*x + 1)*sqrt(2*x - 1) + 2*(sqrt(2)*(2*x + 3)*sqrt(2*x - 1) + sqrt(2)*(6*x - 1))*sqrt(x + sqrt(2*x - 1) + 1) - 24*x + 7) + 2*sqrt(x + sqrt(2*x - 1) + 1)","B",0
722,1,45,0,0.589251," ","integrate((p*x+q)/(a*x+b)^(1/2)/(f+(a*x+b)^(1/2)),x, algorithm=""fricas"")","\frac{a p x - 2 \, \sqrt{a x + b} f p + 2 \, {\left({\left(f^{2} - b\right)} p + a q\right)} \log\left(f + \sqrt{a x + b}\right)}{a^{2}}"," ",0,"(a*p*x - 2*sqrt(a*x + b)*f*p + 2*((f^2 - b)*p + a*q)*log(f + sqrt(a*x + b)))/a^2","A",0
723,1,84,0,2.059221," ","integrate((1-x-x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(8 \, x + 2 \, \sqrt{x} - 11\right)} \sqrt{-x - \sqrt{x} + 1} + \frac{5}{16} \, \arctan\left(-\frac{{\left(8 \, x^{2} - {\left(16 \, x^{2} - 38 \, x + 11\right)} \sqrt{x} - 9 \, x + 3\right)} \sqrt{-x - \sqrt{x} + 1}}{4 \, {\left(4 \, x^{3} - 13 \, x^{2} + 7 \, x - 1\right)}}\right)"," ",0,"1/12*(8*x + 2*sqrt(x) - 11)*sqrt(-x - sqrt(x) + 1) + 5/16*arctan(-1/4*(8*x^2 - (16*x^2 - 38*x + 11)*sqrt(x) - 9*x + 3)*sqrt(-x - sqrt(x) + 1)/(4*x^3 - 13*x^2 + 7*x - 1))","A",0
724,1,15,0,1.191830," ","integrate((9+x+6*x^(1/2))/(x+4*x^(1/2)),x, algorithm=""fricas"")","x + 4 \, \sqrt{x} + 2 \, \log\left(\sqrt{x} + 4\right)"," ",0,"x + 4*sqrt(x) + 2*log(sqrt(x) + 4)","A",0
725,1,49,0,0.590795," ","integrate((6-8*x^(7/2))/(5-9*x^(1/2)),x, algorithm=""fricas"")","\frac{2}{9} \, x^{4} + \frac{200}{2187} \, x^{3} + \frac{2500}{59049} \, x^{2} + \frac{4}{301327047} \, {\left(10628820 \, x^{3} + 4592700 \, x^{2} + 2362500 \, x - 98254849\right)} \sqrt{x} + \frac{125000}{4782969} \, x - \frac{280728140}{387420489} \, \log\left(9 \, \sqrt{x} - 5\right)"," ",0,"2/9*x^4 + 200/2187*x^3 + 2500/59049*x^2 + 4/301327047*(10628820*x^3 + 4592700*x^2 + 2362500*x - 98254849)*sqrt(x) + 125000/4782969*x - 280728140/387420489*log(9*sqrt(x) - 5)","A",0
726,1,302,0,0.599030," ","integrate((x^3+1)*(1+x)^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) + \frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(-2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} - \sqrt{2} - 1\right) - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{-2 \cdot 8^{\frac{1}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + \sqrt{2} + 1\right) + \frac{2}{15} \, {\left(3 \, x^{2} + x - 17\right)} \sqrt{x + 1}"," ",0,"-1/8*8^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) + 1/8*8^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(-2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) - 1/2*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2) + 4)*arctan(1/16*8^(3/4)*sqrt(2)*sqrt(2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*sqrt(2*sqrt(2) + 4) - 1/8*8^(3/4)*sqrt(2)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) - sqrt(2) - 1) - 1/2*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2) + 4)*arctan(1/16*8^(3/4)*sqrt(2)*sqrt(-2*8^(1/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*sqrt(2*sqrt(2) + 4) - 1/8*8^(3/4)*sqrt(2)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + sqrt(2) + 1) + 2/15*(3*x^2 + x - 17)*sqrt(x + 1)","B",0
727,1,87,0,6.642457," ","integrate((-1+x-x^(1/2))^(1/2)/(-1+x)/x^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{{\left({\left(x - 4\right)} \sqrt{x} - 2 \, x + 3\right)} \sqrt{x - \sqrt{x} - 1}}{2 \, {\left(x^{2} - 3 \, x + 1\right)}}\right) + \log\left(-\frac{8 \, x^{2} + 2 \, {\left({\left(4 \, x - 5\right)} \sqrt{x} + 2 \, x - 1\right)} \sqrt{x - \sqrt{x} - 1} - 17 \, x - 2 \, \sqrt{x} + 11}{x - 1}\right)"," ",0,"-arctan(1/2*((x - 4)*sqrt(x) - 2*x + 3)*sqrt(x - sqrt(x) - 1)/(x^2 - 3*x + 1)) + log(-(8*x^2 + 2*((4*x - 5)*sqrt(x) + 2*x - 1)*sqrt(x - sqrt(x) - 1) - 17*x - 2*sqrt(x) + 11)/(x - 1))","A",0
728,1,62,0,4.390028," ","integrate((1+2*(1+x)^(1/2))/x/(1+x)^(1/2)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""fricas"")","\arctan\left(\frac{2 \, \sqrt{x + \sqrt{x + 1}} {\left(\sqrt{x + 1} - 3\right)}}{x - 8}\right) + 3 \, \log\left(\frac{2 \, \sqrt{x + \sqrt{x + 1}} {\left(\sqrt{x + 1} + 1\right)} - 3 \, x - 2 \, \sqrt{x + 1} - 2}{x}\right)"," ",0,"arctan(2*sqrt(x + sqrt(x + 1))*(sqrt(x + 1) - 3)/(x - 8)) + 3*log((2*sqrt(x + sqrt(x + 1))*(sqrt(x + 1) + 1) - 3*x - 2*sqrt(x + 1) - 2)/x)","A",0
729,1,18,0,0.665213," ","integrate(1/x^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","-\log\left(2 \, \sqrt{x + 1} \sqrt{x} - 2 \, x - 1\right)"," ",0,"-log(2*sqrt(x + 1)*sqrt(x) - 2*x - 1)","B",0
730,1,27,0,0.647942," ","integrate((x/(1+x))^(1/2)/x,x, algorithm=""fricas"")","\log\left(\sqrt{\frac{x}{x + 1}} + 1\right) - \log\left(\sqrt{\frac{x}{x + 1}} - 1\right)"," ",0,"log(sqrt(x/(x + 1)) + 1) - log(sqrt(x/(x + 1)) - 1)","B",0
731,1,28,0,0.614078," ","integrate(x^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\sqrt{x + 1} \sqrt{x} + \frac{1}{2} \, \log\left(2 \, \sqrt{x + 1} \sqrt{x} - 2 \, x - 1\right)"," ",0,"sqrt(x + 1)*sqrt(x) + 1/2*log(2*sqrt(x + 1)*sqrt(x) - 2*x - 1)","A",0
732,1,42,0,0.752464," ","integrate((x/(1+x))^(1/2),x, algorithm=""fricas"")","{\left(x + 1\right)} \sqrt{\frac{x}{x + 1}} - \frac{1}{2} \, \log\left(\sqrt{\frac{x}{x + 1}} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{\frac{x}{x + 1}} - 1\right)"," ",0,"(x + 1)*sqrt(x/(x + 1)) - 1/2*log(sqrt(x/(x + 1)) + 1) + 1/2*log(sqrt(x/(x + 1)) - 1)","B",0
733,1,39,0,0.787084," ","integrate((-1+x)^(1/2)/x^2/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, x \arctan\left(\sqrt{x + 1} \sqrt{x - 1} - x\right) - \sqrt{x + 1} \sqrt{x - 1} - x}{x}"," ",0,"(2*x*arctan(sqrt(x + 1)*sqrt(x - 1) - x) - sqrt(x + 1)*sqrt(x - 1) - x)/x","A",0
734,1,36,0,0.786926," ","integrate(((-1+x)/(1+x))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, x \arctan\left(\sqrt{\frac{x - 1}{x + 1}}\right) - {\left(x + 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x}"," ",0,"(2*x*arctan(sqrt((x - 1)/(x + 1))) - (x + 1)*sqrt((x - 1)/(x + 1)))/x","A",0
735,1,46,0,0.987890," ","integrate(x^3*(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(6 \, x^{3} - 8 \, x^{2} + 9 \, x - 16\right)} \sqrt{x + 1} \sqrt{x - 1} - \frac{3}{8} \, \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"1/24*(6*x^3 - 8*x^2 + 9*x - 16)*sqrt(x + 1)*sqrt(x - 1) - 3/8*log(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
736,1,64,0,0.705180," ","integrate(x^3*((-1+x)/(1+x))^(1/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(6 \, x^{4} - 2 \, x^{3} + x^{2} - 7 \, x - 16\right)} \sqrt{\frac{x - 1}{x + 1}} + \frac{3}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{3}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"1/24*(6*x^4 - 2*x^3 + x^2 - 7*x - 16)*sqrt((x - 1)/(x + 1)) + 3/8*log(sqrt((x - 1)/(x + 1)) + 1) - 3/8*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
737,1,13,0,2.000169," ","integrate((-x/(1+x))^(1/2)/x,x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{-\frac{x}{x + 1}}\right)"," ",0,"2*arctan(sqrt(-x/(x + 1)))","A",0
738,1,15,0,0.913600," ","integrate(((1-x)/(1+x))^(1/2)/(-1+x),x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{-\frac{x - 1}{x + 1}}\right)"," ",0,"2*arctan(sqrt(-(x - 1)/(x + 1)))","A",0
739,1,24,0,0.620387," ","integrate(((b*x+a)/(-b*x+c))^(1/2)/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(\sqrt{-\frac{b x + a}{b x - c}}\right)}{b}"," ",0,"2*arctan(sqrt(-(b*x + a)/(b*x - c)))/b","A",0
740,1,105,0,2.265082," ","integrate(((b*x+a)/(d*x+c))^(1/2)/(b*x+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b d} \log\left(2 \, b d x + b c + a d + 2 \, \sqrt{b d} {\left(d x + c\right)} \sqrt{\frac{b x + a}{d x + c}}\right)}{b d}, -\frac{2 \, \sqrt{-b d} \arctan\left(\frac{\sqrt{-b d} {\left(d x + c\right)} \sqrt{\frac{b x + a}{d x + c}}}{b d x + a d}\right)}{b d}\right]"," ",0,"[sqrt(b*d)*log(2*b*d*x + b*c + a*d + 2*sqrt(b*d)*(d*x + c)*sqrt((b*x + a)/(d*x + c)))/(b*d), -2*sqrt(-b*d)*arctan(sqrt(-b*d)*(d*x + c)*sqrt((b*x + a)/(d*x + c))/(b*d*x + a*d))/(b*d)]","A",0
741,1,28,0,0.595247," ","integrate((-x/(1+x))^(1/2),x, algorithm=""fricas"")","{\left(x + 1\right)} \sqrt{-\frac{x}{x + 1}} - \arctan\left(\sqrt{-\frac{x}{x + 1}}\right)"," ",0,"(x + 1)*sqrt(-x/(x + 1)) - arctan(sqrt(-x/(x + 1)))","A",0
742,1,32,0,0.516358," ","integrate(((1-x)/(1+x))^(1/2),x, algorithm=""fricas"")","{\left(x + 1\right)} \sqrt{-\frac{x - 1}{x + 1}} - 2 \, \arctan\left(\sqrt{-\frac{x - 1}{x + 1}}\right)"," ",0,"(x + 1)*sqrt(-(x - 1)/(x + 1)) - 2*arctan(sqrt(-(x - 1)/(x + 1)))","A",0
743,1,38,0,0.697743," ","integrate(((a+x)/(a-x))^(1/2),x, algorithm=""fricas"")","2 \, a \arctan\left(\sqrt{\frac{a + x}{a - x}}\right) - {\left(a - x\right)} \sqrt{\frac{a + x}{a - x}}"," ",0,"2*a*arctan(sqrt((a + x)/(a - x))) - (a - x)*sqrt((a + x)/(a - x))","A",0
744,1,58,0,0.662416," ","integrate(((-a+x)/(a+x))^(1/2),x, algorithm=""fricas"")","-a \log\left(\sqrt{-\frac{a - x}{a + x}} + 1\right) + a \log\left(\sqrt{-\frac{a - x}{a + x}} - 1\right) + {\left(a + x\right)} \sqrt{-\frac{a - x}{a + x}}"," ",0,"-a*log(sqrt(-(a - x)/(a + x)) + 1) + a*log(sqrt(-(a - x)/(a + x)) - 1) + (a + x)*sqrt(-(a - x)/(a + x))","A",0
745,1,180,0,0.623165," ","integrate(((b*x+a)/(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c - a d\right)} \sqrt{b d} \log\left(2 \, b d x + b c + a d + 2 \, \sqrt{b d} {\left(d x + c\right)} \sqrt{\frac{b x + a}{d x + c}}\right) - 2 \, {\left(b d^{2} x + b c d\right)} \sqrt{\frac{b x + a}{d x + c}}}{2 \, b d^{2}}, \frac{{\left(b c - a d\right)} \sqrt{-b d} \arctan\left(\frac{\sqrt{-b d} {\left(d x + c\right)} \sqrt{\frac{b x + a}{d x + c}}}{b d x + a d}\right) + {\left(b d^{2} x + b c d\right)} \sqrt{\frac{b x + a}{d x + c}}}{b d^{2}}\right]"," ",0,"[-1/2*((b*c - a*d)*sqrt(b*d)*log(2*b*d*x + b*c + a*d + 2*sqrt(b*d)*(d*x + c)*sqrt((b*x + a)/(d*x + c))) - 2*(b*d^2*x + b*c*d)*sqrt((b*x + a)/(d*x + c)))/(b*d^2), ((b*c - a*d)*sqrt(-b*d)*arctan(sqrt(-b*d)*(d*x + c)*sqrt((b*x + a)/(d*x + c))/(b*d*x + a*d)) + (b*d^2*x + b*c*d)*sqrt((b*x + a)/(d*x + c)))/(b*d^2)]","A",0
746,1,54,0,0.638749," ","integrate(((-1+x)/(5+3*x))^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(3 \, x + 5\right)} \sqrt{\frac{x - 1}{3 \, x + 5}} + \frac{4}{9} \, \sqrt{3} \log\left(\sqrt{3} {\left(3 \, x + 5\right)} \sqrt{\frac{x - 1}{3 \, x + 5}} - 3 \, x - 1\right)"," ",0,"1/3*(3*x + 5)*sqrt((x - 1)/(3*x + 5)) + 4/9*sqrt(3)*log(sqrt(3)*(3*x + 5)*sqrt((x - 1)/(3*x + 5)) - 3*x - 1)","A",0
747,1,46,0,0.484963," ","integrate(((-1+5*x)/(1+7*x))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{12 \, x \arctan\left(\sqrt{\frac{5 \, x - 1}{7 \, x + 1}}\right) - {\left(7 \, x + 1\right)} \sqrt{\frac{5 \, x - 1}{7 \, x + 1}}}{x}"," ",0,"(12*x*arctan(sqrt((5*x - 1)/(7*x + 1))) - (7*x + 1)*sqrt((5*x - 1)/(7*x + 1)))/x","A",0
748,1,17,0,0.598331," ","integrate(x/(1+x)/((1-x)/(1+x))^(1/2),x, algorithm=""fricas"")","-{\left(x + 1\right)} \sqrt{-\frac{x - 1}{x + 1}}"," ",0,"-(x + 1)*sqrt(-(x - 1)/(x + 1))","A",0
749,1,17,0,0.510255," ","integrate(x/(1+x)/(-1+2/(1+x))^(1/2),x, algorithm=""fricas"")","-{\left(x + 1\right)} \sqrt{-\frac{x - 1}{x + 1}}"," ",0,"-(x + 1)*sqrt(-(x - 1)/(x + 1))","A",0
750,1,83,0,0.637258," ","integrate(x/(1+x)/((2+x)/(3+x))^(1/2),x, algorithm=""fricas"")","{\left(x + 3\right)} \sqrt{\frac{x + 2}{x + 3}} + \sqrt{2} \log\left(\frac{2 \, \sqrt{2} {\left(x + 3\right)} \sqrt{\frac{x + 2}{x + 3}} + 3 \, x + 7}{x + 1}\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{x + 2}{x + 3}} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{\frac{x + 2}{x + 3}} - 1\right)"," ",0,"(x + 3)*sqrt((x + 2)/(x + 3)) + sqrt(2)*log((2*sqrt(2)*(x + 3)*sqrt((x + 2)/(x + 3)) + 3*x + 7)/(x + 1)) - 1/2*log(sqrt((x + 2)/(x + 3)) + 1) + 1/2*log(sqrt((x + 2)/(x + 3)) - 1)","B",0
751,1,17,0,0.782000," ","integrate((1+1/x)^(1/2)/(1+x)^2,x, algorithm=""fricas"")","\frac{2 \, x \sqrt{\frac{x + 1}{x}}}{x + 1}"," ",0,"2*x*sqrt((x + 1)/x)/(x + 1)","A",0
752,1,34,0,0.759994," ","integrate((1+1/x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{2 \, \sqrt{-x^{2} + 1} x \sqrt{\frac{x + 1}{x}}}{2 \, x^{2} + x - 1}\right)"," ",0,"-arctan(2*sqrt(-x^2 + 1)*x*sqrt((x + 1)/x)/(2*x^2 + x - 1))","A",0
753,1,372,0,0.812725," ","integrate(1/(x+(-x^2-2*x+3)^(1/2)),x, algorithm=""fricas"")","\frac{1}{56} \, \sqrt{7} \log\left(\frac{24 \, x^{4} + 62 \, x^{3} - 153 \, x^{2} + 2 \, \sqrt{7} {\left(3 \, x^{4} + x^{3} - 45 \, x^{2} + 45 \, x\right)} - {\left(14 \, x^{3} - 84 \, x^{2} + \sqrt{7} {\left(8 \, x^{3} - 30 \, x^{2} + 27 \, x - 27\right)} + 126 \, x\right)} \sqrt{-x^{2} - 2 \, x + 3} + 180 \, x - 135}{4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9}\right) + \frac{1}{56} \, \sqrt{7} \log\left(\frac{24 \, x^{4} + 62 \, x^{3} - 153 \, x^{2} - 2 \, \sqrt{7} {\left(3 \, x^{4} + x^{3} - 45 \, x^{2} + 45 \, x\right)} + {\left(14 \, x^{3} - 84 \, x^{2} - \sqrt{7} {\left(8 \, x^{3} - 30 \, x^{2} + 27 \, x - 27\right)} + 126 \, x\right)} \sqrt{-x^{2} - 2 \, x + 3} + 180 \, x - 135}{4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9}\right) + \frac{1}{28} \, \sqrt{7} \log\left(\frac{2 \, x^{2} + \sqrt{7} {\left(2 \, x + 1\right)} + 2 \, x + 4}{2 \, x^{2} + 2 \, x - 3}\right) - \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{2} - 2 \, x + 3} {\left(x + 1\right)}}{x^{2} + 2 \, x - 3}\right) + \frac{1}{4} \, \log\left(2 \, x^{2} + 2 \, x - 3\right) - \frac{1}{8} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 2 \, x + 3} x + 2 \, x - 3}{x^{2}}\right) + \frac{1}{8} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 2 \, x + 3} x - 2 \, x + 3}{x^{2}}\right)"," ",0,"1/56*sqrt(7)*log((24*x^4 + 62*x^3 - 153*x^2 + 2*sqrt(7)*(3*x^4 + x^3 - 45*x^2 + 45*x) - (14*x^3 - 84*x^2 + sqrt(7)*(8*x^3 - 30*x^2 + 27*x - 27) + 126*x)*sqrt(-x^2 - 2*x + 3) + 180*x - 135)/(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)) + 1/56*sqrt(7)*log((24*x^4 + 62*x^3 - 153*x^2 - 2*sqrt(7)*(3*x^4 + x^3 - 45*x^2 + 45*x) + (14*x^3 - 84*x^2 - sqrt(7)*(8*x^3 - 30*x^2 + 27*x - 27) + 126*x)*sqrt(-x^2 - 2*x + 3) + 180*x - 135)/(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)) + 1/28*sqrt(7)*log((2*x^2 + sqrt(7)*(2*x + 1) + 2*x + 4)/(2*x^2 + 2*x - 3)) - 1/2*arctan(sqrt(-x^2 - 2*x + 3)*(x + 1)/(x^2 + 2*x - 3)) + 1/4*log(2*x^2 + 2*x - 3) - 1/8*log((2*sqrt(-x^2 - 2*x + 3)*x + 2*x - 3)/x^2) + 1/8*log(-(2*sqrt(-x^2 - 2*x + 3)*x - 2*x + 3)/x^2)","B",0
754,1,171,0,0.731073," ","integrate(1/(x+(-x^2-2*x+3)^(1/2))^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{7} {\left(2 \, x^{2} + 2 \, x - 3\right)} \log\left(\frac{x^{4} + 44 \, x^{3} - \sqrt{7} {\left(3 \, x^{3} + x^{2} - 45 \, x + 45\right)} \sqrt{-x^{2} - 2 \, x + 3} + 26 \, x^{2} - 276 \, x + 207}{4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9}\right) + 4 \, \sqrt{7} {\left(2 \, x^{2} + 2 \, x - 3\right)} \log\left(\frac{2 \, x^{2} + \sqrt{7} {\left(2 \, x + 1\right)} + 2 \, x + 4}{2 \, x^{2} + 2 \, x - 3}\right) - 14 \, \sqrt{-x^{2} - 2 \, x + 3} {\left(x - 3\right)} - 56 \, x + 21}{98 \, {\left(2 \, x^{2} + 2 \, x - 3\right)}}"," ",0,"1/98*(2*sqrt(7)*(2*x^2 + 2*x - 3)*log((x^4 + 44*x^3 - sqrt(7)*(3*x^3 + x^2 - 45*x + 45)*sqrt(-x^2 - 2*x + 3) + 26*x^2 - 276*x + 207)/(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)) + 4*sqrt(7)*(2*x^2 + 2*x - 3)*log((2*x^2 + sqrt(7)*(2*x + 1) + 2*x + 4)/(2*x^2 + 2*x - 3)) - 14*sqrt(-x^2 - 2*x + 3)*(x - 3) - 56*x + 21)/(2*x^2 + 2*x - 3)","A",0
755,1,223,0,0.808185," ","integrate(1/(x+(-x^2-2*x+3)^(1/2))^3,x, algorithm=""fricas"")","-\frac{336 \, x^{3} - 6 \, \sqrt{7} {\left(4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9\right)} \log\left(\frac{x^{4} + 44 \, x^{3} - \sqrt{7} {\left(3 \, x^{3} + x^{2} - 45 \, x + 45\right)} \sqrt{-x^{2} - 2 \, x + 3} + 26 \, x^{2} - 276 \, x + 207}{4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9}\right) - 12 \, \sqrt{7} {\left(4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9\right)} \log\left(\frac{2 \, x^{2} + \sqrt{7} {\left(2 \, x + 1\right)} + 2 \, x + 4}{2 \, x^{2} + 2 \, x - 3}\right) - 182 \, x^{2} + 14 \, {\left(34 \, x^{3} + 58 \, x^{2} - 83 \, x - 15\right)} \sqrt{-x^{2} - 2 \, x + 3} - 2100 \, x + 1953}{1372 \, {\left(4 \, x^{4} + 8 \, x^{3} - 8 \, x^{2} - 12 \, x + 9\right)}}"," ",0,"-1/1372*(336*x^3 - 6*sqrt(7)*(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)*log((x^4 + 44*x^3 - sqrt(7)*(3*x^3 + x^2 - 45*x + 45)*sqrt(-x^2 - 2*x + 3) + 26*x^2 - 276*x + 207)/(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)) - 12*sqrt(7)*(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)*log((2*x^2 + sqrt(7)*(2*x + 1) + 2*x + 4)/(2*x^2 + 2*x - 3)) - 182*x^2 + 14*(34*x^3 + 58*x^2 - 83*x - 15)*sqrt(-x^2 - 2*x + 3) - 2100*x + 1953)/(4*x^4 + 8*x^3 - 8*x^2 - 12*x + 9)","A",0
756,1,77,0,0.717523," ","integrate(1/(x+(x^2-2*x-3)^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{x^{2} - 2 \, x - 3} - \frac{3}{4} \, \log\left(2 \, x + 3\right) - \frac{5}{4} \, \log\left(-x + \sqrt{x^{2} - 2 \, x - 3} + 1\right) + \frac{3}{4} \, \log\left(-x + \sqrt{x^{2} - 2 \, x - 3}\right) - \frac{3}{4} \, \log\left(-x + \sqrt{x^{2} - 2 \, x - 3} - 3\right)"," ",0,"1/2*x - 1/2*sqrt(x^2 - 2*x - 3) - 3/4*log(2*x + 3) - 5/4*log(-x + sqrt(x^2 - 2*x - 3) + 1) + 3/4*log(-x + sqrt(x^2 - 2*x - 3)) - 3/4*log(-x + sqrt(x^2 - 2*x - 3) - 3)","A",0
757,1,97,0,0.849836," ","integrate(1/(x+(x^2-2*x-3)^(1/2))^2,x, algorithm=""fricas"")","\frac{4 \, x^{2} - 8 \, {\left(2 \, x + 3\right)} \log\left(x^{2} - \sqrt{x^{2} - 2 \, x - 3} {\left(x + 1\right)} - 3\right) - 8 \, {\left(2 \, x + 3\right)} \log\left(2 \, x + 3\right) + 8 \, {\left(2 \, x + 3\right)} \log\left(-x + \sqrt{x^{2} - 2 \, x - 3}\right) - 4 \, \sqrt{x^{2} - 2 \, x - 3} {\left(x + 3\right)} + 2 \, x - 15}{4 \, {\left(2 \, x + 3\right)}}"," ",0,"1/4*(4*x^2 - 8*(2*x + 3)*log(x^2 - sqrt(x^2 - 2*x - 3)*(x + 1) - 3) - 8*(2*x + 3)*log(2*x + 3) + 8*(2*x + 3)*log(-x + sqrt(x^2 - 2*x - 3)) - 4*sqrt(x^2 - 2*x - 3)*(x + 3) + 2*x - 15)/(2*x + 3)","A",0
758,1,129,0,0.637909," ","integrate(1/(x+(x^2-2*x-3)^(1/2))^3,x, algorithm=""fricas"")","\frac{8 \, x^{3} - 10 \, x^{2} - 12 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(x^{2} - \sqrt{x^{2} - 2 \, x - 3} {\left(x + 1\right)} - 3\right) - 12 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(2 \, x + 3\right) + 12 \, {\left(4 \, x^{2} + 12 \, x + 9\right)} \log\left(-x + \sqrt{x^{2} - 2 \, x - 3}\right) - 2 \, {\left(4 \, x^{2} + 31 \, x + 33\right)} \sqrt{x^{2} - 2 \, x - 3} - 156 \, x - 171}{4 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/4*(8*x^3 - 10*x^2 - 12*(4*x^2 + 12*x + 9)*log(x^2 - sqrt(x^2 - 2*x - 3)*(x + 1) - 3) - 12*(4*x^2 + 12*x + 9)*log(2*x + 3) + 12*(4*x^2 + 12*x + 9)*log(-x + sqrt(x^2 - 2*x - 3)) - 2*(4*x^2 + 31*x + 33)*sqrt(x^2 - 2*x - 3) - 156*x - 171)/(4*x^2 + 12*x + 9)","A",0
759,1,187,0,0.625216," ","integrate(1/(x+(-x^2-4*x-3)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} {\left(x + 1\right)}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} {\left(x + 2\right)}}{x^{2} + 4 \, x + 3}\right) + \frac{1}{4} \, \log\left(2 \, x^{2} + 4 \, x + 3\right) - \frac{1}{8} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) + \frac{1}{8} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"-1/2*sqrt(2)*arctan(sqrt(2)*(x + 1)) + 1/4*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 1/4*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/2*arctan(sqrt(-x^2 - 4*x - 3)*(x + 2)/(x^2 + 4*x + 3)) + 1/4*log(2*x^2 + 4*x + 3) - 1/8*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) + 1/8*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","B",0
760,1,121,0,0.696153," ","integrate(1/(x+(-x^2-4*x-3)^(1/2))^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(2 \, x^{2} + 4 \, x + 3\right)} \arctan\left(\sqrt{2} {\left(x + 1\right)}\right) - \sqrt{2} {\left(2 \, x^{2} + 4 \, x + 3\right)} \arctan\left(\frac{\sqrt{2} {\left(6 \, x^{2} + 20 \, x + 15\right)} \sqrt{-x^{2} - 4 \, x - 3}}{4 \, {\left(2 \, x^{3} + 11 \, x^{2} + 18 \, x + 9\right)}}\right) + 4 \, \sqrt{-x^{2} - 4 \, x - 3} {\left(2 \, x + 3\right)} + 4 \, x + 12}{8 \, {\left(2 \, x^{2} + 4 \, x + 3\right)}}"," ",0,"1/8*(2*sqrt(2)*(2*x^2 + 4*x + 3)*arctan(sqrt(2)*(x + 1)) - sqrt(2)*(2*x^2 + 4*x + 3)*arctan(1/4*sqrt(2)*(6*x^2 + 20*x + 15)*sqrt(-x^2 - 4*x - 3)/(2*x^3 + 11*x^2 + 18*x + 9)) + 4*sqrt(-x^2 - 4*x - 3)*(2*x + 3) + 4*x + 12)/(2*x^2 + 4*x + 3)","A",0
761,1,171,0,0.710138," ","integrate(1/(x+(-x^2-4*x-3)^(1/2))^3,x, algorithm=""fricas"")","-\frac{24 \, x^{3} + 6 \, \sqrt{2} {\left(4 \, x^{4} + 16 \, x^{3} + 28 \, x^{2} + 24 \, x + 9\right)} \arctan\left(\sqrt{2} {\left(x + 1\right)}\right) - 3 \, \sqrt{2} {\left(4 \, x^{4} + 16 \, x^{3} + 28 \, x^{2} + 24 \, x + 9\right)} \arctan\left(\frac{\sqrt{2} {\left(6 \, x^{2} + 20 \, x + 15\right)} \sqrt{-x^{2} - 4 \, x - 3}}{4 \, {\left(2 \, x^{3} + 11 \, x^{2} + 18 \, x + 9\right)}}\right) + 64 \, x^{2} + 4 \, {\left(8 \, x^{3} + 22 \, x^{2} + 26 \, x + 15\right)} \sqrt{-x^{2} - 4 \, x - 3} + 60 \, x + 36}{16 \, {\left(4 \, x^{4} + 16 \, x^{3} + 28 \, x^{2} + 24 \, x + 9\right)}}"," ",0,"-1/16*(24*x^3 + 6*sqrt(2)*(4*x^4 + 16*x^3 + 28*x^2 + 24*x + 9)*arctan(sqrt(2)*(x + 1)) - 3*sqrt(2)*(4*x^4 + 16*x^3 + 28*x^2 + 24*x + 9)*arctan(1/4*sqrt(2)*(6*x^2 + 20*x + 15)*sqrt(-x^2 - 4*x - 3)/(2*x^3 + 11*x^2 + 18*x + 9)) + 64*x^2 + 4*(8*x^3 + 22*x^2 + 26*x + 15)*sqrt(-x^2 - 4*x - 3) + 60*x + 36)/(4*x^4 + 16*x^3 + 28*x^2 + 24*x + 9)","A",0
762,1,58,0,0.676828," ","integrate(x^3*(1+x)^3*(1+2*x)*(-x^4-2*x^3-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{15} \, {\left(3 \, x^{8} + 12 \, x^{7} + 18 \, x^{6} + 12 \, x^{5} + 2 \, x^{4} - 2 \, x^{3} - x^{2} - 2\right)} \sqrt{-x^{4} - 2 \, x^{3} - x^{2} + 1}"," ",0,"1/15*(3*x^8 + 12*x^7 + 18*x^6 + 12*x^5 + 2*x^4 - 2*x^3 - x^2 - 2)*sqrt(-x^4 - 2*x^3 - x^2 + 1)","A",0
763,1,58,0,0.641262," ","integrate((1+2*x)*(x^2+x)^3*(1-(x^2+x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{15} \, {\left(3 \, x^{8} + 12 \, x^{7} + 18 \, x^{6} + 12 \, x^{5} + 2 \, x^{4} - 2 \, x^{3} - x^{2} - 2\right)} \sqrt{-x^{4} - 2 \, x^{3} - x^{2} + 1}"," ",0,"1/15*(3*x^8 + 12*x^7 + 18*x^6 + 12*x^5 + 2*x^4 - 2*x^3 - x^2 - 2)*sqrt(-x^4 - 2*x^3 - x^2 + 1)","A",0
764,0,0,0,0.718838," ","integrate((-x^4+4*x^3-8*x^2+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-x^4 + 4*x^3 - 8*x^2 + 8*x)^(3/2), x)","F",0
765,0,0,0,0.648478," ","integrate((-x^4+4*x^3-8*x^2+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x), x)","F",0
766,0,0,0,0.538194," ","integrate(1/(-x^4+4*x^3-8*x^2+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - 8 \, x}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x)/(x^4 - 4*x^3 + 8*x^2 - 8*x), x)","F",0
767,0,0,0,0.709710," ","integrate(1/(-x^4+4*x^3-8*x^2+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{8} - 8 \, x^{7} + 32 \, x^{6} - 80 \, x^{5} + 128 \, x^{4} - 128 \, x^{3} + 64 \, x^{2}}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x)/(x^8 - 8*x^7 + 32*x^6 - 80*x^5 + 128*x^4 - 128*x^3 + 64*x^2), x)","F",0
768,0,0,0,0.744430," ","integrate(1/(-x^4+4*x^3-8*x^2+8*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{12} - 12 \, x^{11} + 72 \, x^{10} - 280 \, x^{9} + 768 \, x^{8} - 1536 \, x^{7} + 2240 \, x^{6} - 2304 \, x^{5} + 1536 \, x^{4} - 512 \, x^{3}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x)/(x^12 - 12*x^11 + 72*x^10 - 280*x^9 + 768*x^8 - 1536*x^7 + 2240*x^6 - 2304*x^5 + 1536*x^4 - 512*x^3), x)","F",0
769,0,0,0,0.755538," ","integrate(((2-x)*x*(x^2-2*x+4))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-x^4 + 4*x^3 - 8*x^2 + 8*x)^(3/2), x)","F",0
770,0,0,0,0.849643," ","integrate(((2-x)*x*(x^2-2*x+4))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x), x)","F",0
771,0,0,0,0.660012," ","integrate(1/((2-x)*x*(x^2-2*x+4))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - 8 \, x}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x)/(x^4 - 4*x^3 + 8*x^2 - 8*x), x)","F",0
772,0,0,0,0.537584," ","integrate(1/((2-x)*x*(x^2-2*x+4))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{8} - 8 \, x^{7} + 32 \, x^{6} - 80 \, x^{5} + 128 \, x^{4} - 128 \, x^{3} + 64 \, x^{2}}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x)/(x^8 - 8*x^7 + 32*x^6 - 80*x^5 + 128*x^4 - 128*x^3 + 64*x^2), x)","F",0
773,0,0,0,0.633798," ","integrate(1/((2-x)*x*(x^2-2*x+4))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{12} - 12 \, x^{11} + 72 \, x^{10} - 280 \, x^{9} + 768 \, x^{8} - 1536 \, x^{7} + 2240 \, x^{6} - 2304 \, x^{5} + 1536 \, x^{4} - 512 \, x^{3}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x)/(x^12 - 12*x^11 + 72*x^10 - 280*x^9 + 768*x^8 - 1536*x^7 + 2240*x^6 - 2304*x^5 + 1536*x^4 - 512*x^3), x)","F",0
774,0,0,0,0.677609," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c)^(3/2), x)","F",0
775,0,0,0,0.762134," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c}, x\right)"," ",0,"integral(sqrt(d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c), x)","F",0
776,0,0,0,0.669067," ","integrate(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c}}, x\right)"," ",0,"integral(1/sqrt(d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c), x)","F",0
777,0,0,0,0.594963," ","integrate(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c}}{d^{4} x^{8} + 8 \, c d^{3} x^{7} + 24 \, c^{2} d^{2} x^{6} + 32 \, c^{3} d x^{5} + 32 \, a c^{2} d x^{3} + 32 \, a c^{3} x^{2} + 8 \, {\left(2 \, c^{4} + a c d^{2}\right)} x^{4} + 16 \, a^{2} c^{2}}, x\right)"," ",0,"integral(sqrt(d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c)/(d^4*x^8 + 8*c*d^3*x^7 + 24*c^2*d^2*x^6 + 32*c^3*d*x^5 + 32*a*c^2*d*x^3 + 32*a*c^3*x^2 + 8*(2*c^4 + a*c*d^2)*x^4 + 16*a^2*c^2), x)","F",0
778,0,0,0,0.736731," ","integrate((8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{8 \, e^{3} x^{4} + 8 \, d e^{2} x^{3} - d^{3} x + 8 \, a e^{2}}, x\right)"," ",0,"integral(sqrt(8*e^3*x^4 + 8*d*e^2*x^3 - d^3*x + 8*a*e^2), x)","F",0
779,0,0,0,0.581687," ","integrate(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{8 \, e^{3} x^{4} + 8 \, d e^{2} x^{3} - d^{3} x + 8 \, a e^{2}}}, x\right)"," ",0,"integral(1/sqrt(8*e^3*x^4 + 8*d*e^2*x^3 - d^3*x + 8*a*e^2), x)","F",0
780,0,0,0,0.805455," ","integrate(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{8 \, e^{3} x^{4} + 8 \, d e^{2} x^{3} - d^{3} x + 8 \, a e^{2}}}{64 \, e^{6} x^{8} + 128 \, d e^{5} x^{7} + 64 \, d^{2} e^{4} x^{6} - 16 \, d^{3} e^{3} x^{5} + 128 \, a d e^{4} x^{3} + d^{6} x^{2} - 16 \, a d^{3} e^{2} x + 64 \, a^{2} e^{4} - 16 \, {\left(d^{4} e^{2} - 8 \, a e^{5}\right)} x^{4}}, x\right)"," ",0,"integral(sqrt(8*e^3*x^4 + 8*d*e^2*x^3 - d^3*x + 8*a*e^2)/(64*e^6*x^8 + 128*d*e^5*x^7 + 64*d^2*e^4*x^6 - 16*d^3*e^3*x^5 + 128*a*d*e^4*x^3 + d^6*x^2 - 16*a*d^3*e^2*x + 64*a^2*e^4 - 16*(d^4*e^2 - 8*a*e^5)*x^4), x)","F",0
781,0,0,0,0.500385," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-x^4 + 4*x^3 - 8*x^2 + a + 8*x)^(3/2), x)","F",0
782,0,0,0,1.057132," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
783,0,0,0,1.078290," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)/(x^4 - 4*x^3 + 8*x^2 - a - 8*x), x)","F",0
784,0,0,0,1.365494," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}}{x^{8} - 8 \, x^{7} + 32 \, x^{6} - 2 \, {\left(a - 64\right)} x^{4} - 80 \, x^{5} + 8 \, {\left(a - 16\right)} x^{3} - 16 \, {\left(a - 4\right)} x^{2} + a^{2} + 16 \, a x}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)/(x^8 - 8*x^7 + 32*x^6 - 2*(a - 64)*x^4 - 80*x^5 + 8*(a - 16)*x^3 - 16*(a - 4)*x^2 + a^2 + 16*a*x), x)","F",0
785,0,0,0,0.738958," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}}{x^{12} - 12 \, x^{11} + 72 \, x^{10} - 3 \, {\left(a - 256\right)} x^{8} - 280 \, x^{9} + 24 \, {\left(a - 64\right)} x^{7} - 32 \, {\left(3 \, a - 70\right)} x^{6} + 48 \, {\left(5 \, a - 48\right)} x^{5} + 3 \, {\left(a^{2} - 128 \, a + 512\right)} x^{4} - 4 \, {\left(3 \, a^{2} - 96 \, a + 128\right)} x^{3} - a^{3} - 24 \, a^{2} x + 24 \, {\left(a^{2} - 8 \, a\right)} x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)/(x^12 - 12*x^11 + 72*x^10 - 3*(a - 256)*x^8 - 280*x^9 + 24*(a - 64)*x^7 - 32*(3*a - 70)*x^6 + 48*(5*a - 48)*x^5 + 3*(a^2 - 128*a + 512)*x^4 - 4*(3*a^2 - 96*a + 128)*x^3 - a^3 - 24*a^2*x + 24*(a^2 - 8*a)*x^2), x)","F",0
786,0,0,0,0.827534," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(x^{5} - 4 \, x^{4} + 8 \, x^{3} - a x - 8 \, x^{2}\right)} \sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}, x\right)"," ",0,"integral(-(x^5 - 4*x^4 + 8*x^3 - a*x - 8*x^2)*sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
787,0,0,0,0.755420," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x, x)","F",0
788,0,0,0,0.638571," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x/(x^4 - 4*x^3 + 8*x^2 - a - 8*x), x)","F",0
789,0,0,0,0.657221," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x}{x^{8} - 8 \, x^{7} + 32 \, x^{6} - 2 \, {\left(a - 64\right)} x^{4} - 80 \, x^{5} + 8 \, {\left(a - 16\right)} x^{3} - 16 \, {\left(a - 4\right)} x^{2} + a^{2} + 16 \, a x}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x/(x^8 - 8*x^7 + 32*x^6 - 2*(a - 64)*x^4 - 80*x^5 + 8*(a - 16)*x^3 - 16*(a - 4)*x^2 + a^2 + 16*a*x), x)","F",0
790,0,0,0,0.942740," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x}{x^{12} - 12 \, x^{11} + 72 \, x^{10} - 3 \, {\left(a - 256\right)} x^{8} - 280 \, x^{9} + 24 \, {\left(a - 64\right)} x^{7} - 32 \, {\left(3 \, a - 70\right)} x^{6} + 48 \, {\left(5 \, a - 48\right)} x^{5} + 3 \, {\left(a^{2} - 128 \, a + 512\right)} x^{4} - 4 \, {\left(3 \, a^{2} - 96 \, a + 128\right)} x^{3} - a^{3} - 24 \, a^{2} x + 24 \, {\left(a^{2} - 8 \, a\right)} x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x/(x^12 - 12*x^11 + 72*x^10 - 3*(a - 256)*x^8 - 280*x^9 + 24*(a - 64)*x^7 - 32*(3*a - 70)*x^6 + 48*(5*a - 48)*x^5 + 3*(a^2 - 128*a + 512)*x^4 - 4*(3*a^2 - 96*a + 128)*x^3 - a^3 - 24*a^2*x + 24*(a^2 - 8*a)*x^2), x)","F",0
791,0,0,0,0.787592," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(x^{6} - 4 \, x^{5} + 8 \, x^{4} - a x^{2} - 8 \, x^{3}\right)} \sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}, x\right)"," ",0,"integral(-(x^6 - 4*x^5 + 8*x^4 - a*x^2 - 8*x^3)*sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
792,0,0,0,1.414290," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x^{2}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x^2, x)","F",0
793,0,0,0,0.957093," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x^{2}}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - a - 8 \, x}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x^2/(x^4 - 4*x^3 + 8*x^2 - a - 8*x), x)","F",0
794,0,0,0,0.633738," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x^{2}}{x^{8} - 8 \, x^{7} + 32 \, x^{6} - 2 \, {\left(a - 64\right)} x^{4} - 80 \, x^{5} + 8 \, {\left(a - 16\right)} x^{3} - 16 \, {\left(a - 4\right)} x^{2} + a^{2} + 16 \, a x}, x\right)"," ",0,"integral(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x^2/(x^8 - 8*x^7 + 32*x^6 - 2*(a - 64)*x^4 - 80*x^5 + 8*(a - 16)*x^3 - 16*(a - 4)*x^2 + a^2 + 16*a*x), x)","F",0
795,0,0,0,0.876406," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x^{2}}{x^{12} - 12 \, x^{11} + 72 \, x^{10} - 3 \, {\left(a - 256\right)} x^{8} - 280 \, x^{9} + 24 \, {\left(a - 64\right)} x^{7} - 32 \, {\left(3 \, a - 70\right)} x^{6} + 48 \, {\left(5 \, a - 48\right)} x^{5} + 3 \, {\left(a^{2} - 128 \, a + 512\right)} x^{4} - 4 \, {\left(3 \, a^{2} - 96 \, a + 128\right)} x^{3} - a^{3} - 24 \, a^{2} x + 24 \, {\left(a^{2} - 8 \, a\right)} x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x^2/(x^12 - 12*x^11 + 72*x^10 - 3*(a - 256)*x^8 - 280*x^9 + 24*(a - 64)*x^7 - 32*(3*a - 70)*x^6 + 48*(5*a - 48)*x^5 + 3*(a^2 - 128*a + 512)*x^4 - 4*(3*a^2 - 96*a + 128)*x^3 - a^3 - 24*a^2*x + 24*(a^2 - 8*a)*x^2), x)","F",0
796,0,0,0,0.851750," ","integrate(1/(8*x^4-x^3+8*x+8)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{8 \, x^{4} - x^{3} + 8 \, x + 8}}, x\right)"," ",0,"integral(1/sqrt(8*x^4 - x^3 + 8*x + 8), x)","F",0
797,0,0,0,1.472726," ","integrate(1/(8*x^4-x^3+8*x+8)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{8 \, x^{4} - x^{3} + 8 \, x + 8}}{64 \, x^{8} - 16 \, x^{7} + x^{6} + 128 \, x^{5} + 112 \, x^{4} - 16 \, x^{3} + 64 \, x^{2} + 128 \, x + 64}, x\right)"," ",0,"integral(sqrt(8*x^4 - x^3 + 8*x + 8)/(64*x^8 - 16*x^7 + x^6 + 128*x^5 + 112*x^4 - 16*x^3 + 64*x^2 + 128*x + 64), x)","F",0
798,0,0,0,0.648339," ","integrate(1/(4*x^4+4*x^2+4*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{4 \, x^{4} + 4 \, x^{2} + 4 \, x + 1}}, x\right)"," ",0,"integral(1/sqrt(4*x^4 + 4*x^2 + 4*x + 1), x)","F",0
799,0,0,0,0.707035," ","integrate(1/(4*x^4+4*x^2+4*x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x^{4} + 4 \, x^{2} + 4 \, x + 1}}{16 \, x^{8} + 32 \, x^{6} + 32 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 24 \, x^{2} + 8 \, x + 1}, x\right)"," ",0,"integral(sqrt(4*x^4 + 4*x^2 + 4*x + 1)/(16*x^8 + 32*x^6 + 32*x^5 + 24*x^4 + 32*x^3 + 24*x^2 + 8*x + 1), x)","F",0
800,0,0,0,0.699549," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8}}, x\right)"," ",0,"integral(1/sqrt(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8), x)","F",0
801,0,0,0,0.563001," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8}}{64 \, x^{8} - 240 \, x^{7} + 353 \, x^{6} + 144 \, x^{5} - 528 \, x^{4} + 144 \, x^{3} + 704 \, x^{2} + 384 \, x + 64}, x\right)"," ",0,"integral(sqrt(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)/(64*x^8 - 240*x^7 + 353*x^6 + 144*x^5 - 528*x^4 + 144*x^3 + 704*x^2 + 384*x + 64), x)","F",0
802,0,0,0,0.686335," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8}}{512 \, x^{12} - 2880 \, x^{11} + 6936 \, x^{10} - 4527 \, x^{9} - 8808 \, x^{8} + 16776 \, x^{7} + 5528 \, x^{6} - 17856 \, x^{5} - 384 \, x^{4} + 20160 \, x^{3} + 15360 \, x^{2} + 4608 \, x + 512}, x\right)"," ",0,"integral(sqrt(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)/(512*x^12 - 2880*x^11 + 6936*x^10 - 4527*x^9 - 8808*x^8 + 16776*x^7 + 5528*x^6 - 17856*x^5 - 384*x^4 + 20160*x^3 + 15360*x^2 + 4608*x + 512), x)","F",0
803,0,0,0,1.097149," ","integrate(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9), x)","F",0
804,0,0,0,0.697210," ","integrate(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9}}{9 \, x^{8} + 90 \, x^{7} - 39 \, x^{6} - 1356 \, x^{5} + 1810 \, x^{4} + 798 \, x^{3} - 756 \, x^{2} - 108 \, x + 81}, x\right)"," ",0,"integral(sqrt(3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9)/(9*x^8 + 90*x^7 - 39*x^6 - 1356*x^5 + 1810*x^4 + 798*x^3 - 756*x^2 - 108*x + 81), x)","F",0
805,1,81,0,0.623519," ","integrate((2*(3-x)^(1/2)+3/(1+x)^(1/2))^2/x,x, algorithm=""fricas"")","6 \, \sqrt{3} \log\left(-\frac{\sqrt{3} {\left(x + 3\right)} \sqrt{x + 1} \sqrt{-x + 3} + x^{2} - 6 \, x - 9}{x^{2}}\right) - 4 \, x + 12 \, \arctan\left(\frac{\sqrt{x + 1} {\left(x - 1\right)} \sqrt{-x + 3}}{x^{2} - 2 \, x - 3}\right) - 9 \, \log\left(x + 1\right) + 21 \, \log\left(x\right)"," ",0,"6*sqrt(3)*log(-(sqrt(3)*(x + 3)*sqrt(x + 1)*sqrt(-x + 3) + x^2 - 6*x - 9)/x^2) - 4*x + 12*arctan(sqrt(x + 1)*(x - 1)*sqrt(-x + 3)/(x^2 - 2*x - 3)) - 9*log(x + 1) + 21*log(x)","A",0
806,1,84,0,0.765514," ","integrate((x^2+x-1)/((x^2+1)^(1/2)+1),x, algorithm=""fricas"")","-\frac{2 \, x^{2} + 2 \, x \log\left(x\right) + 2 \, x \log\left(-x + \sqrt{x^{2} + 1} + 1\right) - x \log\left(-x + \sqrt{x^{2} + 1}\right) - 2 \, x \log\left(-x + \sqrt{x^{2} + 1} - 1\right) - {\left(x^{2} + 2 \, x + 2\right)} \sqrt{x^{2} + 1} - 2 \, x + 2}{2 \, x}"," ",0,"-1/2*(2*x^2 + 2*x*log(x) + 2*x*log(-x + sqrt(x^2 + 1) + 1) - x*log(-x + sqrt(x^2 + 1)) - 2*x*log(-x + sqrt(x^2 + 1) - 1) - (x^2 + 2*x + 2)*sqrt(x^2 + 1) - 2*x + 2)/x","A",0
807,1,78,0,0.601860," ","integrate((x^2+x-1)/(1+x+(x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{1}{6} \, x^{3} + \frac{1}{2} \, x^{2} - \frac{1}{12} \, {\left(2 \, x^{2} + 3 \, x - 4\right)} \sqrt{x^{2} + 1} - \frac{1}{2} \, \log\left(x\right) - \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1} + 1\right) + \frac{1}{4} \, \log\left(-x + \sqrt{x^{2} + 1}\right) + \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1} - 1\right)"," ",0,"1/6*x^3 + 1/2*x^2 - 1/12*(2*x^2 + 3*x - 4)*sqrt(x^2 + 1) - 1/2*log(x) - 1/2*log(-x + sqrt(x^2 + 1) + 1) + 1/4*log(-x + sqrt(x^2 + 1)) + 1/2*log(-x + sqrt(x^2 + 1) - 1)","A",0
808,1,12,0,0.613378," ","integrate((x+2*(-1+x)^(1/2))/x/(-1+x)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x - 1} + 2 \, \log\left(x\right)"," ",0,"2*sqrt(x - 1) + 2*log(x)","A",0
809,1,43,0,0.671546," ","integrate((a+b*x^(2/3)+c*x^(1/2))^2,x, algorithm=""fricas"")","\frac{3}{7} \, b^{2} x^{\frac{7}{3}} + \frac{12}{13} \, b c x^{\frac{13}{6}} + \frac{1}{2} \, c^{2} x^{2} + \frac{6}{5} \, a b x^{\frac{5}{3}} + \frac{4}{3} \, a c x^{\frac{3}{2}} + a^{2} x"," ",0,"3/7*b^2*x^(7/3) + 12/13*b*c*x^(13/6) + 1/2*c^2*x^2 + 6/5*a*b*x^(5/3) + 4/3*a*c*x^(3/2) + a^2*x","A",0
810,1,91,0,1.544454," ","integrate((a+b*x^(2/3)+c*x^(1/2))^3,x, algorithm=""fricas"")","\frac{1}{3} \, b^{3} x^{3} + \frac{18}{17} \, b^{2} c x^{\frac{17}{6}} + \frac{9}{7} \, a b^{2} x^{\frac{7}{3}} + \frac{36}{13} \, a b c x^{\frac{13}{6}} + \frac{3}{2} \, a c^{2} x^{2} + a^{3} x + \frac{9}{40} \, {\left(5 \, b c^{2} x^{2} + 8 \, a^{2} b x\right)} x^{\frac{2}{3}} + \frac{2}{5} \, {\left(c^{3} x^{2} + 5 \, a^{2} c x\right)} \sqrt{x}"," ",0,"1/3*b^3*x^3 + 18/17*b^2*c*x^(17/6) + 9/7*a*b^2*x^(7/3) + 36/13*a*b*c*x^(13/6) + 3/2*a*c^2*x^2 + a^3*x + 9/40*(5*b*c^2*x^2 + 8*a^2*b*x)*x^(2/3) + 2/5*(c^3*x^2 + 5*a^2*c*x)*sqrt(x)","A",0
811,1,180,0,1.283886," ","integrate((x^2-1)/x^3/(a-b+b/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a - b} b \log\left(-2 \, {\left(a - b\right)} x^{2} - 2 \, \sqrt{a - b} x^{2} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}}}{2 \, {\left(a b - b^{2}\right)}}, \frac{\sqrt{-a + b} b \arctan\left(-\frac{\sqrt{-a + b} x^{2} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}}}{{\left(a - b\right)} x^{2} + b}\right) + {\left(a - b\right)} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}}}{a b - b^{2}}\right]"," ",0,"[1/2*(sqrt(a - b)*b*log(-2*(a - b)*x^2 - 2*sqrt(a - b)*x^2*sqrt(((a - b)*x^2 + b)/x^2) - b) + 2*(a - b)*sqrt(((a - b)*x^2 + b)/x^2))/(a*b - b^2), (sqrt(-a + b)*b*arctan(-sqrt(-a + b)*x^2*sqrt(((a - b)*x^2 + b)/x^2)/((a - b)*x^2 + b)) + (a - b)*sqrt(((a - b)*x^2 + b)/x^2))/(a*b - b^2)]","A",0
812,1,180,0,0.867911," ","integrate((x^2-1)/x^3/(a+b*(-1+1/x^2))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a - b} b \log\left(-2 \, {\left(a - b\right)} x^{2} - 2 \, \sqrt{a - b} x^{2} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}}}{2 \, {\left(a b - b^{2}\right)}}, \frac{\sqrt{-a + b} b \arctan\left(-\frac{\sqrt{-a + b} x^{2} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}}}{{\left(a - b\right)} x^{2} + b}\right) + {\left(a - b\right)} \sqrt{\frac{{\left(a - b\right)} x^{2} + b}{x^{2}}}}{a b - b^{2}}\right]"," ",0,"[1/2*(sqrt(a - b)*b*log(-2*(a - b)*x^2 - 2*sqrt(a - b)*x^2*sqrt(((a - b)*x^2 + b)/x^2) - b) + 2*(a - b)*sqrt(((a - b)*x^2 + b)/x^2))/(a*b - b^2), (sqrt(-a + b)*b*arctan(-sqrt(-a + b)*x^2*sqrt(((a - b)*x^2 + b)/x^2)/((a - b)*x^2 + b)) + (a - b)*sqrt(((a - b)*x^2 + b)/x^2))/(a*b - b^2)]","A",0
813,1,182,0,0.556062," ","integrate((1+x)/(x^2+4)/(x^2+9)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{x^{2} - \sqrt{x^{2} + 9} {\left(x + \sqrt{5}\right)} + \sqrt{5} x + 9} + \frac{1}{2} \, x + \frac{1}{2} \, \sqrt{5} - \frac{1}{2} \, \sqrt{x^{2} + 9}\right) - \frac{1}{5} \, \sqrt{5} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{x^{2} - \sqrt{x^{2} + 9} {\left(x - \sqrt{5}\right)} - \sqrt{5} x + 9} + \frac{1}{2} \, x - \frac{1}{2} \, \sqrt{5} - \frac{1}{2} \, \sqrt{x^{2} + 9}\right) + \frac{1}{10} \, \sqrt{5} \log\left(50 \, x^{2} - 50 \, \sqrt{x^{2} + 9} {\left(x + \sqrt{5}\right)} + 50 \, \sqrt{5} x + 450\right) - \frac{1}{10} \, \sqrt{5} \log\left(50 \, x^{2} - 50 \, \sqrt{x^{2} + 9} {\left(x - \sqrt{5}\right)} - 50 \, \sqrt{5} x + 450\right)"," ",0,"1/5*sqrt(5)*arctan(1/2*sqrt(2)*sqrt(x^2 - sqrt(x^2 + 9)*(x + sqrt(5)) + sqrt(5)*x + 9) + 1/2*x + 1/2*sqrt(5) - 1/2*sqrt(x^2 + 9)) - 1/5*sqrt(5)*arctan(1/2*sqrt(2)*sqrt(x^2 - sqrt(x^2 + 9)*(x - sqrt(5)) - sqrt(5)*x + 9) + 1/2*x - 1/2*sqrt(5) - 1/2*sqrt(x^2 + 9)) + 1/10*sqrt(5)*log(50*x^2 - 50*sqrt(x^2 + 9)*(x + sqrt(5)) + 50*sqrt(5)*x + 450) - 1/10*sqrt(5)*log(50*x^2 - 50*sqrt(x^2 + 9)*(x - sqrt(5)) - 50*sqrt(5)*x + 450)","B",0
814,1,22,0,0.780189," ","integrate(x*(1+(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{1}{3} \, {\left(x^{2} - 1\right)} \sqrt{-x^{2} + 1}"," ",0,"1/2*x^2 + 1/3*(x^2 - 1)*sqrt(-x^2 + 1)","A",0
815,1,25,0,0.724382," ","integrate(x*(1+(1-x)^(1/2)*(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{1}{3} \, {\left(x^{2} - 1\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"1/2*x^2 + 1/3*(x^2 - 1)*sqrt(x + 1)*sqrt(-x + 1)","A",0
816,1,37,0,0.730999," ","integrate(x*(1+1/(2+x)^(1/2)/(3+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \sqrt{x + 3} \sqrt{x + 2} + \frac{5}{2} \, \log\left(2 \, \sqrt{x + 3} \sqrt{x + 2} - 2 \, x - 5\right)"," ",0,"1/2*x^2 + sqrt(x + 3)*sqrt(x + 2) + 5/2*log(2*sqrt(x + 3)*sqrt(x + 2) - 2*x - 5)","A",0
817,1,2,0,1.063822," ","integrate((x-(x^6)^(1/2))/x/(-x^4+1),x, algorithm=""fricas"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
818,1,2,0,0.825328," ","integrate((1-(x^6)^(1/2)/x)/(-x^4+1),x, algorithm=""fricas"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
819,1,2,0,1.417331," ","integrate((x-(x^6)^(1/2))/(-x^5+x),x, algorithm=""fricas"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
820,1,2,0,0.470840," ","integrate(x/(x+(x^6)^(1/2)),x, algorithm=""fricas"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
821,1,6,0,0.810672," ","integrate((x^(1/2)-(x^3)^(1/2))/(-x^3+x),x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{x}\right)"," ",0,"2*arctan(sqrt(x))","A",0
822,1,6,0,1.413918," ","integrate(1/(x^(1/2)+(x^3)^(1/2)),x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{x}\right)"," ",0,"2*arctan(sqrt(x))","A",0
823,1,8,0,0.496974," ","integrate(1/((-1+x)^(1/2)+((-1+x)^3)^(1/2)),x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{x - 1}\right)"," ",0,"2*arctan(sqrt(x - 1))","A",0
824,1,25,0,0.653354," ","integrate(-3/(4+5*x)^2+(-5-4*x)/(4+5*x)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{25 \, x + 20 \, \sqrt{-x^{2} + 1} + 32}{20 \, {\left(5 \, x + 4\right)}}"," ",0,"1/20*(25*x + 20*sqrt(-x^2 + 1) + 32)/(5*x + 4)","A",0
825,1,25,0,1.094276," ","integrate((-5-4*x-3*(-x^2+1)^(1/2))/(4+5*x)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{25 \, x + 20 \, \sqrt{-x^{2} + 1} + 32}{20 \, {\left(5 \, x + 4\right)}}"," ",0,"1/20*(25*x + 20*sqrt(-x^2 + 1) + 32)/(5*x + 4)","A",0
826,1,25,0,0.819124," ","integrate(1/(-3*x^2+3+(-5-4*x)*(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{25 \, x + 20 \, \sqrt{-x^{2} + 1} + 32}{20 \, {\left(5 \, x + 4\right)}}"," ",0,"1/20*(25*x + 20*sqrt(-x^2 + 1) + 32)/(5*x + 4)","A",0
827,1,25,0,0.824914," ","integrate(1/(3-3*x^2-5*(-x^2+1)^(1/2)-4*x*(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{25 \, x + 20 \, \sqrt{-x^{2} + 1} + 32}{20 \, {\left(5 \, x + 4\right)}}"," ",0,"1/20*(25*x + 20*sqrt(-x^2 + 1) + 32)/(5*x + 4)","A",0
828,1,25,0,0.749117," ","integrate((-1+(-x^2+1)^(1/2))/(2+x-2*(-x^2+1)^(1/2))^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{25 \, x + 20 \, \sqrt{-x^{2} + 1} + 32}{20 \, {\left(5 \, x + 4\right)}}"," ",0,"1/20*(25*x + 20*sqrt(-x^2 + 1) + 32)/(5*x + 4)","A",0
829,1,44,0,0.761801," ","integrate((a+b*x^(-1+n))/(c*x+d*x^n),x, algorithm=""fricas"")","\frac{{\left(b c - a d\right)} \log\left(c x + d x^{n}\right) + {\left(a d n - b c\right)} \log\left(x\right)}{c d n - c d}"," ",0,"((b*c - a*d)*log(c*x + d*x^n) + (a*d*n - b*c)*log(x))/(c*d*n - c*d)","A",0
830,1,44,0,0.842057," ","integrate((2*x^2+1)^(1/2)/(1+(2*x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{\sqrt{2} x \log\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right) + 2 \, x^{2} + \sqrt{2 \, x^{2} + 1} - 1}{2 \, x}"," ",0,"1/2*(sqrt(2)*x*log(sqrt(2)*x - sqrt(2*x^2 + 1)) + 2*x^2 + sqrt(2*x^2 + 1) - 1)/x","A",0
831,1,80,0,1.040056," ","integrate((4*x^2-1)^(1/2)/(x+(4*x^2-1)^(1/2)),x, algorithm=""fricas"")","\frac{1}{18} \, \sqrt{3} \log\left(\frac{6 \, x^{2} + \sqrt{3} \sqrt{4 \, x^{2} - 1} - 1}{3 \, x^{2} - 1}\right) + \frac{1}{18} \, \sqrt{3} \log\left(\frac{3 \, x^{2} - 2 \, \sqrt{3} x + 1}{3 \, x^{2} - 1}\right) + \frac{4}{3} \, x - \frac{1}{3} \, \sqrt{4 \, x^{2} - 1}"," ",0,"1/18*sqrt(3)*log((6*x^2 + sqrt(3)*sqrt(4*x^2 - 1) - 1)/(3*x^2 - 1)) + 1/18*sqrt(3)*log((3*x^2 - 2*sqrt(3)*x + 1)/(3*x^2 - 1)) + 4/3*x - 1/3*sqrt(4*x^2 - 1)","A",0
832,1,1174,0,0.597758," ","integrate((c*x^2+b*x+a)/(e*x+d)^3/(x^2-1)^(1/2),x, algorithm=""fricas"")","\left[\frac{c d^{7} + b d^{6} e - {\left(3 \, a + 5 \, c\right)} d^{5} e^{2} + b d^{4} e^{3} + {\left(3 \, a + 4 \, c\right)} d^{3} e^{4} - 2 \, b d^{2} e^{5} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x^{2} + {\left({\left(2 \, a + c\right)} d^{4} e^{2} - 3 \, b d^{3} e^{3} + {\left(a + 2 \, c\right)} d^{2} e^{4} + {\left({\left(2 \, a + c\right)} d^{2} e^{4} - 3 \, b d e^{5} + {\left(a + 2 \, c\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(2 \, a + c\right)} d^{3} e^{3} - 3 \, b d^{2} e^{4} + {\left(a + 2 \, c\right)} d e^{5}\right)} x\right)} \sqrt{d^{2} - e^{2}} \log\left(\frac{d^{2} x + d e + \sqrt{d^{2} - e^{2}} {\left(d x + e\right)} + {\left(d^{2} - e^{2} + \sqrt{d^{2} - e^{2}} d\right)} \sqrt{x^{2} - 1}}{e x + d}\right) + 2 \, {\left(c d^{6} e + b d^{5} e^{2} - {\left(3 \, a + 5 \, c\right)} d^{4} e^{3} + b d^{3} e^{4} + {\left(3 \, a + 4 \, c\right)} d^{2} e^{5} - 2 \, b d e^{6}\right)} x + {\left(2 \, b d^{5} e^{2} - {\left(4 \, a + 3 \, c\right)} d^{4} e^{3} - b d^{3} e^{4} + {\left(5 \, a + 3 \, c\right)} d^{2} e^{5} - b d e^{6} - a e^{7} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x\right)} \sqrt{x^{2} - 1}}{2 \, {\left(d^{8} e^{2} - 3 \, d^{6} e^{4} + 3 \, d^{4} e^{6} - d^{2} e^{8} + {\left(d^{6} e^{4} - 3 \, d^{4} e^{6} + 3 \, d^{2} e^{8} - e^{10}\right)} x^{2} + 2 \, {\left(d^{7} e^{3} - 3 \, d^{5} e^{5} + 3 \, d^{3} e^{7} - d e^{9}\right)} x\right)}}, \frac{c d^{7} + b d^{6} e - {\left(3 \, a + 5 \, c\right)} d^{5} e^{2} + b d^{4} e^{3} + {\left(3 \, a + 4 \, c\right)} d^{3} e^{4} - 2 \, b d^{2} e^{5} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x^{2} - 2 \, {\left({\left(2 \, a + c\right)} d^{4} e^{2} - 3 \, b d^{3} e^{3} + {\left(a + 2 \, c\right)} d^{2} e^{4} + {\left({\left(2 \, a + c\right)} d^{2} e^{4} - 3 \, b d e^{5} + {\left(a + 2 \, c\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(2 \, a + c\right)} d^{3} e^{3} - 3 \, b d^{2} e^{4} + {\left(a + 2 \, c\right)} d e^{5}\right)} x\right)} \sqrt{-d^{2} + e^{2}} \arctan\left(-\frac{\sqrt{-d^{2} + e^{2}} \sqrt{x^{2} - 1} e - \sqrt{-d^{2} + e^{2}} {\left(e x + d\right)}}{d^{2} - e^{2}}\right) + 2 \, {\left(c d^{6} e + b d^{5} e^{2} - {\left(3 \, a + 5 \, c\right)} d^{4} e^{3} + b d^{3} e^{4} + {\left(3 \, a + 4 \, c\right)} d^{2} e^{5} - 2 \, b d e^{6}\right)} x + {\left(2 \, b d^{5} e^{2} - {\left(4 \, a + 3 \, c\right)} d^{4} e^{3} - b d^{3} e^{4} + {\left(5 \, a + 3 \, c\right)} d^{2} e^{5} - b d e^{6} - a e^{7} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x\right)} \sqrt{x^{2} - 1}}{2 \, {\left(d^{8} e^{2} - 3 \, d^{6} e^{4} + 3 \, d^{4} e^{6} - d^{2} e^{8} + {\left(d^{6} e^{4} - 3 \, d^{4} e^{6} + 3 \, d^{2} e^{8} - e^{10}\right)} x^{2} + 2 \, {\left(d^{7} e^{3} - 3 \, d^{5} e^{5} + 3 \, d^{3} e^{7} - d e^{9}\right)} x\right)}}\right]"," ",0,"[1/2*(c*d^7 + b*d^6*e - (3*a + 5*c)*d^5*e^2 + b*d^4*e^3 + (3*a + 4*c)*d^3*e^4 - 2*b*d^2*e^5 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x^2 + ((2*a + c)*d^4*e^2 - 3*b*d^3*e^3 + (a + 2*c)*d^2*e^4 + ((2*a + c)*d^2*e^4 - 3*b*d*e^5 + (a + 2*c)*e^6)*x^2 + 2*((2*a + c)*d^3*e^3 - 3*b*d^2*e^4 + (a + 2*c)*d*e^5)*x)*sqrt(d^2 - e^2)*log((d^2*x + d*e + sqrt(d^2 - e^2)*(d*x + e) + (d^2 - e^2 + sqrt(d^2 - e^2)*d)*sqrt(x^2 - 1))/(e*x + d)) + 2*(c*d^6*e + b*d^5*e^2 - (3*a + 5*c)*d^4*e^3 + b*d^3*e^4 + (3*a + 4*c)*d^2*e^5 - 2*b*d*e^6)*x + (2*b*d^5*e^2 - (4*a + 3*c)*d^4*e^3 - b*d^3*e^4 + (5*a + 3*c)*d^2*e^5 - b*d*e^6 - a*e^7 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x)*sqrt(x^2 - 1))/(d^8*e^2 - 3*d^6*e^4 + 3*d^4*e^6 - d^2*e^8 + (d^6*e^4 - 3*d^4*e^6 + 3*d^2*e^8 - e^10)*x^2 + 2*(d^7*e^3 - 3*d^5*e^5 + 3*d^3*e^7 - d*e^9)*x), 1/2*(c*d^7 + b*d^6*e - (3*a + 5*c)*d^5*e^2 + b*d^4*e^3 + (3*a + 4*c)*d^3*e^4 - 2*b*d^2*e^5 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x^2 - 2*((2*a + c)*d^4*e^2 - 3*b*d^3*e^3 + (a + 2*c)*d^2*e^4 + ((2*a + c)*d^2*e^4 - 3*b*d*e^5 + (a + 2*c)*e^6)*x^2 + 2*((2*a + c)*d^3*e^3 - 3*b*d^2*e^4 + (a + 2*c)*d*e^5)*x)*sqrt(-d^2 + e^2)*arctan(-(sqrt(-d^2 + e^2)*sqrt(x^2 - 1)*e - sqrt(-d^2 + e^2)*(e*x + d))/(d^2 - e^2)) + 2*(c*d^6*e + b*d^5*e^2 - (3*a + 5*c)*d^4*e^3 + b*d^3*e^4 + (3*a + 4*c)*d^2*e^5 - 2*b*d*e^6)*x + (2*b*d^5*e^2 - (4*a + 3*c)*d^4*e^3 - b*d^3*e^4 + (5*a + 3*c)*d^2*e^5 - b*d*e^6 - a*e^7 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x)*sqrt(x^2 - 1))/(d^8*e^2 - 3*d^6*e^4 + 3*d^4*e^6 - d^2*e^8 + (d^6*e^4 - 3*d^4*e^6 + 3*d^2*e^8 - e^10)*x^2 + 2*(d^7*e^3 - 3*d^5*e^5 + 3*d^3*e^7 - d*e^9)*x)]","B",0
833,1,52,0,0.747852," ","integrate((2*x^8+1)/x/(x^8+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(x^{8} + 1\right)} \log\left(\sqrt{x^{8} + 1} + 1\right) - {\left(x^{8} + 1\right)} \log\left(\sqrt{x^{8} + 1} - 1\right) + 2 \, \sqrt{x^{8} + 1}}{8 \, {\left(x^{8} + 1\right)}}"," ",0,"-1/8*((x^8 + 1)*log(sqrt(x^8 + 1) + 1) - (x^8 + 1)*log(sqrt(x^8 + 1) - 1) + 2*sqrt(x^8 + 1))/(x^8 + 1)","B",0
834,1,52,0,0.759169," ","integrate((2*x^8+1)*(x^8+1)^(1/2)/(x^17+2*x^9+x),x, algorithm=""fricas"")","-\frac{{\left(x^{8} + 1\right)} \log\left(\sqrt{x^{8} + 1} + 1\right) - {\left(x^{8} + 1\right)} \log\left(\sqrt{x^{8} + 1} - 1\right) + 2 \, \sqrt{x^{8} + 1}}{8 \, {\left(x^{8} + 1\right)}}"," ",0,"-1/8*((x^8 + 1)*log(sqrt(x^8 + 1) + 1) - (x^8 + 1)*log(sqrt(x^8 + 1) - 1) + 2*sqrt(x^8 + 1))/(x^8 + 1)","B",0
835,1,18,0,0.530209," ","integrate(1-9*x^2+x/(-9*x^2+1)^(1/2),x, algorithm=""fricas"")","-3 \, x^{3} + x - \frac{1}{9} \, \sqrt{-9 \, x^{2} + 1}"," ",0,"-3*x^3 + x - 1/9*sqrt(-9*x^2 + 1)","A",0
836,1,18,0,0.642684," ","integrate((x+(-9*x^2+1)^(3/2))/(-9*x^2+1)^(1/2),x, algorithm=""fricas"")","-3 \, x^{3} + x - \frac{1}{9} \, \sqrt{-9 \, x^{2} + 1}"," ",0,"-3*x^3 + x - 1/9*sqrt(-9*x^2 + 1)","A",0
837,1,11,0,0.573136," ","integrate((x-3*x^(1/2))^(2/3)*(-3+2*x^(1/2))/x^(1/2),x, algorithm=""fricas"")","\frac{6}{5} \, {\left(x - 3 \, \sqrt{x}\right)}^{\frac{5}{3}}"," ",0,"6/5*(x - 3*sqrt(x))^(5/3)","A",0
838,1,11,0,0.590730," ","integrate((9+2*x-9*x^(1/2))/(x-3*x^(1/2))^(1/3),x, algorithm=""fricas"")","\frac{6}{5} \, {\left(x - 3 \, \sqrt{x}\right)}^{\frac{5}{3}}"," ",0,"6/5*(x - 3*sqrt(x))^(5/3)","A",0
839,1,19,0,0.700232," ","integrate(1/(-9*x^2+4)^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \arctan\left(\frac{\sqrt{-9 \, x^{2} + 4} - 2}{3 \, x}\right)"," ",0,"-2/3*arctan(1/3*(sqrt(-9*x^2 + 4) - 2)/x)","B",0
840,1,25,0,0.608279," ","integrate(1/(2-3*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \arctan\left(\frac{\sqrt{3 \, x + 2} \sqrt{-3 \, x + 2} - 2}{3 \, x}\right)"," ",0,"-2/3*arctan(1/3*(sqrt(3*x + 2)*sqrt(-3*x + 2) - 2)/x)","B",0
841,1,19,0,0.857130," ","integrate(1/((2-3*x)*(2+3*x))^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \arctan\left(\frac{\sqrt{-9 \, x^{2} + 4} - 2}{3 \, x}\right)"," ",0,"-2/3*arctan(1/3*(sqrt(-9*x^2 + 4) - 2)/x)","B",0
842,1,29,0,0.738348," ","integrate(1/(-x^2-2*x+15)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{2} - 2 \, x + 15} {\left(x + 1\right)}}{x^{2} + 2 \, x - 15}\right)"," ",0,"-arctan(sqrt(-x^2 - 2*x + 15)*(x + 1)/(x^2 + 2*x - 15))","B",0
843,1,29,0,0.625679," ","integrate(1/(3-x)^(1/2)/(5+x)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{x + 5} {\left(x + 1\right)} \sqrt{-x + 3}}{x^{2} + 2 \, x - 15}\right)"," ",0,"-arctan(sqrt(x + 5)*(x + 1)*sqrt(-x + 3)/(x^2 + 2*x - 15))","B",0
844,1,29,0,0.590927," ","integrate(1/((3-x)*(5+x))^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{2} - 2 \, x + 15} {\left(x + 1\right)}}{x^{2} + 2 \, x - 15}\right)"," ",0,"-arctan(sqrt(-x^2 - 2*x + 15)*(x + 1)/(x^2 + 2*x - 15))","B",0
845,1,29,0,0.767784," ","integrate(1/(-x^2-8*x-15)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{2} - 8 \, x - 15} {\left(x + 4\right)}}{x^{2} + 8 \, x + 15}\right)"," ",0,"-arctan(sqrt(-x^2 - 8*x - 15)*(x + 4)/(x^2 + 8*x + 15))","B",0
846,1,29,0,0.576824," ","integrate(1/(-3-x)^(1/2)/(5+x)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{x + 5} {\left(x + 4\right)} \sqrt{-x - 3}}{x^{2} + 8 \, x + 15}\right)"," ",0,"-arctan(sqrt(x + 5)*(x + 4)*sqrt(-x - 3)/(x^2 + 8*x + 15))","B",0
847,1,29,0,0.949026," ","integrate(1/((-3-x)*(5+x))^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{2} - 8 \, x - 15} {\left(x + 4\right)}}{x^{2} + 8 \, x + 15}\right)"," ",0,"-arctan(sqrt(-x^2 - 8*x - 15)*(x + 4)/(x^2 + 8*x + 15))","B",0
848,1,7,0,0.624471," ","integrate(1-x^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, x^{\frac{3}{2}} + x"," ",0,"-2/3*x^(3/2) + x","A",0
849,1,7,0,0.626399," ","integrate((1-x)/(1+x^(1/2)),x, algorithm=""fricas"")","-\frac{2}{3} \, x^{\frac{3}{2}} + x"," ",0,"-2/3*x^(3/2) + x","A",0
850,1,26,0,0.537048," ","integrate((1/(-x^2+1))^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(\frac{{\left(x^{2} - 1\right)} \sqrt{-\frac{1}{x^{2} - 1}} + 1}{x}\right)"," ",0,"2*arctan(((x^2 - 1)*sqrt(-1/(x^2 - 1)) + 1)/x)","A",0
851,1,26,0,0.627365," ","integrate(((x^2+1)/(-x^4+1))^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(\frac{{\left(x^{2} - 1\right)} \sqrt{-\frac{1}{x^{2} - 1}} + 1}{x}\right)"," ",0,"2*arctan(((x^2 - 1)*sqrt(-1/(x^2 - 1)) + 1)/x)","A",0
852,1,14,0,0.686378," ","integrate((1/(x^2-1))^(1/2),x, algorithm=""fricas"")","-\log\left(-x + \sqrt{x^{2} - 1}\right)"," ",0,"-log(-x + sqrt(x^2 - 1))","A",0
853,1,14,0,0.622996," ","integrate(((x^2+1)/(x^4-1))^(1/2),x, algorithm=""fricas"")","-\log\left(-x + \sqrt{x^{2} - 1}\right)"," ",0,"-log(-x + sqrt(x^2 - 1))","A",0
854,1,9,0,0.575233," ","integrate(1/(1-x)^(1/2),x, algorithm=""fricas"")","-2 \, \sqrt{-x + 1}"," ",0,"-2*sqrt(-x + 1)","A",0
855,1,16,0,0.764852," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-x^{2} + 1}}{\sqrt{x + 1}}"," ",0,"-2*sqrt(-x^2 + 1)/sqrt(x + 1)","C",0
856,1,7,0,0.657274," ","integrate(1/(1+x)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x + 1}"," ",0,"2*sqrt(x + 1)","A",0
857,1,23,0,0.875715," ","integrate((1-x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-x^{2} + 1} \sqrt{-x + 1}}{x - 1}"," ",0,"-2*sqrt(-x^2 + 1)*sqrt(-x + 1)/(x - 1)","C",0
858,1,12,0,0.563311," ","integrate((1-x)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x - 1\right)} \sqrt{-x + 1}"," ",0,"2/3*(x - 1)*sqrt(-x + 1)","A",0
859,1,19,0,0.710620," ","integrate((-x^2+1)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-x^{2} + 1} {\left(x - 1\right)}}{3 \, \sqrt{x + 1}}"," ",0,"2/3*sqrt(-x^2 + 1)*(x - 1)/sqrt(x + 1)","B",0
860,1,7,0,0.579971," ","integrate((1+x)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}}"," ",0,"2/3*(x + 1)^(3/2)","A",0
861,1,26,0,0.838191," ","integrate((-x^2+1)^(1/2)/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-x^{2} + 1} {\left(x + 1\right)} \sqrt{-x + 1}}{3 \, {\left(x - 1\right)}}"," ",0,"-2/3*sqrt(-x^2 + 1)*(x + 1)*sqrt(-x + 1)/(x - 1)","B",0
862,1,52,0,0.863273," ","integrate((2+3*x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-4 \, \sqrt{3} {\left(6 \, x + 5\right)} \sqrt{3 \, x + 2} \sqrt{x + 1} + 72 \, x^{2} + 120 \, x + 49\right) + \sqrt{3 \, x + 2} \sqrt{x + 1}"," ",0,"1/12*sqrt(3)*log(-4*sqrt(3)*(6*x + 5)*sqrt(3*x + 2)*sqrt(x + 1) + 72*x^2 + 120*x + 49) + sqrt(3*x + 2)*sqrt(x + 1)","A",0
863,1,96,0,0.900973," ","integrate((1-x)^(1/2)*(2+3*x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{3} {\left(x - 1\right)} \log\left(-\frac{72 \, x^{3} + 4 \, \sqrt{3} \sqrt{-x^{2} + 1} {\left(6 \, x + 5\right)} \sqrt{3 \, x + 2} \sqrt{-x + 1} + 48 \, x^{2} - 71 \, x - 49}{x - 1}\right) - 12 \, \sqrt{-x^{2} + 1} \sqrt{3 \, x + 2} \sqrt{-x + 1}}{12 \, {\left(x - 1\right)}}"," ",0,"1/12*(sqrt(3)*(x - 1)*log(-(72*x^3 + 4*sqrt(3)*sqrt(-x^2 + 1)*(6*x + 5)*sqrt(3*x + 2)*sqrt(-x + 1) + 48*x^2 - 71*x - 49)/(x - 1)) - 12*sqrt(-x^2 + 1)*sqrt(3*x + 2)*sqrt(-x + 1))/(x - 1)","B",0
864,1,74,0,0.710168," ","integrate((1+x)^(3/2)/(1-x)^(3/2)/x,x, algorithm=""fricas"")","\frac{2 \, {\left(x - 1\right)} \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + {\left(x - 1\right)} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + 4 \, x - 4 \, \sqrt{x + 1} \sqrt{-x + 1} - 4}{x - 1}"," ",0,"(2*(x - 1)*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + (x - 1)*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + 4*x - 4*sqrt(x + 1)*sqrt(-x + 1) - 4)/(x - 1)","B",0
865,1,63,0,0.787029," ","integrate((1+x)^3/x/(-x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x - 1\right)} \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + {\left(x - 1\right)} \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + 4 \, x - 4 \, \sqrt{-x^{2} + 1} - 4}{x - 1}"," ",0,"(2*(x - 1)*arctan((sqrt(-x^2 + 1) - 1)/x) + (x - 1)*log((sqrt(-x^2 + 1) - 1)/x) + 4*x - 4*sqrt(-x^2 + 1) - 4)/(x - 1)","B",0
866,1,93,0,0.827103," ","integrate((a*x+1)^(3/2)/x/(-a*x+1)^(3/2),x, algorithm=""fricas"")","\frac{4 \, a x + 2 \, {\left(a x - 1\right)} \arctan\left(\frac{\sqrt{a x + 1} \sqrt{-a x + 1} - 1}{a x}\right) + {\left(a x - 1\right)} \log\left(\frac{\sqrt{a x + 1} \sqrt{-a x + 1} - 1}{x}\right) - 4 \, \sqrt{a x + 1} \sqrt{-a x + 1} - 4}{a x - 1}"," ",0,"(4*a*x + 2*(a*x - 1)*arctan((sqrt(a*x + 1)*sqrt(-a*x + 1) - 1)/(a*x)) + (a*x - 1)*log((sqrt(a*x + 1)*sqrt(-a*x + 1) - 1)/x) - 4*sqrt(a*x + 1)*sqrt(-a*x + 1) - 4)/(a*x - 1)","B",0
867,1,82,0,0.948405," ","integrate((a*x+1)^3/x/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{4 \, a x + 2 \, {\left(a x - 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + {\left(a x - 1\right)} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) - 4 \, \sqrt{-a^{2} x^{2} + 1} - 4}{a x - 1}"," ",0,"(4*a*x + 2*(a*x - 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + (a*x - 1)*log((sqrt(-a^2*x^2 + 1) - 1)/x) - 4*sqrt(-a^2*x^2 + 1) - 4)/(a*x - 1)","A",0
868,1,18,0,0.630360," ","integrate(1/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
869,1,27,0,0.833541," ","integrate((x^2+1)^(1/2)/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{4} + 1} \sqrt{x^{2} + 1}}{x^{3} + x}\right)"," ",0,"-arctan(sqrt(-x^4 + 1)*sqrt(x^2 + 1)/(x^3 + x))","B",0
870,1,14,0,0.836159," ","integrate(1/(x^2+1)^(1/2),x, algorithm=""fricas"")","-\log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-log(-x + sqrt(x^2 + 1))","B",0
871,1,81,0,0.561334," ","integrate((-x^2+1)^(1/2)/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{x^{3} + \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} - x}{x^{3} - x}\right) + \frac{1}{2} \, \log\left(-\frac{x^{3} - \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} - x}{x^{3} - x}\right)"," ",0,"-1/2*log((x^3 + sqrt(-x^4 + 1)*sqrt(-x^2 + 1) - x)/(x^3 - x)) + 1/2*log(-(x^3 - sqrt(-x^4 + 1)*sqrt(-x^2 + 1) - x)/(x^3 - x))","B",0
872,1,31,0,0.621466," ","integrate((-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x - \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/2*sqrt(-x^2 + 1)*x - arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
873,1,60,0,0.514641," ","integrate((-x^4+1)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-x^{4} + 1} \sqrt{x^{2} + 1} x - {\left(x^{2} + 1\right)} \arctan\left(\frac{\sqrt{-x^{4} + 1} \sqrt{x^{2} + 1}}{x^{3} + x}\right)}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(sqrt(-x^4 + 1)*sqrt(x^2 + 1)*x - (x^2 + 1)*arctan(sqrt(-x^4 + 1)*sqrt(x^2 + 1)/(x^3 + x)))/(x^2 + 1)","B",0
874,1,25,0,0.590480," ","integrate((x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{x^{2} + 1} x - \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"1/2*sqrt(x^2 + 1)*x - 1/2*log(-x + sqrt(x^2 + 1))","A",0
875,1,120,0,0.560266," ","integrate((-x^4+1)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} x + {\left(x^{2} - 1\right)} \log\left(\frac{x^{3} + \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} - x}{x^{3} - x}\right) - {\left(x^{2} - 1\right)} \log\left(-\frac{x^{3} - \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} - x}{x^{3} - x}\right)}{4 \, {\left(x^{2} - 1\right)}}"," ",0,"-1/4*(2*sqrt(-x^4 + 1)*sqrt(-x^2 + 1)*x + (x^2 - 1)*log((x^3 + sqrt(-x^4 + 1)*sqrt(-x^2 + 1) - x)/(x^3 - x)) - (x^2 - 1)*log(-(x^3 - sqrt(-x^4 + 1)*sqrt(-x^2 + 1) - x)/(x^3 - x)))/(x^2 - 1)","B",0
876,0,0,0,0.700647," ","integrate(((c*x^2+a+b)/d)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{c x^{2} + a + b}{d}\right)^{m}, x\right)"," ",0,"integral(((c*x^2 + a + b)/d)^m, x)","F",0
877,1,30,0,0.515611," ","integrate(1/(x-(x^2+1)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, x^{2} - \frac{1}{2} \, \sqrt{x^{2} + 1} x + \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-1/2*x^2 - 1/2*sqrt(x^2 + 1)*x + 1/2*log(-x + sqrt(x^2 + 1))","A",0
878,1,84,0,0.598088," ","integrate(1/(x-(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + \frac{1}{4} \, \log\left(2 \, x^{2} - 1\right) + \frac{1}{4} \, \log\left(-\frac{x^{2} + \sqrt{-x^{2} + 1} {\left(x + 1\right)} - x - 1}{x^{2}}\right) - \frac{1}{4} \, \log\left(-\frac{x^{2} - \sqrt{-x^{2} + 1} {\left(x - 1\right)} + x - 1}{x^{2}}\right)"," ",0,"arctan((sqrt(-x^2 + 1) - 1)/x) + 1/4*log(2*x^2 - 1) + 1/4*log(-(x^2 + sqrt(-x^2 + 1)*(x + 1) - x - 1)/x^2) - 1/4*log(-(x^2 - sqrt(-x^2 + 1)*(x - 1) + x - 1)/x^2)","B",0
879,1,90,0,0.549168," ","integrate(1/(x-(2*x^2+1)^(1/2)),x, algorithm=""fricas"")","\sqrt{2} \log\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) - \frac{1}{2} \, \log\left(\frac{2 \, x^{2} - \sqrt{2 \, x^{2} + 1} {\left(x + 1\right)} + x + 1}{x^{2}}\right) + \frac{1}{2} \, \log\left(\frac{2 \, x^{2} + \sqrt{2 \, x^{2} + 1} {\left(x - 1\right)} - x + 1}{x^{2}}\right)"," ",0,"sqrt(2)*log(sqrt(2)*x - sqrt(2*x^2 + 1)) - 1/2*log(x^2 + 1) - 1/2*log((2*x^2 - sqrt(2*x^2 + 1)*(x + 1) + x + 1)/x^2) + 1/2*log((2*x^2 + sqrt(2*x^2 + 1)*(x - 1) - x + 1)/x^2)","B",0
880,1,67,0,0.578829," ","integrate((2*x-x^3+x^2*(-x^2+2)^(1/2))/(2*x^2-2),x, algorithm=""fricas"")","-\frac{1}{4} \, x^{2} + \frac{1}{4} \, \sqrt{-x^{2} + 2} x + \frac{1}{4} \, \log\left(x^{2} - 1\right) - \frac{1}{8} \, \log\left(-\frac{\sqrt{-x^{2} + 2} x + 1}{x^{2}}\right) + \frac{1}{8} \, \log\left(\frac{\sqrt{-x^{2} + 2} x - 1}{x^{2}}\right)"," ",0,"-1/4*x^2 + 1/4*sqrt(-x^2 + 2)*x + 1/4*log(x^2 - 1) - 1/8*log(-(sqrt(-x^2 + 2)*x + 1)/x^2) + 1/8*log((sqrt(-x^2 + 2)*x - 1)/x^2)","A",0
881,1,67,0,0.632168," ","integrate(x*(-x^2+2)^(1/2)/(x-(-x^2+2)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{4} \, x^{2} + \frac{1}{4} \, \sqrt{-x^{2} + 2} x + \frac{1}{4} \, \log\left(x^{2} - 1\right) - \frac{1}{8} \, \log\left(-\frac{\sqrt{-x^{2} + 2} x + 1}{x^{2}}\right) + \frac{1}{8} \, \log\left(\frac{\sqrt{-x^{2} + 2} x - 1}{x^{2}}\right)"," ",0,"-1/4*x^2 + 1/4*sqrt(-x^2 + 2)*x + 1/4*log(x^2 - 1) - 1/8*log(-(sqrt(-x^2 + 2)*x + 1)/x^2) + 1/8*log((sqrt(-x^2 + 2)*x - 1)/x^2)","A",0
882,1,66,0,0.418010," ","integrate(x/(-x+(-x^2+2*x)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} - \frac{1}{2} \, \log\left(x - 1\right) + \frac{1}{2} \, \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"-1/2*x - 1/2*sqrt(-x^2 + 2*x) - 1/2*log(x - 1) + 1/2*log((x + sqrt(-x^2 + 2*x))/x) - 1/2*log(-(x - sqrt(-x^2 + 2*x))/x)","A",0
883,1,66,0,0.395817," ","integrate((x+(-x^2+2*x)^(1/2))/(2-2*x),x, algorithm=""fricas"")","-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} - \frac{1}{2} \, \log\left(x - 1\right) + \frac{1}{2} \, \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"-1/2*x - 1/2*sqrt(-x^2 + 2*x) - 1/2*log(x - 1) + 1/2*log((x + sqrt(-x^2 + 2*x))/x) - 1/2*log(-(x - sqrt(-x^2 + 2*x))/x)","A",0
884,1,64,0,0.400398," ","integrate((x+(2-x)^(1/2)*x^(1/2))/(2-2*x),x, algorithm=""fricas"")","-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{x} \sqrt{-x + 2} - \frac{1}{2} \, \log\left(x - 1\right) + \frac{1}{2} \, \log\left(\frac{x + \sqrt{x} \sqrt{-x + 2}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{x} \sqrt{-x + 2}}{x}\right)"," ",0,"-1/2*x - 1/2*sqrt(x)*sqrt(-x + 2) - 1/2*log(x - 1) + 1/2*log((x + sqrt(x)*sqrt(-x + 2))/x) - 1/2*log(-(x - sqrt(x)*sqrt(-x + 2))/x)","A",0
885,1,64,0,0.394319," ","integrate(x^(1/2)/((2-x)^(1/2)-x^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{x} \sqrt{-x + 2} - \frac{1}{2} \, \log\left(x - 1\right) + \frac{1}{2} \, \log\left(\frac{x + \sqrt{x} \sqrt{-x + 2}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{x} \sqrt{-x + 2}}{x}\right)"," ",0,"-1/2*x - 1/2*sqrt(x)*sqrt(-x + 2) - 1/2*log(x - 1) + 1/2*log((x + sqrt(x)*sqrt(-x + 2))/x) - 1/2*log(-(x - sqrt(x)*sqrt(-x + 2))/x)","A",0
886,1,20,0,0.397803," ","integrate(1/((1+x)*(x^2-1))^(2/3),x, algorithm=""fricas"")","\frac{3 \, {\left(x^{3} + x^{2} - x - 1\right)}^{\frac{1}{3}}}{2 \, {\left(x + 1\right)}}"," ",0,"3/2*(x^3 + x^2 - x - 1)^(1/3)/(x + 1)","A",0
887,1,16,0,0.481870," ","integrate((x^2-1)/(x^2+1)/(x*(x^2+1))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x^{3} + x}}{x^{2} + 1}"," ",0,"-2*sqrt(x^3 + x)/(x^2 + 1)","A",0
888,1,16,0,0.399874," ","integrate((x^2-1)/(x^2+1)/(x^3+x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x^{3} + x}}{x^{2} + 1}"," ",0,"-2*sqrt(x^3 + x)/(x^2 + 1)","A",0
889,1,30,0,0.401096," ","integrate(((x^2-1)^2/x/(x^2+1))^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{2 \, x \sqrt{\frac{x^{4} - 2 \, x^{2} + 1}{x^{3} + x}}}{x^{2} - 1}"," ",0,"-2*x*sqrt((x^4 - 2*x^2 + 1)/(x^3 + x))/(x^2 - 1)","A",0
890,1,30,0,0.470790," ","integrate(((x^2-1)^2/(x^3+x))^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{2 \, x \sqrt{\frac{x^{4} - 2 \, x^{2} + 1}{x^{3} + x}}}{x^{2} - 1}"," ",0,"-2*x*sqrt((x^4 - 2*x^2 + 1)/(x^3 + x))/(x^2 - 1)","A",0
891,1,208,0,0.463719," ","integrate(1/(a+b/x^2)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a d} \log\left(8 \, a^{2} d^{2} x^{4} + a^{2} c^{2} + 6 \, a b c d + b^{2} d^{2} + 8 \, {\left(a^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, a d x^{3} + {\left(a c + b d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{a d} \sqrt{\frac{a x^{2} + b}{x^{2}}}\right)}{4 \, a d}, -\frac{\sqrt{-a d} \arctan\left(\frac{{\left(2 \, a d x^{3} + {\left(a c + b d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-a d} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{2 \, {\left(a^{2} d^{2} x^{4} + a b c d + {\left(a^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right)}{2 \, a d}\right]"," ",0,"[1/4*sqrt(a*d)*log(8*a^2*d^2*x^4 + a^2*c^2 + 6*a*b*c*d + b^2*d^2 + 8*(a^2*c*d + a*b*d^2)*x^2 + 4*(2*a*d*x^3 + (a*c + b*d)*x)*sqrt(d*x^2 + c)*sqrt(a*d)*sqrt((a*x^2 + b)/x^2))/(a*d), -1/2*sqrt(-a*d)*arctan(1/2*(2*a*d*x^3 + (a*c + b*d)*x)*sqrt(d*x^2 + c)*sqrt(-a*d)*sqrt((a*x^2 + b)/x^2)/(a^2*d^2*x^4 + a*b*c*d + (a^2*c*d + a*b*d^2)*x^2))/(a*d)]","A",0
892,1,38,0,0.433615," ","integrate((x^4-2*x^2)^(1/2)/(x^2-1)/(x^2+2),x, algorithm=""fricas"")","-\frac{1}{3} \, \arctan\left(\frac{\sqrt{x^{4} - 2 \, x^{2}}}{x}\right) + \frac{2}{3} \, \arctan\left(\frac{\sqrt{x^{4} - 2 \, x^{2}}}{2 \, x}\right)"," ",0,"-1/3*arctan(sqrt(x^4 - 2*x^2)/x) + 2/3*arctan(1/2*sqrt(x^4 - 2*x^2)/x)","A",0
893,1,36,0,0.398846," ","integrate((1-1/(x^2-1)^2)^(1/2)/(-x^2+2),x, algorithm=""fricas"")","-\arctan\left(\frac{{\left(x^{2} - 1\right)} \sqrt{\frac{x^{4} - 2 \, x^{2}}{x^{4} - 2 \, x^{2} + 1}}}{x}\right)"," ",0,"-arctan((x^2 - 1)*sqrt((x^4 - 2*x^2)/(x^4 - 2*x^2 + 1))/x)","A",0
894,1,74,0,0.409949," ","integrate(((x^4-2*x^2)/(x^2-1)^2)^(1/2)/(x^2+2),x, algorithm=""fricas"")","-\frac{1}{3} \, \arctan\left(\frac{{\left(x^{2} - 1\right)} \sqrt{\frac{x^{4} - 2 \, x^{2}}{x^{4} - 2 \, x^{2} + 1}}}{x}\right) + \frac{2}{3} \, \arctan\left(\frac{{\left(x^{2} - 1\right)} \sqrt{\frac{x^{4} - 2 \, x^{2}}{x^{4} - 2 \, x^{2} + 1}}}{2 \, x}\right)"," ",0,"-1/3*arctan((x^2 - 1)*sqrt((x^4 - 2*x^2)/(x^4 - 2*x^2 + 1))/x) + 2/3*arctan(1/2*(x^2 - 1)*sqrt((x^4 - 2*x^2)/(x^4 - 2*x^2 + 1))/x)","A",0
895,1,117,0,0.401119," ","integrate((1+2*x/(x^2+1))^(5/2),x, algorithm=""fricas"")","-\frac{8 \, x^{3} + 8 \, x^{2} + 15 \, {\left(x^{3} + x^{2} + x + 1\right)} \log\left(-\frac{x^{2} - {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + x}{x + 1}\right) - {\left(3 \, x^{4} - 8 \, x^{3} - 18 \, x^{2} - 12 \, x - 17\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + 8 \, x + 8}{3 \, {\left(x^{3} + x^{2} + x + 1\right)}}"," ",0,"-1/3*(8*x^3 + 8*x^2 + 15*(x^3 + x^2 + x + 1)*log(-(x^2 - (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + x)/(x + 1)) - (3*x^4 - 8*x^3 - 18*x^2 - 12*x - 17)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + 8*x + 8)/(x^3 + x^2 + x + 1)","A",0
896,1,83,0,0.397117," ","integrate((1+2*x/(x^2+1))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(x + 1\right)} \log\left(-\frac{x^{2} - {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + x}{x + 1}\right) - {\left(x^{2} - 2 \, x - 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + 2 \, x + 2}{x + 1}"," ",0,"-(3*(x + 1)*log(-(x^2 - (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + x)/(x + 1)) - (x^2 - 2*x - 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + 2*x + 2)/(x + 1)","A",0
897,1,75,0,0.402216," ","integrate((1+2*x/(x^2+1))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(x + 1\right)} \log\left(-\frac{x^{2} - {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + x}{x + 1}\right) - {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}}}{x + 1}"," ",0,"-((x + 1)*log(-(x^2 - (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + x)/(x + 1)) - (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)))/(x + 1)","A",0
898,1,142,0,0.404186," ","integrate(1/(1+2*x/(x^2+1))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(x + 1\right)} \log\left(-\frac{x^{2} + \sqrt{2} {\left(x^{2} - 1\right)} + {\left(2 \, x^{2} + \sqrt{2} {\left(x^{2} + 1\right)} + 2\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} - 1}{x^{2} + 2 \, x + 1}\right) + {\left(x + 1\right)} \log\left(-\frac{x^{2} - {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + x}{x + 1}\right) + {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}}}{x + 1}"," ",0,"(sqrt(2)*(x + 1)*log(-(x^2 + sqrt(2)*(x^2 - 1) + (2*x^2 + sqrt(2)*(x^2 + 1) + 2)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) - 1)/(x^2 + 2*x + 1)) + (x + 1)*log(-(x^2 - (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + x)/(x + 1)) + (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)))/(x + 1)","A",0
899,1,205,0,0.415656," ","integrate(1/(1+2*x/(x^2+1))^(3/2),x, algorithm=""fricas"")","\frac{10 \, x^{3} + 9 \, \sqrt{2} {\left(x^{3} + 3 \, x^{2} + 3 \, x + 1\right)} \log\left(-\frac{x^{2} + \sqrt{2} {\left(x^{2} - 1\right)} + {\left(2 \, x^{2} + \sqrt{2} {\left(x^{2} + 1\right)} + 2\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} - 1}{x^{2} + 2 \, x + 1}\right) + 30 \, x^{2} + 12 \, {\left(x^{3} + 3 \, x^{2} + 3 \, x + 1\right)} \log\left(-\frac{x^{2} - {\left(x^{2} + 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + x}{x + 1}\right) + 2 \, {\left(2 \, x^{4} + 9 \, x^{3} + 7 \, x^{2} + 9 \, x + 5\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + 30 \, x + 10}{4 \, {\left(x^{3} + 3 \, x^{2} + 3 \, x + 1\right)}}"," ",0,"1/4*(10*x^3 + 9*sqrt(2)*(x^3 + 3*x^2 + 3*x + 1)*log(-(x^2 + sqrt(2)*(x^2 - 1) + (2*x^2 + sqrt(2)*(x^2 + 1) + 2)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) - 1)/(x^2 + 2*x + 1)) + 30*x^2 + 12*(x^3 + 3*x^2 + 3*x + 1)*log(-(x^2 - (x^2 + 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + x)/(x + 1)) + 2*(2*x^4 + 9*x^3 + 7*x^2 + 9*x + 5)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + 30*x + 10)/(x^3 + 3*x^2 + 3*x + 1)","A",0
900,1,31,0,0.419562," ","integrate((1+2*x/(x^2+1))^(1/2)/(x^2+1),x, algorithm=""fricas"")","\frac{{\left(x - 1\right)} \sqrt{\frac{x^{2} + 2 \, x + 1}{x^{2} + 1}} + x + 1}{x + 1}"," ",0,"((x - 1)*sqrt((x^2 + 2*x + 1)/(x^2 + 1)) + x + 1)/(x + 1)","A",0
901,0,0,0,0.400904," ","integrate(F(x)*(-x^2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{2} + x} F\left(x\right), x\right)"," ",0,"integral(sqrt(-x^2 + x)*F(x), x)","F",0
902,0,0,0,0.422280," ","integrate(F(x)/(-x^2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + x} F\left(x\right)}{x^{2} - x}, x\right)"," ",0,"integral(-sqrt(-x^2 + x)*F(x)/(x^2 - x), x)","F",0
903,0,0,0,0.402169," ","integrate(F(x)*(1-x)^(1/2)*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x} \sqrt{-x + 1} F\left(x\right), x\right)"," ",0,"integral(sqrt(x)*sqrt(-x + 1)*F(x), x)","F",0
904,0,0,0,0.398429," ","integrate(F(x)/(1-x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x} \sqrt{-x + 1} F\left(x\right)}{x^{2} - x}, x\right)"," ",0,"integral(-sqrt(x)*sqrt(-x + 1)*F(x)/(x^2 - x), x)","F",0
905,0,0,0,0.395267," ","integrate(F((b*x+a)/x),x, algorithm=""fricas"")","{\rm integral}\left(F\left(\frac{b x + a}{x}\right), x\right)"," ",0,"integral(F((b*x + a)/x), x)","F",0
906,0,0,0,0.390484," ","integrate(F((b*x^2+a)/x^2),x, algorithm=""fricas"")","{\rm integral}\left(F\left(\frac{b x^{2} + a}{x^{2}}\right), x\right)"," ",0,"integral(F((b*x^2 + a)/x^2), x)","F",0
907,0,0,0,0.399883," ","integrate(F(x/(b*x+a)),x, algorithm=""fricas"")","{\rm integral}\left(F\left(\frac{x}{b x + a}\right), x\right)"," ",0,"integral(F(x/(b*x + a)), x)","F",0
908,0,0,0,0.426470," ","integrate(F(x^2/(b*x^2+a)),x, algorithm=""fricas"")","{\rm integral}\left(F\left(\frac{x^{2}}{b x^{2} + a}\right), x\right)"," ",0,"integral(F(x^2/(b*x^2 + a)), x)","F",0
909,0,0,0,0.410579," ","integrate(F(x^2/(b*x+a)^2),x, algorithm=""fricas"")","{\rm integral}\left(F\left(\frac{x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right), x\right)"," ",0,"integral(F(x^2/(b^2*x^2 + 2*a*b*x + a^2)), x)","F",0
910,0,0,0,0.406047," ","integrate(F(x^4/(b*x^2+a)^2),x, algorithm=""fricas"")","{\rm integral}\left(F\left(\frac{x^{4}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right), x\right)"," ",0,"integral(F(x^4/(b^2*x^4 + 2*a*b*x^2 + a^2)), x)","F",0
911,1,135,0,1.802898," ","integrate((b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(4 \, b^{2} x^{4} + 4 \, \sqrt{b^{2} x^{4} + a} b x^{2} + 2 \, {\left(\sqrt{2} b^{\frac{3}{2}} x^{3} + \sqrt{2} \sqrt{b^{2} x^{4} + a} \sqrt{b} x\right)} \sqrt{b x^{2} + \sqrt{b^{2} x^{4} + a}} + a\right)}{4 \, \sqrt{b}}, -\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{1}{b}} \arctan\left(\frac{\sqrt{2} \sqrt{b x^{2} + \sqrt{b^{2} x^{4} + a}} \sqrt{-\frac{1}{b}}}{2 \, x}\right)\right]"," ",0,"[1/4*sqrt(2)*log(4*b^2*x^4 + 4*sqrt(b^2*x^4 + a)*b*x^2 + 2*(sqrt(2)*b^(3/2)*x^3 + sqrt(2)*sqrt(b^2*x^4 + a)*sqrt(b)*x)*sqrt(b*x^2 + sqrt(b^2*x^4 + a)) + a)/sqrt(b), -1/2*sqrt(2)*sqrt(-1/b)*arctan(1/2*sqrt(2)*sqrt(b*x^2 + sqrt(b^2*x^4 + a))*sqrt(-1/b)/x)]","A",0
912,1,146,0,1.773559," ","integrate((-b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{1}{b}} \log\left(4 \, b^{2} x^{4} - 4 \, \sqrt{b^{2} x^{4} + a} b x^{2} + 2 \, {\left(\sqrt{2} b^{2} x^{3} \sqrt{-\frac{1}{b}} - \sqrt{2} \sqrt{b^{2} x^{4} + a} b x \sqrt{-\frac{1}{b}}\right)} \sqrt{-b x^{2} + \sqrt{b^{2} x^{4} + a}} + a\right), -\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-b x^{2} + \sqrt{b^{2} x^{4} + a}}}{2 \, \sqrt{b} x}\right)}{2 \, \sqrt{b}}\right]"," ",0,"[1/4*sqrt(2)*sqrt(-1/b)*log(4*b^2*x^4 - 4*sqrt(b^2*x^4 + a)*b*x^2 + 2*(sqrt(2)*b^2*x^3*sqrt(-1/b) - sqrt(2)*sqrt(b^2*x^4 + a)*b*x*sqrt(-1/b))*sqrt(-b*x^2 + sqrt(b^2*x^4 + a)) + a), -1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-b*x^2 + sqrt(b^2*x^4 + a))/(sqrt(b)*x))/sqrt(b)]","A",0
913,-1,0,0,0.000000," ","integrate((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)/(4*x^4+3)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
914,-1,0,0,0.000000," ","integrate((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)^2/(4*x^4+3)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
915,1,25,0,1.069803," ","integrate((-4+x)/(1+x^(1/3))/x^(1/2),x, algorithm=""fricas"")","\frac{6}{7} \, {\left(x - 35\right)} x^{\frac{1}{6}} - \frac{6}{5} \, x^{\frac{5}{6}} + 2 \, \sqrt{x} + 30 \, \arctan\left(x^{\frac{1}{6}}\right)"," ",0,"6/7*(x - 35)*x^(1/6) - 6/5*x^(5/6) + 2*sqrt(x) + 30*arctan(x^(1/6))","A",0
916,1,20,0,0.858558," ","integrate((1+x^(1/2))/(x^(5/6)+x^(7/6)),x, algorithm=""fricas"")","3 \, x^{\frac{1}{3}} + 6 \, \arctan\left(x^{\frac{1}{6}}\right) - 3 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"3*x^(1/3) + 6*arctan(x^(1/6)) - 3*log(x^(1/3) + 1)","A",0
917,1,30,0,1.257305," ","integrate((1+x^(1/2))/(1+x^(1/3))/x^(1/2),x, algorithm=""fricas"")","\frac{3}{2} \, x^{\frac{2}{3}} - 3 \, x^{\frac{1}{3}} + 6 \, x^{\frac{1}{6}} - 6 \, \arctan\left(x^{\frac{1}{6}}\right) + 3 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"3/2*x^(2/3) - 3*x^(1/3) + 6*x^(1/6) - 6*arctan(x^(1/6)) + 3*log(x^(1/3) + 1)","A",0
918,1,75,0,1.223595," ","integrate((2+b/x^2)^(1/2)/(2*x^2+b),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{x^{2} - \sqrt{b} x \sqrt{\frac{2 \, x^{2} + b}{x^{2}}} + b}{x^{2}}\right)}{2 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{2 \, x^{2} + b}{x^{2}}}}{2 \, x^{2} + b}\right)}{b}\right]"," ",0,"[1/2*log(-(x^2 - sqrt(b)*x*sqrt((2*x^2 + b)/x^2) + b)/x^2)/sqrt(b), sqrt(-b)*arctan(sqrt(-b)*x*sqrt((2*x^2 + b)/x^2)/(2*x^2 + b))/b]","B",0
919,1,84,0,1.079959," ","integrate((2-b/x^2)^(1/2)/(2*x^2-b),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b} \log\left(-\frac{x^{2} - \sqrt{-b} x \sqrt{\frac{2 \, x^{2} - b}{x^{2}}} - b}{x^{2}}\right)}{2 \, b}, -\frac{\arctan\left(\frac{\sqrt{b} x \sqrt{\frac{2 \, x^{2} - b}{x^{2}}}}{2 \, x^{2} - b}\right)}{\sqrt{b}}\right]"," ",0,"[-1/2*sqrt(-b)*log(-(x^2 - sqrt(-b)*x*sqrt((2*x^2 - b)/x^2) - b)/x^2)/b, -arctan(sqrt(b)*x*sqrt((2*x^2 - b)/x^2)/(2*x^2 - b))/sqrt(b)]","B",0
920,1,1532,0,2.518044," ","integrate((a+c/x^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} d \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}} - c\right) + \sqrt{c} e \log\left(-\frac{a x^{2} - 2 \, \sqrt{c} x \sqrt{\frac{a x^{2} + c}{x^{2}}} + 2 \, c}{x^{2}}\right) + \sqrt{a d^{2} + c e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, c^{2} e^{2} - {\left(2 \, a^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, {\left(a d x^{2} - c e x\right)} \sqrt{a d^{2} + c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-a} d \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) - \sqrt{c} e \log\left(-\frac{a x^{2} - 2 \, \sqrt{c} x \sqrt{\frac{a x^{2} + c}{x^{2}}} + 2 \, c}{x^{2}}\right) - \sqrt{a d^{2} + c e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, c^{2} e^{2} - {\left(2 \, a^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, {\left(a d x^{2} - c e x\right)} \sqrt{a d^{2} + c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, \frac{\sqrt{a} d \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}} - c\right) + \sqrt{c} e \log\left(-\frac{a x^{2} - 2 \, \sqrt{c} x \sqrt{\frac{a x^{2} + c}{x^{2}}} + 2 \, c}{x^{2}}\right) + 2 \, \sqrt{-a d^{2} - c e^{2}} \arctan\left(\frac{{\left(a d x^{2} - c e x\right)} \sqrt{-a d^{2} - c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a c d^{2} + c^{2} e^{2} + {\left(a^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-a} d \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) - \sqrt{c} e \log\left(-\frac{a x^{2} - 2 \, \sqrt{c} x \sqrt{\frac{a x^{2} + c}{x^{2}}} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{-a d^{2} - c e^{2}} \arctan\left(\frac{{\left(a d x^{2} - c e x\right)} \sqrt{-a d^{2} - c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a c d^{2} + c^{2} e^{2} + {\left(a^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, d e}, \frac{2 \, \sqrt{-c} e \arctan\left(\frac{\sqrt{-c} x \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) + \sqrt{a} d \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}} - c\right) + \sqrt{a d^{2} + c e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, c^{2} e^{2} - {\left(2 \, a^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, {\left(a d x^{2} - c e x\right)} \sqrt{a d^{2} + c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-a} d \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) - 2 \, \sqrt{-c} e \arctan\left(\frac{\sqrt{-c} x \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) - \sqrt{a d^{2} + c e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, c^{2} e^{2} - {\left(2 \, a^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, {\left(a d x^{2} - c e x\right)} \sqrt{a d^{2} + c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, \frac{2 \, \sqrt{-c} e \arctan\left(\frac{\sqrt{-c} x \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) + \sqrt{a} d \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}} - c\right) + 2 \, \sqrt{-a d^{2} - c e^{2}} \arctan\left(\frac{{\left(a d x^{2} - c e x\right)} \sqrt{-a d^{2} - c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a c d^{2} + c^{2} e^{2} + {\left(a^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, d e}, -\frac{\sqrt{-a} d \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) - \sqrt{-c} e \arctan\left(\frac{\sqrt{-c} x \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a x^{2} + c}\right) - \sqrt{-a d^{2} - c e^{2}} \arctan\left(\frac{{\left(a d x^{2} - c e x\right)} \sqrt{-a d^{2} - c e^{2}} \sqrt{\frac{a x^{2} + c}{x^{2}}}}{a c d^{2} + c^{2} e^{2} + {\left(a^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{d e}\right]"," ",0,"[1/2*(sqrt(a)*d*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + c)/x^2) - c) + sqrt(c)*e*log(-(a*x^2 - 2*sqrt(c)*x*sqrt((a*x^2 + c)/x^2) + 2*c)/x^2) + sqrt(a*d^2 + c*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*c^2*e^2 - (2*a^2*d^2 + a*c*e^2)*x^2 + 2*(a*d*x^2 - c*e*x)*sqrt(a*d^2 + c*e^2)*sqrt((a*x^2 + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), -1/2*(2*sqrt(-a)*d*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) - sqrt(c)*e*log(-(a*x^2 - 2*sqrt(c)*x*sqrt((a*x^2 + c)/x^2) + 2*c)/x^2) - sqrt(a*d^2 + c*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*c^2*e^2 - (2*a^2*d^2 + a*c*e^2)*x^2 + 2*(a*d*x^2 - c*e*x)*sqrt(a*d^2 + c*e^2)*sqrt((a*x^2 + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), 1/2*(sqrt(a)*d*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + c)/x^2) - c) + sqrt(c)*e*log(-(a*x^2 - 2*sqrt(c)*x*sqrt((a*x^2 + c)/x^2) + 2*c)/x^2) + 2*sqrt(-a*d^2 - c*e^2)*arctan((a*d*x^2 - c*e*x)*sqrt(-a*d^2 - c*e^2)*sqrt((a*x^2 + c)/x^2)/(a*c*d^2 + c^2*e^2 + (a^2*d^2 + a*c*e^2)*x^2)))/(d*e), -1/2*(2*sqrt(-a)*d*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) - sqrt(c)*e*log(-(a*x^2 - 2*sqrt(c)*x*sqrt((a*x^2 + c)/x^2) + 2*c)/x^2) - 2*sqrt(-a*d^2 - c*e^2)*arctan((a*d*x^2 - c*e*x)*sqrt(-a*d^2 - c*e^2)*sqrt((a*x^2 + c)/x^2)/(a*c*d^2 + c^2*e^2 + (a^2*d^2 + a*c*e^2)*x^2)))/(d*e), 1/2*(2*sqrt(-c)*e*arctan(sqrt(-c)*x*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) + sqrt(a)*d*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + c)/x^2) - c) + sqrt(a*d^2 + c*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*c^2*e^2 - (2*a^2*d^2 + a*c*e^2)*x^2 + 2*(a*d*x^2 - c*e*x)*sqrt(a*d^2 + c*e^2)*sqrt((a*x^2 + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), -1/2*(2*sqrt(-a)*d*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) - 2*sqrt(-c)*e*arctan(sqrt(-c)*x*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) - sqrt(a*d^2 + c*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*c^2*e^2 - (2*a^2*d^2 + a*c*e^2)*x^2 + 2*(a*d*x^2 - c*e*x)*sqrt(a*d^2 + c*e^2)*sqrt((a*x^2 + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), 1/2*(2*sqrt(-c)*e*arctan(sqrt(-c)*x*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) + sqrt(a)*d*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + c)/x^2) - c) + 2*sqrt(-a*d^2 - c*e^2)*arctan((a*d*x^2 - c*e*x)*sqrt(-a*d^2 - c*e^2)*sqrt((a*x^2 + c)/x^2)/(a*c*d^2 + c^2*e^2 + (a^2*d^2 + a*c*e^2)*x^2)))/(d*e), -(sqrt(-a)*d*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) - sqrt(-c)*e*arctan(sqrt(-c)*x*sqrt((a*x^2 + c)/x^2)/(a*x^2 + c)) - sqrt(-a*d^2 - c*e^2)*arctan((a*d*x^2 - c*e*x)*sqrt(-a*d^2 - c*e^2)*sqrt((a*x^2 + c)/x^2)/(a*c*d^2 + c^2*e^2 + (a^2*d^2 + a*c*e^2)*x^2)))/(d*e)]","A",0
921,1,2411,0,76.215747," ","integrate((a+c/x^2+b/x)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} d \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + \sqrt{c} e \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) + \sqrt{a d^{2} - b d e + c e^{2}} \log\left(\frac{8 \, b c d e - 8 \, c^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, a^{2} d^{2} - 8 \, a b d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 2 \, {\left(4 \, a b d^{2} + 4 \, b c e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x + 4 \, \sqrt{a d^{2} - b d e + c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-a} d \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) - \sqrt{c} e \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) - \sqrt{a d^{2} - b d e + c e^{2}} \log\left(\frac{8 \, b c d e - 8 \, c^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, a^{2} d^{2} - 8 \, a b d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 2 \, {\left(4 \, a b d^{2} + 4 \, b c e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x + 4 \, \sqrt{a d^{2} - b d e + c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, \frac{\sqrt{a} d \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + \sqrt{c} e \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) - 2 \, \sqrt{-a d^{2} + b d e - c e^{2}} \arctan\left(-\frac{\sqrt{-a d^{2} + b d e - c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c d^{2} - b c d e + c^{2} e^{2} + {\left(a^{2} d^{2} - a b d e + a c e^{2}\right)} x^{2} + {\left(a b d^{2} - b^{2} d e + b c e^{2}\right)} x\right)}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-a} d \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) - \sqrt{c} e \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) + 2 \, \sqrt{-a d^{2} + b d e - c e^{2}} \arctan\left(-\frac{\sqrt{-a d^{2} + b d e - c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c d^{2} - b c d e + c^{2} e^{2} + {\left(a^{2} d^{2} - a b d e + a c e^{2}\right)} x^{2} + {\left(a b d^{2} - b^{2} d e + b c e^{2}\right)} x\right)}}\right)}{2 \, d e}, \frac{2 \, \sqrt{-c} e \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) + \sqrt{a} d \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + \sqrt{a d^{2} - b d e + c e^{2}} \log\left(\frac{8 \, b c d e - 8 \, c^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, a^{2} d^{2} - 8 \, a b d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 2 \, {\left(4 \, a b d^{2} + 4 \, b c e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x + 4 \, \sqrt{a d^{2} - b d e + c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-a} d \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) - 2 \, \sqrt{-c} e \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) - \sqrt{a d^{2} - b d e + c e^{2}} \log\left(\frac{8 \, b c d e - 8 \, c^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, a^{2} d^{2} - 8 \, a b d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 2 \, {\left(4 \, a b d^{2} + 4 \, b c e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x + 4 \, \sqrt{a d^{2} - b d e + c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, \frac{2 \, \sqrt{-c} e \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) + \sqrt{a} d \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) - 2 \, \sqrt{-a d^{2} + b d e - c e^{2}} \arctan\left(-\frac{\sqrt{-a d^{2} + b d e - c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c d^{2} - b c d e + c^{2} e^{2} + {\left(a^{2} d^{2} - a b d e + a c e^{2}\right)} x^{2} + {\left(a b d^{2} - b^{2} d e + b c e^{2}\right)} x\right)}}\right)}{2 \, d e}, -\frac{\sqrt{-a} d \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) - \sqrt{-c} e \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) + \sqrt{-a d^{2} + b d e - c e^{2}} \arctan\left(-\frac{\sqrt{-a d^{2} + b d e - c e^{2}} {\left({\left(2 \, a d - b e\right)} x^{2} + {\left(b d - 2 \, c e\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c d^{2} - b c d e + c^{2} e^{2} + {\left(a^{2} d^{2} - a b d e + a c e^{2}\right)} x^{2} + {\left(a b d^{2} - b^{2} d e + b c e^{2}\right)} x\right)}}\right)}{d e}\right]"," ",0,"[1/2*(sqrt(a)*d*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + sqrt(c)*e*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) + sqrt(a*d^2 - b*d*e + c*e^2)*log((8*b*c*d*e - 8*c^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*a^2*d^2 - 8*a*b*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 2*(4*a*b*d^2 + 4*b*c*e^2 - (3*b^2 + 4*a*c)*d*e)*x + 4*sqrt(a*d^2 - b*d*e + c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), -1/2*(2*sqrt(-a)*d*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) - sqrt(c)*e*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) - sqrt(a*d^2 - b*d*e + c*e^2)*log((8*b*c*d*e - 8*c^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*a^2*d^2 - 8*a*b*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 2*(4*a*b*d^2 + 4*b*c*e^2 - (3*b^2 + 4*a*c)*d*e)*x + 4*sqrt(a*d^2 - b*d*e + c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), 1/2*(sqrt(a)*d*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + sqrt(c)*e*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) - 2*sqrt(-a*d^2 + b*d*e - c*e^2)*arctan(-1/2*sqrt(-a*d^2 + b*d*e - c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*d^2 - b*c*d*e + c^2*e^2 + (a^2*d^2 - a*b*d*e + a*c*e^2)*x^2 + (a*b*d^2 - b^2*d*e + b*c*e^2)*x)))/(d*e), -1/2*(2*sqrt(-a)*d*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) - sqrt(c)*e*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) + 2*sqrt(-a*d^2 + b*d*e - c*e^2)*arctan(-1/2*sqrt(-a*d^2 + b*d*e - c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*d^2 - b*c*d*e + c^2*e^2 + (a^2*d^2 - a*b*d*e + a*c*e^2)*x^2 + (a*b*d^2 - b^2*d*e + b*c*e^2)*x)))/(d*e), 1/2*(2*sqrt(-c)*e*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) + sqrt(a)*d*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + sqrt(a*d^2 - b*d*e + c*e^2)*log((8*b*c*d*e - 8*c^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*a^2*d^2 - 8*a*b*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 2*(4*a*b*d^2 + 4*b*c*e^2 - (3*b^2 + 4*a*c)*d*e)*x + 4*sqrt(a*d^2 - b*d*e + c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), -1/2*(2*sqrt(-a)*d*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) - 2*sqrt(-c)*e*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) - sqrt(a*d^2 - b*d*e + c*e^2)*log((8*b*c*d*e - 8*c^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*a^2*d^2 - 8*a*b*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 2*(4*a*b*d^2 + 4*b*c*e^2 - (3*b^2 + 4*a*c)*d*e)*x + 4*sqrt(a*d^2 - b*d*e + c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), 1/2*(2*sqrt(-c)*e*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) + sqrt(a)*d*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) - 2*sqrt(-a*d^2 + b*d*e - c*e^2)*arctan(-1/2*sqrt(-a*d^2 + b*d*e - c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*d^2 - b*c*d*e + c^2*e^2 + (a^2*d^2 - a*b*d*e + a*c*e^2)*x^2 + (a*b*d^2 - b^2*d*e + b*c*e^2)*x)))/(d*e), -(sqrt(-a)*d*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) - sqrt(-c)*e*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) + sqrt(-a*d^2 + b*d*e - c*e^2)*arctan(-1/2*sqrt(-a*d^2 + b*d*e - c*e^2)*((2*a*d - b*e)*x^2 + (b*d - 2*c*e)*x)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*d^2 - b*c*d*e + c^2*e^2 + (a^2*d^2 - a*b*d*e + a*c*e^2)*x^2 + (a*b*d^2 - b^2*d*e + b*c*e^2)*x)))/(d*e)]","A",0
922,1,16,0,0.406921," ","integrate((x^(1/6)+(x^3)^(1/5))/x^(1/2),x, algorithm=""fricas"")","\frac{10}{11} \, {\left(x^{3}\right)}^{\frac{1}{5}} \sqrt{x} + \frac{3}{2} \, x^{\frac{2}{3}}"," ",0,"10/11*(x^3)^(1/5)*sqrt(x) + 3/2*x^(2/3)","A",0
923,1,32,0,0.410848," ","integrate((2+x)/(-x^2+4*x)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 4 \, x} - 8 \, \arctan\left(\frac{\sqrt{-x^{2} + 4 \, x}}{x}\right)"," ",0,"-sqrt(-x^2 + 4*x) - 8*arctan(sqrt(-x^2 + 4*x)/x)","A",0
924,1,11,0,0.438390," ","integrate((3+x)/(x^2+6*x)^(1/3),x, algorithm=""fricas"")","\frac{3}{4} \, {\left(x^{2} + 6 \, x\right)}^{\frac{2}{3}}"," ",0,"3/4*(x^2 + 6*x)^(2/3)","A",0
925,1,27,0,0.404097," ","integrate((4+x)/(-x^2+6*x)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{2} + 6 \, x} {\left(7 \, x - 12\right)}}{9 \, {\left(x^{2} - 6 \, x\right)}}"," ",0,"-1/9*sqrt(-x^2 + 6*x)*(7*x - 12)/(x^2 - 6*x)","A",0
926,1,17,0,0.410084," ","integrate(1/(1+x)/(x^2+2*x)^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(-x + \sqrt{x^{2} + 2 \, x} - 1\right)"," ",0,"2*arctan(-x + sqrt(x^2 + 2*x) - 1)","A",0
927,1,17,0,0.409465," ","integrate(1/(1+2*x)/(x^2+x)^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(-2 \, x + 2 \, \sqrt{x^{2} + x} - 1\right)"," ",0,"2*arctan(-2*x + 2*sqrt(x^2 + x) - 1)","A",0
928,1,13,0,0.402907," ","integrate((-1+x)/(-x^2+2*x)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 2 \, x}"," ",0,"-sqrt(-x^2 + 2*x)","A",0
929,1,49,0,0.420714," ","integrate((-x^2+x)^(1/2)/(1+x),x, algorithm=""fricas"")","2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-x^{2} + x}}{2 \, x}\right) + \sqrt{-x^{2} + x} - 3 \, \arctan\left(\frac{\sqrt{-x^{2} + x}}{x}\right)"," ",0,"2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x^2 + x)/x) + sqrt(-x^2 + x) - 3*arctan(sqrt(-x^2 + x)/x)","A",0
930,-1,0,0,0.000000," ","integrate((x^(1/4)+x)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
931,1,30,0,0.849032," ","integrate((x+x^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(15 \, x^{2} + {\left(3 \, x + 8\right)} \sqrt{x} - 4 \, x\right)} \sqrt{x^{\frac{3}{2}} + x}}{105 \, x}"," ",0,"4/105*(15*x^2 + (3*x + 8)*sqrt(x) - 4*x)*sqrt(x^(3/2) + x)/x","A",0
932,1,40,0,0.872360," ","integrate(x*(x+x^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(315 \, x^{3} - 40 \, x^{2} + {\left(35 \, x^{2} + 48 \, x + 128\right)} \sqrt{x} - 64 \, x\right)} \sqrt{x^{\frac{3}{2}} + x}}{3465 \, x}"," ",0,"4/3465*(315*x^3 - 40*x^2 + (35*x^2 + 48*x + 128)*sqrt(x) - 64*x)*sqrt(x^(3/2) + x)/x","A",0
933,1,20,0,1.008894," ","integrate((-x^2+1)*(1/(-x^2+2))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x^{3} - 2 \, x\right)} \sqrt{-\frac{1}{x^{2} - 2}}"," ",0,"-1/2*(x^3 - 2*x)*sqrt(-1/(x^2 - 2))","A",0
934,1,62,0,0.596511," ","integrate((-x^4+x^3+x^2)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, x \arctan\left(-\frac{x - \sqrt{-x^{4} + x^{3} + x^{2}}}{x^{2}}\right) - \sqrt{-x^{4} + x^{3} + x^{2}} {\left(8 \, x^{2} - 2 \, x - 11\right)} + 11 \, x}{24 \, x}"," ",0,"-1/24*(15*x*arctan(-(x - sqrt(-x^4 + x^3 + x^2))/x^2) - sqrt(-x^4 + x^3 + x^2)*(8*x^2 - 2*x - 11) + 11*x)/x","A",0
935,1,64,0,0.803623," ","integrate(1/((a^2+x^2)^3)^(1/2),x, algorithm=""fricas"")","\frac{a^{4} + 2 \, a^{2} x^{2} + x^{4} + \sqrt{a^{6} + 3 \, a^{4} x^{2} + 3 \, a^{2} x^{4} + x^{6}} x}{a^{6} + 2 \, a^{4} x^{2} + a^{2} x^{4}}"," ",0,"(a^4 + 2*a^2*x^2 + x^4 + sqrt(a^6 + 3*a^4*x^2 + 3*a^2*x^4 + x^6)*x)/(a^6 + 2*a^4*x^2 + a^2*x^4)","B",0
936,1,35,0,0.753912," ","integrate(x^(1/2)/(1+x+x^(1/2)),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x} + \frac{1}{3} \, \sqrt{3}\right) + 2 \, \sqrt{x} - \log\left(x + \sqrt{x} + 1\right)"," ",0,"-2/3*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x) + 1/3*sqrt(3)) + 2*sqrt(x) - log(x + sqrt(x) + 1)","A",0
937,1,27,0,0.800287," ","integrate(x/(1+x+x^(1/2)),x, algorithm=""fricas"")","\frac{4}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x} + \frac{1}{3} \, \sqrt{3}\right) + x - 2 \, \sqrt{x}"," ",0,"4/3*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x) + 1/3*sqrt(3)) + x - 2*sqrt(x)","A",0
938,1,95,0,0.923808," ","integrate(1/x^(1/2)/(1+x+x^(1/2))^(7/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(128 \, x^{5} + 272 \, x^{4} + 455 \, x^{3} + 232 \, x^{2} - {\left(256 \, x^{5} + 736 \, x^{4} + 1366 \, x^{3} + 1427 \, x^{2} + 839 \, x + 101\right)} \sqrt{x} - 128 \, x - 203\right)} \sqrt{x + \sqrt{x} + 1}}{405 \, {\left(x^{6} + 3 \, x^{5} + 6 \, x^{4} + 7 \, x^{3} + 6 \, x^{2} + 3 \, x + 1\right)}}"," ",0,"-4/405*(128*x^5 + 272*x^4 + 455*x^3 + 232*x^2 - (256*x^5 + 736*x^4 + 1366*x^3 + 1427*x^2 + 839*x + 101)*sqrt(x) - 128*x - 203)*sqrt(x + sqrt(x) + 1)/(x^6 + 3*x^5 + 6*x^4 + 7*x^3 + 6*x^2 + 3*x + 1)","A",0
939,1,64,0,0.706705," ","integrate((-1+x)/((x^2+1)^(1/2)+1),x, algorithm=""fricas"")","\frac{x \log\left(2 \, x^{2} - \sqrt{x^{2} + 1} {\left(2 \, x + 1\right)} + x + 1\right) - x \log\left(x\right) - x \log\left(-x + \sqrt{x^{2} + 1} + 1\right) + \sqrt{x^{2} + 1} {\left(x + 1\right)} + x - 1}{x}"," ",0,"(x*log(2*x^2 - sqrt(x^2 + 1)*(2*x + 1) + x + 1) - x*log(x) - x*log(-x + sqrt(x^2 + 1) + 1) + sqrt(x^2 + 1)*(x + 1) + x - 1)/x","A",0
940,1,14,0,0.734632," ","integrate(1/(1+x)^(2/3)/(x^2-1)^(2/3),x, algorithm=""fricas"")","\frac{3 \, {\left(x^{2} - 1\right)}^{\frac{1}{3}}}{2 \, {\left(x + 1\right)}^{\frac{2}{3}}}"," ",0,"3/2*(x^2 - 1)^(1/3)/(x + 1)^(2/3)","A",0
941,1,19,0,0.686342," ","integrate((-x^6+1)^(2/3)+(-x^6+1)^(2/3)/x^6,x, algorithm=""fricas"")","\frac{{\left(x^{6} - 1\right)} {\left(-x^{6} + 1\right)}^{\frac{2}{3}}}{5 \, x^{5}}"," ",0,"1/5*(x^6 - 1)*(-x^6 + 1)^(2/3)/x^5","A",0
942,1,16,0,0.591058," ","integrate(1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\frac{x x^{m - 1}}{\sqrt{b x^{n} + a}}"," ",0,"x*x^(m - 1)/sqrt(b*x^n + a)","A",0
943,1,24,0,0.622952," ","integrate((-2*x^3+x)/(2+3*x)^(1/2),x, algorithm=""fricas"")","-\frac{2}{2835} \, {\left(270 \, x^{3} - 216 \, x^{2} - 123 \, x + 164\right)} \sqrt{3 \, x + 2}"," ",0,"-2/2835*(270*x^3 - 216*x^2 - 123*x + 164)*sqrt(3*x + 2)","A",0
944,1,25,0,0.594335," ","integrate(1/((1+x)^(1/4)+(1+x)^(1/2)),x, algorithm=""fricas"")","2 \, \sqrt{x + 1} - 4 \, {\left(x + 1\right)}^{\frac{1}{4}} + 4 \, \log\left({\left(x + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"2*sqrt(x + 1) - 4*(x + 1)^(1/4) + 4*log((x + 1)^(1/4) + 1)","A",0
945,1,9,0,0.696649," ","integrate((1+2*x)/(x^2+x)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x^{2} + x}"," ",0,"2*sqrt(x^2 + x)","A",0
946,1,4,0,0.882624," ","integrate(1/2/(1+x)/x^(1/2),x, algorithm=""fricas"")","\arctan\left(\sqrt{x}\right)"," ",0,"arctan(sqrt(x))","A",0
947,1,16,0,0.457747," ","integrate(1/x/(-x^2+6*x)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{2} + 6 \, x}}{3 \, x}"," ",0,"-1/3*sqrt(-x^2 + 6*x)/x","A",0
948,1,11,0,0.429509," ","integrate(x^(1/2)*(1+x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{2}{3} \, x^{\frac{3}{2}}"," ",0,"1/2*x^2 + 2/3*x^(3/2)","A",0
949,1,11,0,0.506228," ","integrate((1-x^(1/2))/x^(1/3),x, algorithm=""fricas"")","-\frac{6}{7} \, x^{\frac{7}{6}} + \frac{3}{2} \, x^{\frac{2}{3}}"," ",0,"-6/7*x^(7/6) + 3/2*x^(2/3)","A",0
950,1,25,0,0.448778," ","integrate(x^(1/2)/(1+x^(1/3)),x, algorithm=""fricas"")","\frac{6}{7} \, {\left(x - 7\right)} x^{\frac{1}{6}} - \frac{6}{5} \, x^{\frac{5}{6}} + 2 \, \sqrt{x} + 6 \, \arctan\left(x^{\frac{1}{6}}\right)"," ",0,"6/7*(x - 7)*x^(1/6) - 6/5*x^(5/6) + 2*sqrt(x) + 6*arctan(x^(1/6))","A",0
951,1,65,0,0.464444," ","integrate((1+x^(1/2))^(1/3)/x,x, algorithm=""fricas"")","-2 \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 6 \, {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} - \log\left({\left(\sqrt{x} + 1\right)}^{\frac{2}{3}} + {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} + 1\right) + 2 \, \log\left({\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-2*sqrt(3)*arctan(2/3*sqrt(3)*(sqrt(x) + 1)^(1/3) + 1/3*sqrt(3)) + 6*(sqrt(x) + 1)^(1/3) - log((sqrt(x) + 1)^(2/3) + (sqrt(x) + 1)^(1/3) + 1) + 2*log((sqrt(x) + 1)^(1/3) - 1)","A",0
952,1,7,0,0.437234," ","integrate(1-x^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, x^{\frac{3}{2}} + x"," ",0,"-2/3*x^(3/2) + x","A",0
953,1,7,0,0.431890," ","integrate(1-x^(1/4),x, algorithm=""fricas"")","-\frac{4}{5} \, x^{\frac{5}{4}} + x"," ",0,"-4/5*x^(5/4) + x","A",0
954,1,7,0,0.431915," ","integrate((1-x^(1/2))/(1+x^(1/4)),x, algorithm=""fricas"")","-\frac{4}{5} \, x^{\frac{5}{4}} + x"," ",0,"-4/5*x^(5/4) + x","A",0
955,1,192,0,0.436102," ","integrate(1/((b*x+a)*(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, \sqrt{b d x^{2} + a c + {\left(b c + a d\right)} x} {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{2 \, b d}, -\frac{\sqrt{-b d} \arctan\left(\frac{\sqrt{b d x^{2} + a c + {\left(b c + a d\right)} x} {\left(2 \, b d x + b c + a d\right)} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{b d}\right]"," ",0,"[1/2*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*sqrt(b*d*x^2 + a*c + (b*c + a*d)*x)*(2*b*d*x + b*c + a*d)*sqrt(b*d) + 8*(b^2*c*d + a*b*d^2)*x)/(b*d), -sqrt(-b*d)*arctan(1/2*sqrt(b*d*x^2 + a*c + (b*c + a*d)*x)*(2*b*d*x + b*c + a*d)*sqrt(-b*d)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x))/(b*d)]","A",0
956,1,202,0,0.437465," ","integrate(1/((b*x+a)*(-d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2} - 4 \, \sqrt{-b d x^{2} + a c + {\left(b c - a d\right)} x} {\left(2 \, b d x - b c + a d\right)} \sqrt{-b d} - 8 \, {\left(b^{2} c d - a b d^{2}\right)} x\right)}{2 \, b d}, -\frac{\sqrt{b d} \arctan\left(\frac{\sqrt{-b d x^{2} + a c + {\left(b c - a d\right)} x} {\left(2 \, b d x - b c + a d\right)} \sqrt{b d}}{2 \, {\left(b^{2} d^{2} x^{2} - a b c d - {\left(b^{2} c d - a b d^{2}\right)} x\right)}}\right)}{b d}\right]"," ",0,"[-1/2*sqrt(-b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 - 6*a*b*c*d + a^2*d^2 - 4*sqrt(-b*d*x^2 + a*c + (b*c - a*d)*x)*(2*b*d*x - b*c + a*d)*sqrt(-b*d) - 8*(b^2*c*d - a*b*d^2)*x)/(b*d), -sqrt(b*d)*arctan(1/2*sqrt(-b*d*x^2 + a*c + (b*c - a*d)*x)*(2*b*d*x - b*c + a*d)*sqrt(b*d)/(b^2*d^2*x^2 - a*b*c*d - (b^2*c*d - a*b*d^2)*x))/(b*d)]","A",0
957,1,21,0,0.415585," ","integrate(1/(-x^2+1)/x^(1/2),x, algorithm=""fricas"")","\arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{x} - 1\right)"," ",0,"arctan(sqrt(x)) + 1/2*log(sqrt(x) + 1) - 1/2*log(sqrt(x) - 1)","B",0
958,1,21,0,0.415894," ","integrate(x^(1/2)/(-x^3+x),x, algorithm=""fricas"")","\arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{x} - 1\right)"," ",0,"arctan(sqrt(x)) + 1/2*log(sqrt(x) + 1) - 1/2*log(sqrt(x) - 1)","B",0
959,1,100,0,0.426809," ","integrate(x/(2+x^2-3^(1/2)+x*(1+3^(1/2))),x, algorithm=""fricas"")","\frac{1}{46} \, \sqrt{23} \sqrt{8 \, \sqrt{3} + 13} \log\left(-\frac{\sqrt{23} \sqrt{8 \, \sqrt{3} + 13} {\left(5 \, \sqrt{3} - 11\right)} - 46 \, x - 23 \, \sqrt{3} - 23}{\sqrt{23} \sqrt{8 \, \sqrt{3} + 13} {\left(5 \, \sqrt{3} - 11\right)} + 46 \, x + 23 \, \sqrt{3} + 23}\right) + \frac{1}{2} \, \log\left(x^{2} + x {\left(\sqrt{3} + 1\right)} - \sqrt{3} + 2\right)"," ",0,"1/46*sqrt(23)*sqrt(8*sqrt(3) + 13)*log(-(sqrt(23)*sqrt(8*sqrt(3) + 13)*(5*sqrt(3) - 11) - 46*x - 23*sqrt(3) - 23)/(sqrt(23)*sqrt(8*sqrt(3) + 13)*(5*sqrt(3) - 11) + 46*x + 23*sqrt(3) + 23)) + 1/2*log(x^2 + x*(sqrt(3) + 1) - sqrt(3) + 2)","A",0
960,1,22,0,0.398697," ","integrate((x^3+x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{x^{3} + x^{2}} {\left(3 \, x^{2} + x - 2\right)}}{15 \, x}"," ",0,"2/15*sqrt(x^3 + x^2)*(3*x^2 + x - 2)/x","A",0
961,1,17,0,0.400600," ","integrate(1/(1+x)/(x^2+2*x)^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(-x + \sqrt{x^{2} + 2 \, x} - 1\right)"," ",0,"2*arctan(-x + sqrt(x^2 + 2*x) - 1)","A",0
962,1,89,0,1.533211," ","integrate(x^(1/2)*(1-x-x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{96} \, {\left(2 \, {\left(24 \, x - 17\right)} \sqrt{x} + 8 \, x + 67\right)} \sqrt{-x - \sqrt{x} + 1} - \frac{45}{128} \, \arctan\left(-\frac{{\left(8 \, x^{2} - {\left(16 \, x^{2} - 38 \, x + 11\right)} \sqrt{x} - 9 \, x + 3\right)} \sqrt{-x - \sqrt{x} + 1}}{4 \, {\left(4 \, x^{3} - 13 \, x^{2} + 7 \, x - 1\right)}}\right)"," ",0,"1/96*(2*(24*x - 17)*sqrt(x) + 8*x + 67)*sqrt(-x - sqrt(x) + 1) - 45/128*arctan(-1/4*(8*x^2 - (16*x^2 - 38*x + 11)*sqrt(x) - 9*x + 3)*sqrt(-x - sqrt(x) + 1)/(4*x^3 - 13*x^2 + 7*x - 1))","A",0
963,1,21,0,0.418924," ","integrate((1+(-3+x)^(1/2))^(1/3),x, algorithm=""fricas"")","\frac{3}{14} \, {\left(4 \, x + \sqrt{x - 3} - 15\right)} {\left(\sqrt{x - 3} + 1\right)}^{\frac{1}{3}}"," ",0,"3/14*(4*x + sqrt(x - 3) - 15)*(sqrt(x - 3) + 1)^(1/3)","A",0
964,1,22,0,0.428654," ","integrate(1/(3+(-1+2*x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{\sqrt{2 \, x - 1} + 3} {\left(\sqrt{2 \, x - 1} - 6\right)}"," ",0,"2/3*sqrt(sqrt(2*x - 1) + 3)*(sqrt(2*x - 1) - 6)","A",0
965,1,33,0,0.442562," ","integrate((1-x)^(1/2)/(1+x^(1/2)),x, algorithm=""fricas"")","\sqrt{x} \sqrt{-x + 1} - 2 \, \sqrt{-x + 1} + \arctan\left(\frac{\sqrt{-x + 1}}{\sqrt{x}}\right)"," ",0,"sqrt(x)*sqrt(-x + 1) - 2*sqrt(-x + 1) + arctan(sqrt(-x + 1)/sqrt(x))","A",0
966,1,36,0,0.421084," ","integrate((1-x)^(1/2)/(1-x^(1/2)),x, algorithm=""fricas"")","-\sqrt{x} \sqrt{-x + 1} - 2 \, \sqrt{-x + 1} - \arctan\left(\frac{\sqrt{-x + 1}}{\sqrt{x}}\right)"," ",0,"-sqrt(x)*sqrt(-x + 1) - 2*sqrt(-x + 1) - arctan(sqrt(-x + 1)/sqrt(x))","A",0
967,1,15,0,0.405897," ","integrate(x/(x-(x^2+1)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{3} \, x^{3} - \frac{1}{3} \, {\left(x^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"-1/3*x^3 - 1/3*(x^2 + 1)^(3/2)","A",0
968,1,97,0,0.404017," ","integrate(x/(x-(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{6 \, x^{2} - 2 \, \sqrt{2} {\left(2 \, x^{2} - 3\right)} + 2 \, \sqrt{-x^{2} + 1} {\left(3 \, \sqrt{2} - 4\right)} - 9}{2 \, x^{2} - 1}\right) + \frac{1}{8} \, \sqrt{2} \log\left(\frac{2 \, x^{2} - 2 \, \sqrt{2} x + 1}{2 \, x^{2} - 1}\right) + \frac{1}{2} \, x + \frac{1}{2} \, \sqrt{-x^{2} + 1}"," ",0,"1/8*sqrt(2)*log((6*x^2 - 2*sqrt(2)*(2*x^2 - 3) + 2*sqrt(-x^2 + 1)*(3*sqrt(2) - 4) - 9)/(2*x^2 - 1)) + 1/8*sqrt(2)*log((2*x^2 - 2*sqrt(2)*x + 1)/(2*x^2 - 1)) + 1/2*x + 1/2*sqrt(-x^2 + 1)","B",0
969,1,41,0,0.416658," ","integrate(x/(x-(2*x^2+1)^(1/2)),x, algorithm=""fricas"")","-x - \sqrt{2 \, x^{2} + 1} + \arctan\left(x\right) - \arctan\left(-\frac{x^{2} - \sqrt{2 \, x^{2} + 1} + 1}{x^{2}}\right)"," ",0,"-x - sqrt(2*x^2 + 1) + arctan(x) - arctan(-(x^2 - sqrt(2*x^2 + 1) + 1)/x^2)","A",0
970,1,54,0,0.975710," ","integrate(x^(1/2)*(x+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{96} \, {\left(2 \, {\left(24 \, x - 5\right)} \sqrt{x} + 8 \, x + 15\right)} \sqrt{x + \sqrt{x}} + \frac{5}{128} \, \log\left(4 \, \sqrt{x + \sqrt{x}} {\left(2 \, \sqrt{x} + 1\right)} - 8 \, x - 8 \, \sqrt{x} - 1\right)"," ",0,"1/96*(2*(24*x - 5)*sqrt(x) + 8*x + 15)*sqrt(x + sqrt(x)) + 5/128*log(4*sqrt(x + sqrt(x))*(2*sqrt(x) + 1) - 8*x - 8*sqrt(x) - 1)","A",0
971,1,57,0,0.420159," ","integrate((1+x^(1/3))/(1+x^(1/2)),x, algorithm=""fricas"")","2 \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) + \frac{6}{5} \, x^{\frac{5}{6}} + 2 \, \sqrt{x} - 3 \, x^{\frac{1}{3}} - \log\left(x^{\frac{1}{3}} - x^{\frac{1}{6}} + 1\right) - 4 \, \log\left(x^{\frac{1}{6}} + 1\right)"," ",0,"2*sqrt(3)*arctan(2/3*sqrt(3)*x^(1/6) - 1/3*sqrt(3)) + 6/5*x^(5/6) + 2*sqrt(x) - 3*x^(1/3) - log(x^(1/3) - x^(1/6) + 1) - 4*log(x^(1/6) + 1)","A",0
972,1,80,0,0.418918," ","integrate((1+x^(1/3))/(1+x^(1/4)),x, algorithm=""fricas"")","-4 \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{\frac{1}{12}} - \frac{1}{3} \, \sqrt{3}\right) + \frac{12}{13} \, {\left(x + 13\right)} x^{\frac{1}{12}} - \frac{6}{5} \, x^{\frac{5}{6}} + \frac{4}{3} \, x^{\frac{3}{4}} + \frac{12}{7} \, x^{\frac{7}{12}} - 2 \, \sqrt{x} - 3 \, x^{\frac{1}{3}} + 4 \, x^{\frac{1}{4}} - 2 \, \log\left(x^{\frac{1}{6}} - x^{\frac{1}{12}} + 1\right) - 8 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"-4*sqrt(3)*arctan(2/3*sqrt(3)*x^(1/12) - 1/3*sqrt(3)) + 12/13*(x + 13)*x^(1/12) - 6/5*x^(5/6) + 4/3*x^(3/4) + 12/7*x^(7/12) - 2*sqrt(x) - 3*x^(1/3) + 4*x^(1/4) - 2*log(x^(1/6) - x^(1/12) + 1) - 8*log(x^(1/12) + 1)","A",0
973,1,20,0,0.396217," ","integrate(x^2/(-1+x^2+(-x^2+1)^(1/2)),x, algorithm=""fricas"")","x - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"x - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
974,1,40,0,0.430454," ","integrate(((1+x)/x)^(1/2),x, algorithm=""fricas"")","x \sqrt{\frac{x + 1}{x}} + \frac{1}{2} \, \log\left(\sqrt{\frac{x + 1}{x}} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{x + 1}{x}} - 1\right)"," ",0,"x*sqrt((x + 1)/x) + 1/2*log(sqrt((x + 1)/x) + 1) - 1/2*log(sqrt((x + 1)/x) - 1)","B",0
975,1,26,0,0.412012," ","integrate(((1-x)/x)^(1/2),x, algorithm=""fricas"")","x \sqrt{-\frac{x - 1}{x}} - \arctan\left(\sqrt{-\frac{x - 1}{x}}\right)"," ",0,"x*sqrt(-(x - 1)/x) - arctan(sqrt(-(x - 1)/x))","A",0
976,1,40,0,0.424220," ","integrate(((-1+x)/x)^(1/2),x, algorithm=""fricas"")","x \sqrt{\frac{x - 1}{x}} - \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x}} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x}} - 1\right)"," ",0,"x*sqrt((x - 1)/x) - 1/2*log(sqrt((x - 1)/x) + 1) + 1/2*log(sqrt((x - 1)/x) - 1)","B",0
977,1,38,0,0.421903," ","integrate(((1+x)/x)^(1/2)/x,x, algorithm=""fricas"")","-2 \, \sqrt{\frac{x + 1}{x}} + \log\left(\sqrt{\frac{x + 1}{x}} + 1\right) - \log\left(\sqrt{\frac{x + 1}{x}} - 1\right)"," ",0,"-2*sqrt((x + 1)/x) + log(sqrt((x + 1)/x) + 1) - log(sqrt((x + 1)/x) - 1)","A",0
978,1,42,0,0.408961," ","integrate((x/(1+x))^(1/2),x, algorithm=""fricas"")","{\left(x + 1\right)} \sqrt{\frac{x}{x + 1}} - \frac{1}{2} \, \log\left(\sqrt{\frac{x}{x + 1}} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{\frac{x}{x + 1}} - 1\right)"," ",0,"(x + 1)*sqrt(x/(x + 1)) - 1/2*log(sqrt(x/(x + 1)) + 1) + 1/2*log(sqrt(x/(x + 1)) - 1)","B",0
979,1,25,0,0.437981," ","integrate(1/((-1-x)/x)^(1/2),x, algorithm=""fricas"")","-x \sqrt{-\frac{x + 1}{x}} + \arctan\left(\sqrt{-\frac{x + 1}{x}}\right)"," ",0,"-x*sqrt(-(x + 1)/x) + arctan(sqrt(-(x + 1)/x))","A",0
980,1,35,0,0.407729," ","integrate(((4-x)*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-x^{2} + 4 \, x} {\left(x - 2\right)} - 4 \, \arctan\left(\frac{\sqrt{-x^{2} + 4 \, x}}{x}\right)"," ",0,"1/2*sqrt(-x^2 + 4*x)*(x - 2) - 4*arctan(sqrt(-x^2 + 4*x)/x)","A",0
981,1,16,0,0.412350," ","integrate(1/((1-x)*x)^(1/2),x, algorithm=""fricas"")","-2 \, \arctan\left(\frac{\sqrt{-x^{2} + x}}{x}\right)"," ",0,"-2*arctan(sqrt(-x^2 + x)/x)","B",0
982,1,18,0,0.456007," ","integrate(x/(x*(2+x))^(3/2),x, algorithm=""fricas"")","\frac{x + \sqrt{x^{2} + 2 \, x} + 2}{x + 2}"," ",0,"(x + sqrt(x^2 + 2*x) + 2)/(x + 2)","A",0
983,1,33,0,0.424814," ","integrate((1+1/x)^(1/2)/(-x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} x \sqrt{\frac{x + 1}{x}} + 3 \, x + 1}{x - 1}\right)"," ",0,"1/2*sqrt(2)*log(-(2*sqrt(2)*x*sqrt((x + 1)/x) + 3*x + 1)/(x - 1))","A",0
984,1,11,0,0.479923," ","integrate(1/(1-x^2+5^(1/2)+x^2*5^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(\frac{1}{2} \, x {\left(\sqrt{5} - 1\right)}\right)"," ",0,"1/2*arctan(1/2*x*(sqrt(5) - 1))","A",0
985,1,62,0,0.445164," ","integrate(1/(b*x^2+a*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right)}{b}\right]"," ",0,"[log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b))/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x))/b]","A",0
986,1,62,0,0.455717," ","integrate(1/(x*(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right)}{b}\right]"," ",0,"[log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b))/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x))/b]","A",0
987,1,62,0,0.429907," ","integrate(1/((a/x+b)*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right)}{b}\right]"," ",0,"[log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b))/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x))/b]","A",0
988,1,62,0,0.436971," ","integrate(1/((a/x^2+b/x)*x^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right)}{b}\right]"," ",0,"[log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b))/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x))/b]","A",0
989,1,62,0,0.457335," ","integrate(1/((b*x^3+a*x^2)/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right)}{b}\right]"," ",0,"[log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b))/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x))/b]","A",0
990,1,62,0,0.439248," ","integrate(1/((b*x^4+a*x^3)/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right)}{b}\right]"," ",0,"[log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b))/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x))/b]","A",0
991,1,87,0,0.434008," ","integrate(1/(b*c*x^2+a*c*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b c} \log\left(2 \, b c x + a c + 2 \, \sqrt{b c x^{2} + a c x} \sqrt{b c}\right)}{b c}, -\frac{2 \, \sqrt{-b c} \arctan\left(\frac{\sqrt{b c x^{2} + a c x} \sqrt{-b c}}{b c x}\right)}{b c}\right]"," ",0,"[sqrt(b*c)*log(2*b*c*x + a*c + 2*sqrt(b*c*x^2 + a*c*x)*sqrt(b*c))/(b*c), -2*sqrt(-b*c)*arctan(sqrt(b*c*x^2 + a*c*x)*sqrt(-b*c)/(b*c*x))/(b*c)]","A",0
992,1,87,0,0.467629," ","integrate(1/(c*(b*x^2+a*x))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b c} \log\left(2 \, b c x + a c + 2 \, \sqrt{b c x^{2} + a c x} \sqrt{b c}\right)}{b c}, -\frac{2 \, \sqrt{-b c} \arctan\left(\frac{\sqrt{b c x^{2} + a c x} \sqrt{-b c}}{b c x}\right)}{b c}\right]"," ",0,"[sqrt(b*c)*log(2*b*c*x + a*c + 2*sqrt(b*c*x^2 + a*c*x)*sqrt(b*c))/(b*c), -2*sqrt(-b*c)*arctan(sqrt(b*c*x^2 + a*c*x)*sqrt(-b*c)/(b*c*x))/(b*c)]","A",0
993,1,87,0,0.448826," ","integrate(1/(c*x*(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b c} \log\left(2 \, b c x + a c + 2 \, \sqrt{b c x^{2} + a c x} \sqrt{b c}\right)}{b c}, -\frac{2 \, \sqrt{-b c} \arctan\left(\frac{\sqrt{b c x^{2} + a c x} \sqrt{-b c}}{b c x}\right)}{b c}\right]"," ",0,"[sqrt(b*c)*log(2*b*c*x + a*c + 2*sqrt(b*c*x^2 + a*c*x)*sqrt(b*c))/(b*c), -2*sqrt(-b*c)*arctan(sqrt(b*c*x^2 + a*c*x)*sqrt(-b*c)/(b*c*x))/(b*c)]","A",0
994,1,87,0,0.428856," ","integrate(1/(c*(a/x+b)*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b c} \log\left(2 \, b c x + a c + 2 \, \sqrt{b c x^{2} + a c x} \sqrt{b c}\right)}{b c}, -\frac{2 \, \sqrt{-b c} \arctan\left(\frac{\sqrt{b c x^{2} + a c x} \sqrt{-b c}}{b c x}\right)}{b c}\right]"," ",0,"[sqrt(b*c)*log(2*b*c*x + a*c + 2*sqrt(b*c*x^2 + a*c*x)*sqrt(b*c))/(b*c), -2*sqrt(-b*c)*arctan(sqrt(b*c*x^2 + a*c*x)*sqrt(-b*c)/(b*c*x))/(b*c)]","A",0
995,1,68,0,0.977574," ","integrate((1-x^2+x*(x^2-1)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-x^{2} + \sqrt{x^{2} - 1} x + 1} {\left(3 \, x + \sqrt{x^{2} - 1}\right)} + \frac{3}{8} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-x^{2} + \sqrt{x^{2} - 1} x + 1}}{2 \, \sqrt{x^{2} - 1}}\right)"," ",0,"1/4*sqrt(-x^2 + sqrt(x^2 - 1)*x + 1)*(3*x + sqrt(x^2 - 1)) + 3/8*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x^2 + sqrt(x^2 - 1)*x + 1)/sqrt(x^2 - 1))","A",0
996,-1,0,0,0.000000," ","integrate((-x+x^(1/2)*(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
997,1,383,0,0.944304," ","integrate((-x-2*(x^2+1)^(1/2))/(x+x^3+(x^2+1)^(1/2)),x, algorithm=""fricas"")","\sqrt{2} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{4} \, \sqrt{2} \sqrt{4 \, x^{4} + 4 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} + 1\right)} - 2 \, {\left(2 \, x^{3} + \sqrt{5} x + x\right)} \sqrt{x^{2} + 1} + 1} {\left(\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + 1}\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{2} \, \sqrt{2} \sqrt{x^{2} + 1} \sqrt{\sqrt{5} + 1}\right) + \sqrt{2} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{8} \, \sqrt{4 \, x^{2} + 2 \, \sqrt{5} + 2} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{4} \, {\left(\sqrt{5} \sqrt{2} x - \sqrt{2} x\right)} \sqrt{\sqrt{5} + 1}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(4 \, x^{2} - 4 \, \sqrt{x^{2} + 1} x + {\left(\sqrt{5} \sqrt{2} x - \sqrt{x^{2} + 1} {\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} + \sqrt{2} x\right)} \sqrt{\sqrt{5} - 1} + 4\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(4 \, x^{2} - 4 \, \sqrt{x^{2} + 1} x - {\left(\sqrt{5} \sqrt{2} x - \sqrt{x^{2} + 1} {\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} + \sqrt{2} x\right)} \sqrt{\sqrt{5} - 1} + 4\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(2 \, x + \sqrt{2} \sqrt{\sqrt{5} - 1}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(2 \, x - \sqrt{2} \sqrt{\sqrt{5} - 1}\right)"," ",0,"sqrt(2)*sqrt(sqrt(5) + 1)*arctan(1/4*sqrt(2)*sqrt(4*x^4 + 4*x^2 + sqrt(5)*(2*x^2 + 1) - 2*(2*x^3 + sqrt(5)*x + x)*sqrt(x^2 + 1) + 1)*(sqrt(2)*x + sqrt(2)*sqrt(x^2 + 1))*sqrt(sqrt(5) + 1) - 1/2*sqrt(2)*sqrt(x^2 + 1)*sqrt(sqrt(5) + 1)) + sqrt(2)*sqrt(sqrt(5) + 1)*arctan(1/8*sqrt(4*x^2 + 2*sqrt(5) + 2)*(sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 1) - 1/4*(sqrt(5)*sqrt(2)*x - sqrt(2)*x)*sqrt(sqrt(5) + 1)) - 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(4*x^2 - 4*sqrt(x^2 + 1)*x + (sqrt(5)*sqrt(2)*x - sqrt(x^2 + 1)*(sqrt(5)*sqrt(2) + sqrt(2)) + sqrt(2)*x)*sqrt(sqrt(5) - 1) + 4) + 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(4*x^2 - 4*sqrt(x^2 + 1)*x - (sqrt(5)*sqrt(2)*x - sqrt(x^2 + 1)*(sqrt(5)*sqrt(2) + sqrt(2)) + sqrt(2)*x)*sqrt(sqrt(5) - 1) + 4) - 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(2*x + sqrt(2)*sqrt(sqrt(5) - 1)) + 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(2*x - sqrt(2)*sqrt(sqrt(5) - 1))","B",0
998,1,770,0,0.732450," ","integrate((1+2*x)/(x^2+1)/(x^2+2*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \cdot 5^{\frac{3}{4}} \sqrt{2} \sqrt{\sqrt{5} + 5} \arctan\left(\frac{1}{200} \, \sqrt{20 \, x^{2} - 20 \, \sqrt{x^{2} + 2 \, x + 2} x - {\left(2 \cdot 5^{\frac{3}{4}} \sqrt{2} \sqrt{x^{2} + 2 \, x + 2} - 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} {\left(2 \, x + 1\right)} - 5 \, \sqrt{2}\right)}\right)} \sqrt{\sqrt{5} + 5} + 20 \, x + 10 \, \sqrt{5} + 30} {\left(\sqrt{10} {\left(5^{\frac{3}{4}} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} + 2 \cdot 5^{\frac{3}{4}} \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} + 10 \, \sqrt{10} {\left(\sqrt{5} + 3\right)}\right)} + \frac{1}{10} \, \sqrt{5} {\left(\sqrt{5} {\left(2 \, x + 1\right)} + 5\right)} + \frac{1}{2} \, \sqrt{5} x + \frac{1}{20} \, {\left(5^{\frac{3}{4}} {\left(\sqrt{5} \sqrt{2} x - \sqrt{2} {\left(x - 2\right)}\right)} - \sqrt{x^{2} + 2 \, x + 2} {\left(5^{\frac{3}{4}} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} + 2 \cdot 5^{\frac{3}{4}} \sqrt{2}\right)} + 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} {\left(2 \, x + 1\right)} + 5 \, \sqrt{2}\right)}\right)} \sqrt{\sqrt{5} + 5} - \frac{1}{2} \, \sqrt{x^{2} + 2 \, x + 2} {\left(\sqrt{5} + 3\right)} + \frac{1}{2} \, x + 1\right) + \frac{1}{5} \cdot 5^{\frac{3}{4}} \sqrt{2} \sqrt{\sqrt{5} + 5} \arctan\left(\frac{1}{200} \, \sqrt{20 \, x^{2} - 20 \, \sqrt{x^{2} + 2 \, x + 2} x + {\left(2 \cdot 5^{\frac{3}{4}} \sqrt{2} \sqrt{x^{2} + 2 \, x + 2} - 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} {\left(2 \, x + 1\right)} - 5 \, \sqrt{2}\right)}\right)} \sqrt{\sqrt{5} + 5} + 20 \, x + 10 \, \sqrt{5} + 30} {\left(\sqrt{10} {\left(5^{\frac{3}{4}} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} + 2 \cdot 5^{\frac{3}{4}} \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} - 10 \, \sqrt{10} {\left(\sqrt{5} + 3\right)}\right)} - \frac{1}{10} \, \sqrt{5} {\left(\sqrt{5} {\left(2 \, x + 1\right)} + 5\right)} - \frac{1}{2} \, \sqrt{5} x + \frac{1}{20} \, {\left(5^{\frac{3}{4}} {\left(\sqrt{5} \sqrt{2} x - \sqrt{2} {\left(x - 2\right)}\right)} - \sqrt{x^{2} + 2 \, x + 2} {\left(5^{\frac{3}{4}} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} + 2 \cdot 5^{\frac{3}{4}} \sqrt{2}\right)} + 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} {\left(2 \, x + 1\right)} + 5 \, \sqrt{2}\right)}\right)} \sqrt{\sqrt{5} + 5} + \frac{1}{2} \, \sqrt{x^{2} + 2 \, x + 2} {\left(\sqrt{5} + 3\right)} - \frac{1}{2} \, x - 1\right) + \frac{1}{40} \cdot 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} \log\left(2 \, x^{2} - 2 \, \sqrt{x^{2} + 2 \, x + 2} x + \frac{1}{10} \, {\left(2 \cdot 5^{\frac{3}{4}} \sqrt{2} \sqrt{x^{2} + 2 \, x + 2} - 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} {\left(2 \, x + 1\right)} - 5 \, \sqrt{2}\right)}\right)} \sqrt{\sqrt{5} + 5} + 2 \, x + \sqrt{5} + 3\right) - \frac{1}{40} \cdot 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} \log\left(2 \, x^{2} - 2 \, \sqrt{x^{2} + 2 \, x + 2} x - \frac{1}{10} \, {\left(2 \cdot 5^{\frac{3}{4}} \sqrt{2} \sqrt{x^{2} + 2 \, x + 2} - 5^{\frac{1}{4}} {\left(\sqrt{5} \sqrt{2} {\left(2 \, x + 1\right)} - 5 \, \sqrt{2}\right)}\right)} \sqrt{\sqrt{5} + 5} + 2 \, x + \sqrt{5} + 3\right)"," ",0,"1/5*5^(3/4)*sqrt(2)*sqrt(sqrt(5) + 5)*arctan(1/200*sqrt(20*x^2 - 20*sqrt(x^2 + 2*x + 2)*x - (2*5^(3/4)*sqrt(2)*sqrt(x^2 + 2*x + 2) - 5^(1/4)*(sqrt(5)*sqrt(2)*(2*x + 1) - 5*sqrt(2)))*sqrt(sqrt(5) + 5) + 20*x + 10*sqrt(5) + 30)*(sqrt(10)*(5^(3/4)*(sqrt(5)*sqrt(2) - sqrt(2)) + 2*5^(3/4)*sqrt(2))*sqrt(sqrt(5) + 5) + 10*sqrt(10)*(sqrt(5) + 3)) + 1/10*sqrt(5)*(sqrt(5)*(2*x + 1) + 5) + 1/2*sqrt(5)*x + 1/20*(5^(3/4)*(sqrt(5)*sqrt(2)*x - sqrt(2)*(x - 2)) - sqrt(x^2 + 2*x + 2)*(5^(3/4)*(sqrt(5)*sqrt(2) - sqrt(2)) + 2*5^(3/4)*sqrt(2)) + 5^(1/4)*(sqrt(5)*sqrt(2)*(2*x + 1) + 5*sqrt(2)))*sqrt(sqrt(5) + 5) - 1/2*sqrt(x^2 + 2*x + 2)*(sqrt(5) + 3) + 1/2*x + 1) + 1/5*5^(3/4)*sqrt(2)*sqrt(sqrt(5) + 5)*arctan(1/200*sqrt(20*x^2 - 20*sqrt(x^2 + 2*x + 2)*x + (2*5^(3/4)*sqrt(2)*sqrt(x^2 + 2*x + 2) - 5^(1/4)*(sqrt(5)*sqrt(2)*(2*x + 1) - 5*sqrt(2)))*sqrt(sqrt(5) + 5) + 20*x + 10*sqrt(5) + 30)*(sqrt(10)*(5^(3/4)*(sqrt(5)*sqrt(2) - sqrt(2)) + 2*5^(3/4)*sqrt(2))*sqrt(sqrt(5) + 5) - 10*sqrt(10)*(sqrt(5) + 3)) - 1/10*sqrt(5)*(sqrt(5)*(2*x + 1) + 5) - 1/2*sqrt(5)*x + 1/20*(5^(3/4)*(sqrt(5)*sqrt(2)*x - sqrt(2)*(x - 2)) - sqrt(x^2 + 2*x + 2)*(5^(3/4)*(sqrt(5)*sqrt(2) - sqrt(2)) + 2*5^(3/4)*sqrt(2)) + 5^(1/4)*(sqrt(5)*sqrt(2)*(2*x + 1) + 5*sqrt(2)))*sqrt(sqrt(5) + 5) + 1/2*sqrt(x^2 + 2*x + 2)*(sqrt(5) + 3) - 1/2*x - 1) + 1/40*5^(1/4)*(sqrt(5)*sqrt(2) - 5*sqrt(2))*sqrt(sqrt(5) + 5)*log(2*x^2 - 2*sqrt(x^2 + 2*x + 2)*x + 1/10*(2*5^(3/4)*sqrt(2)*sqrt(x^2 + 2*x + 2) - 5^(1/4)*(sqrt(5)*sqrt(2)*(2*x + 1) - 5*sqrt(2)))*sqrt(sqrt(5) + 5) + 2*x + sqrt(5) + 3) - 1/40*5^(1/4)*(sqrt(5)*sqrt(2) - 5*sqrt(2))*sqrt(sqrt(5) + 5)*log(2*x^2 - 2*sqrt(x^2 + 2*x + 2)*x - 1/10*(2*5^(3/4)*sqrt(2)*sqrt(x^2 + 2*x + 2) - 5^(1/4)*(sqrt(5)*sqrt(2)*(2*x + 1) - 5*sqrt(2)))*sqrt(sqrt(5) + 5) + 2*x + sqrt(5) + 3)","B",0
999,1,62,0,1.501807," ","integrate(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \arctan\left(\frac{4 \, {\left(10 \, x^{7} - 6 \, x^{3} + {\left(7 \, x^{5} - x\right)} \sqrt{x^{4} + 1}\right)} \sqrt{-x^{2} + \sqrt{x^{4} + 1}}}{17 \, x^{8} - 46 \, x^{4} + 1}\right)"," ",0,"-1/4*arctan(4*(10*x^7 - 6*x^3 + (7*x^5 - x)*sqrt(x^4 + 1))*sqrt(-x^2 + sqrt(x^4 + 1))/(17*x^8 - 46*x^4 + 1))","B",0
1000,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)/(c*x^2+d*(b*x^4+a)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1001,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)/(-c*x^2+d*(b*x^4+a)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1002,0,0,0,1.725851," ","integrate(x/(b*d^4*x^4+4*b*c*d^3*x^3+6*b*c^2*d^2*x^2+4*b*c^3*d*x+b*c^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a}}, x\right)"," ",0,"integral(x/sqrt(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a), x)","F",0
1003,0,0,0,1.516837," ","integrate(1/(b*d^4*x^4+4*b*c*d^3*x^3+6*b*c^2*d^2*x^2+4*b*c^3*d*x+b*c^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a}}, x\right)"," ",0,"integral(1/sqrt(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a), x)","F",0
1004,1,305,0,37.187914," ","integrate((-c*x^4+a)/(c*d*x^4+a*e*x^2+a*d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{c^{2} d^{2} x^{8} + 2 \, {\left(4 \, b c d^{2} - 3 \, a c d e\right)} x^{6} - {\left(8 \, a b d e - a^{2} e^{2} - 2 \, {\left(4 \, b^{2} + a c\right)} d^{2}\right)} x^{4} + a^{2} d^{2} + 2 \, {\left(4 \, a b d^{2} - 3 \, a^{2} d e\right)} x^{2} + 4 \, {\left(c d x^{5} + {\left(2 \, b d - a e\right)} x^{3} + a d x\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{b d^{2} - a d e}}{c^{2} d^{2} x^{8} + 2 \, a c d e x^{6} + 2 \, a^{2} d e x^{2} + {\left(2 \, a c d^{2} + a^{2} e^{2}\right)} x^{4} + a^{2} d^{2}}\right)}{4 \, \sqrt{b d^{2} - a d e}}, -\frac{\sqrt{-b d^{2} + a d e} \arctan\left(\frac{2 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{-b d^{2} + a d e} x}{c d x^{4} + {\left(2 \, b d - a e\right)} x^{2} + a d}\right)}{2 \, {\left(b d^{2} - a d e\right)}}\right]"," ",0,"[1/4*log(-(c^2*d^2*x^8 + 2*(4*b*c*d^2 - 3*a*c*d*e)*x^6 - (8*a*b*d*e - a^2*e^2 - 2*(4*b^2 + a*c)*d^2)*x^4 + a^2*d^2 + 2*(4*a*b*d^2 - 3*a^2*d*e)*x^2 + 4*(c*d*x^5 + (2*b*d - a*e)*x^3 + a*d*x)*sqrt(c*x^4 + b*x^2 + a)*sqrt(b*d^2 - a*d*e))/(c^2*d^2*x^8 + 2*a*c*d*e*x^6 + 2*a^2*d*e*x^2 + (2*a*c*d^2 + a^2*e^2)*x^4 + a^2*d^2))/sqrt(b*d^2 - a*d*e), -1/2*sqrt(-b*d^2 + a*d*e)*arctan(2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-b*d^2 + a*d*e)*x/(c*d*x^4 + (2*b*d - a*e)*x^2 + a*d))/(b*d^2 - a*d*e)]","A",0
1005,1,304,0,35.746590," ","integrate((-c*x^4+a)/(c*d*x^4+a*e*x^2+a*d)/(c*x^4-b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b d^{2} - a d e} \log\left(-\frac{c^{2} d^{2} x^{8} - 2 \, {\left(4 \, b c d^{2} + 3 \, a c d e\right)} x^{6} + {\left(8 \, a b d e + a^{2} e^{2} + 2 \, {\left(4 \, b^{2} + a c\right)} d^{2}\right)} x^{4} + a^{2} d^{2} - 2 \, {\left(4 \, a b d^{2} + 3 \, a^{2} d e\right)} x^{2} + 4 \, {\left(c d x^{5} - {\left(2 \, b d + a e\right)} x^{3} + a d x\right)} \sqrt{c x^{4} - b x^{2} + a} \sqrt{-b d^{2} - a d e}}{c^{2} d^{2} x^{8} + 2 \, a c d e x^{6} + 2 \, a^{2} d e x^{2} + {\left(2 \, a c d^{2} + a^{2} e^{2}\right)} x^{4} + a^{2} d^{2}}\right)}{4 \, {\left(b d^{2} + a d e\right)}}, \frac{\arctan\left(\frac{2 \, \sqrt{c x^{4} - b x^{2} + a} \sqrt{b d^{2} + a d e} x}{c d x^{4} - {\left(2 \, b d + a e\right)} x^{2} + a d}\right)}{2 \, \sqrt{b d^{2} + a d e}}\right]"," ",0,"[-1/4*sqrt(-b*d^2 - a*d*e)*log(-(c^2*d^2*x^8 - 2*(4*b*c*d^2 + 3*a*c*d*e)*x^6 + (8*a*b*d*e + a^2*e^2 + 2*(4*b^2 + a*c)*d^2)*x^4 + a^2*d^2 - 2*(4*a*b*d^2 + 3*a^2*d*e)*x^2 + 4*(c*d*x^5 - (2*b*d + a*e)*x^3 + a*d*x)*sqrt(c*x^4 - b*x^2 + a)*sqrt(-b*d^2 - a*d*e))/(c^2*d^2*x^8 + 2*a*c*d*e*x^6 + 2*a^2*d*e*x^2 + (2*a*c*d^2 + a^2*e^2)*x^4 + a^2*d^2))/(b*d^2 + a*d*e), 1/2*arctan(2*sqrt(c*x^4 - b*x^2 + a)*sqrt(b*d^2 + a*d*e)*x/(c*d*x^4 - (2*b*d + a*e)*x^2 + a*d))/sqrt(b*d^2 + a*d*e)]","A",0
1006,1,154,0,0.975946," ","integrate(1/(x^3+8)/(x^2-2*x+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - 2\right)} + \frac{1}{3} \, \sqrt{3} \sqrt{x^{2} - 2 \, x + 5}\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} x + \frac{1}{3} \, \sqrt{3} \sqrt{x^{2} - 2 \, x + 5}\right) + \frac{1}{156} \, \sqrt{13} \log\left(-\frac{\sqrt{13} {\left(3 \, x - 7\right)} + \sqrt{x^{2} - 2 \, x + 5} {\left(3 \, \sqrt{13} + 13\right)} + 9 \, x - 21}{x + 2}\right) + \frac{1}{24} \, \log\left(x^{2} - \sqrt{x^{2} - 2 \, x + 5} {\left(x - 2\right)} - 3 \, x + 6\right) - \frac{1}{24} \, \log\left(x^{2} - \sqrt{x^{2} - 2 \, x + 5} x - x + 4\right)"," ",0,"1/12*sqrt(3)*arctan(-1/3*sqrt(3)*(x - 2) + 1/3*sqrt(3)*sqrt(x^2 - 2*x + 5)) - 1/12*sqrt(3)*arctan(-1/3*sqrt(3)*x + 1/3*sqrt(3)*sqrt(x^2 - 2*x + 5)) + 1/156*sqrt(13)*log(-(sqrt(13)*(3*x - 7) + sqrt(x^2 - 2*x + 5)*(3*sqrt(13) + 13) + 9*x - 21)/(x + 2)) + 1/24*log(x^2 - sqrt(x^2 - 2*x + 5)*(x - 2) - 3*x + 6) - 1/24*log(x^2 - sqrt(x^2 - 2*x + 5)*x - x + 4)","B",0
1007,1,22,0,0.990489," ","integrate((x^2/(x^2+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \sqrt{\frac{x^{2}}{x^{2} + 1}}}{x}"," ",0,"(x^2 + 1)*sqrt(x^2/(x^2 + 1))/x","A",0
1008,-2,0,0,0.000000," ","integrate((x^n/(1+x^n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1009,1,324,0,9.006881," ","integrate((-e*f*x^2+e*f)/(a*d*x^2+b*d*x+a*d)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, a + c} e f \log\left(\frac{2 \, a b^{3} x^{3} + 2 \, a b^{3} x - {\left(8 \, a^{4} - a^{2} b^{2} - 4 \, a^{3} c\right)} x^{4} - 8 \, a^{4} + a^{2} b^{2} + 4 \, a^{3} c + {\left(16 \, a^{4} + 10 \, a^{2} b^{2} + b^{4} + 8 \, a^{2} c^{2} - 4 \, {\left(6 \, a^{3} + a b^{2}\right)} c\right)} x^{2} - 4 \, {\left(a^{2} b x^{2} + a^{2} b + {\left(4 \, a^{3} + a b^{2} - 2 \, a^{2} c\right)} x\right)} \sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} \sqrt{-2 \, a + c}}{a^{2} x^{4} + 2 \, a b x^{3} + 2 \, a b x + {\left(2 \, a^{2} + b^{2}\right)} x^{2} + a^{2}}\right)}{2 \, {\left(2 \, a^{2} - a c\right)} d}, -\frac{\sqrt{2 \, a - c} e f \arctan\left(\frac{2 \, \sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} \sqrt{2 \, a - c} a}{a b x^{2} + a b + {\left(4 \, a^{2} + b^{2} - 2 \, a c\right)} x}\right)}{{\left(2 \, a^{2} - a c\right)} d}\right]"," ",0,"[-1/2*sqrt(-2*a + c)*e*f*log((2*a*b^3*x^3 + 2*a*b^3*x - (8*a^4 - a^2*b^2 - 4*a^3*c)*x^4 - 8*a^4 + a^2*b^2 + 4*a^3*c + (16*a^4 + 10*a^2*b^2 + b^4 + 8*a^2*c^2 - 4*(6*a^3 + a*b^2)*c)*x^2 - 4*(a^2*b*x^2 + a^2*b + (4*a^3 + a*b^2 - 2*a^2*c)*x)*sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*sqrt(-2*a + c))/(a^2*x^4 + 2*a*b*x^3 + 2*a*b*x + (2*a^2 + b^2)*x^2 + a^2))/((2*a^2 - a*c)*d), -sqrt(2*a - c)*e*f*arctan(2*sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*sqrt(2*a - c)*a/(a*b*x^2 + a*b + (4*a^2 + b^2 - 2*a*c)*x))/((2*a^2 - a*c)*d)]","A",0
1010,1,331,0,9.269387," ","integrate((-e*f*x^2+e*f)/(-a*d*x^2+b*d*x-a*d)/(-a*x^4+b*x^3+c*x^2+b*x-a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2 \, a + c} e f \log\left(\frac{2 \, a b^{3} x^{3} + 2 \, a b^{3} x + {\left(8 \, a^{4} - a^{2} b^{2} + 4 \, a^{3} c\right)} x^{4} + 8 \, a^{4} - a^{2} b^{2} + 4 \, a^{3} c - {\left(16 \, a^{4} + 10 \, a^{2} b^{2} + b^{4} + 8 \, a^{2} c^{2} + 4 \, {\left(6 \, a^{3} + a b^{2}\right)} c\right)} x^{2} - 4 \, {\left(a^{2} b x^{2} + a^{2} b - {\left(4 \, a^{3} + a b^{2} + 2 \, a^{2} c\right)} x\right)} \sqrt{-a x^{4} + b x^{3} + c x^{2} + b x - a} \sqrt{2 \, a + c}}{a^{2} x^{4} - 2 \, a b x^{3} - 2 \, a b x + {\left(2 \, a^{2} + b^{2}\right)} x^{2} + a^{2}}\right)}{2 \, {\left(2 \, a^{2} + a c\right)} d}, -\frac{\sqrt{-2 \, a - c} e f \arctan\left(\frac{2 \, \sqrt{-a x^{4} + b x^{3} + c x^{2} + b x - a} a \sqrt{-2 \, a - c}}{a b x^{2} + a b - {\left(4 \, a^{2} + b^{2} + 2 \, a c\right)} x}\right)}{{\left(2 \, a^{2} + a c\right)} d}\right]"," ",0,"[1/2*sqrt(2*a + c)*e*f*log((2*a*b^3*x^3 + 2*a*b^3*x + (8*a^4 - a^2*b^2 + 4*a^3*c)*x^4 + 8*a^4 - a^2*b^2 + 4*a^3*c - (16*a^4 + 10*a^2*b^2 + b^4 + 8*a^2*c^2 + 4*(6*a^3 + a*b^2)*c)*x^2 - 4*(a^2*b*x^2 + a^2*b - (4*a^3 + a*b^2 + 2*a^2*c)*x)*sqrt(-a*x^4 + b*x^3 + c*x^2 + b*x - a)*sqrt(2*a + c))/(a^2*x^4 - 2*a*b*x^3 - 2*a*b*x + (2*a^2 + b^2)*x^2 + a^2))/((2*a^2 + a*c)*d), -sqrt(-2*a - c)*e*f*arctan(2*sqrt(-a*x^4 + b*x^3 + c*x^2 + b*x - a)*a*sqrt(-2*a - c)/(a*b*x^2 + a*b - (4*a^2 + b^2 + 2*a*c)*x))/((2*a^2 + a*c)*d)]","A",0
1011,1,161,0,25.049788," ","integrate((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2)/x/(-a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} b \log\left(-4 \, a x^{2} - 4 \, b x \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}} - 2 \, \sqrt{a x^{2} + b x \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}}} {\left(\sqrt{2} \sqrt{a} x + \frac{\sqrt{2} b \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}}}{\sqrt{a}}\right)} + 1\right)}{2 \, \sqrt{a}}, -\sqrt{2} b \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a x^{2} + b x \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}}} \sqrt{-\frac{1}{a}}}{2 \, x}\right)\right]"," ",0,"[1/2*sqrt(2)*b*log(-4*a*x^2 - 4*b*x*sqrt((a^2*x^2 - a)/b^2) - 2*sqrt(a*x^2 + b*x*sqrt((a^2*x^2 - a)/b^2))*(sqrt(2)*sqrt(a)*x + sqrt(2)*b*sqrt((a^2*x^2 - a)/b^2)/sqrt(a)) + 1)/sqrt(a), -sqrt(2)*b*sqrt(-1/a)*arctan(1/2*sqrt(2)*sqrt(a*x^2 + b*x*sqrt((a^2*x^2 - a)/b^2))*sqrt(-1/a)/x)]","A",0
1012,1,161,0,22.677098," ","integrate((-a*x^2+b*x*(a/b^2+a^2*x^2/b^2)^(1/2))^(1/2)/x/(a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{2} b \sqrt{-\frac{1}{a}} \log\left(4 \, a x^{2} - 4 \, b x \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}} + 2 \, \sqrt{-a x^{2} + b x \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}}} {\left(\sqrt{2} a x \sqrt{-\frac{1}{a}} - \sqrt{2} b \sqrt{-\frac{1}{a}} \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}}\right)} + 1\right), -\frac{\sqrt{2} b \arctan\left(\frac{\sqrt{2} \sqrt{-a x^{2} + b x \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}}}}{2 \, \sqrt{a} x}\right)}{\sqrt{a}}\right]"," ",0,"[1/2*sqrt(2)*b*sqrt(-1/a)*log(4*a*x^2 - 4*b*x*sqrt((a^2*x^2 + a)/b^2) + 2*sqrt(-a*x^2 + b*x*sqrt((a^2*x^2 + a)/b^2))*(sqrt(2)*a*x*sqrt(-1/a) - sqrt(2)*b*sqrt(-1/a)*sqrt((a^2*x^2 + a)/b^2)) + 1), -sqrt(2)*b*arctan(1/2*sqrt(2)*sqrt(-a*x^2 + b*x*sqrt((a^2*x^2 + a)/b^2))/(sqrt(a)*x))/sqrt(a)]","A",0
1013,1,161,0,24.441193," ","integrate((x*(a*x+b*(-a/b^2+a^2*x^2/b^2)^(1/2)))^(1/2)/x/(-a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} b \log\left(-4 \, a x^{2} - 4 \, b x \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}} - 2 \, \sqrt{a x^{2} + b x \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}}} {\left(\sqrt{2} \sqrt{a} x + \frac{\sqrt{2} b \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}}}{\sqrt{a}}\right)} + 1\right)}{2 \, \sqrt{a}}, -\sqrt{2} b \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a x^{2} + b x \sqrt{\frac{a^{2} x^{2} - a}{b^{2}}}} \sqrt{-\frac{1}{a}}}{2 \, x}\right)\right]"," ",0,"[1/2*sqrt(2)*b*log(-4*a*x^2 - 4*b*x*sqrt((a^2*x^2 - a)/b^2) - 2*sqrt(a*x^2 + b*x*sqrt((a^2*x^2 - a)/b^2))*(sqrt(2)*sqrt(a)*x + sqrt(2)*b*sqrt((a^2*x^2 - a)/b^2)/sqrt(a)) + 1)/sqrt(a), -sqrt(2)*b*sqrt(-1/a)*arctan(1/2*sqrt(2)*sqrt(a*x^2 + b*x*sqrt((a^2*x^2 - a)/b^2))*sqrt(-1/a)/x)]","A",0
1014,1,161,0,22.630144," ","integrate((x*(b*(a/b^2+a^2*x^2/b^2)^(1/2)-a*x))^(1/2)/x/(a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{2} b \sqrt{-\frac{1}{a}} \log\left(4 \, a x^{2} - 4 \, b x \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}} + 2 \, \sqrt{-a x^{2} + b x \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}}} {\left(\sqrt{2} a x \sqrt{-\frac{1}{a}} - \sqrt{2} b \sqrt{-\frac{1}{a}} \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}}\right)} + 1\right), -\frac{\sqrt{2} b \arctan\left(\frac{\sqrt{2} \sqrt{-a x^{2} + b x \sqrt{\frac{a^{2} x^{2} + a}{b^{2}}}}}{2 \, \sqrt{a} x}\right)}{\sqrt{a}}\right]"," ",0,"[1/2*sqrt(2)*b*sqrt(-1/a)*log(4*a*x^2 - 4*b*x*sqrt((a^2*x^2 + a)/b^2) + 2*sqrt(-a*x^2 + b*x*sqrt((a^2*x^2 + a)/b^2))*(sqrt(2)*a*x*sqrt(-1/a) - sqrt(2)*b*sqrt(-1/a)*sqrt((a^2*x^2 + a)/b^2)) + 1), -sqrt(2)*b*arctan(1/2*sqrt(2)*sqrt(-a*x^2 + b*x*sqrt((a^2*x^2 + a)/b^2))/(sqrt(a)*x))/sqrt(a)]","A",0
1015,1,96,0,0.878279," ","integrate((-(-4+x)^(1/2)+x*(-4+x)^(1/2)-4*(-1+x)^(1/2)+x*(-1+x)^(1/2))/(x^2-5*x+4)/(1+(-4+x)^(1/2)+(-1+x)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(-{\left(4 \, x - 11\right)} \sqrt{x - 1} \sqrt{x - 4} + 4 \, x^{2} - 21 \, x + 23\right) + \frac{1}{2} \, \log\left(\sqrt{x - 1} \sqrt{x - 4} - x + 7\right) + \frac{1}{2} \, \log\left(x - 5\right) + \frac{1}{2} \, \log\left(\sqrt{x - 1} + 2\right) - \frac{1}{2} \, \log\left(\sqrt{x - 1} - 2\right) - \frac{1}{2} \, \log\left(\sqrt{x - 4} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{x - 4} - 1\right)"," ",0,"-1/2*log(-(4*x - 11)*sqrt(x - 1)*sqrt(x - 4) + 4*x^2 - 21*x + 23) + 1/2*log(sqrt(x - 1)*sqrt(x - 4) - x + 7) + 1/2*log(x - 5) + 1/2*log(sqrt(x - 1) + 2) - 1/2*log(sqrt(x - 1) - 2) - 1/2*log(sqrt(x - 4) + 1) + 1/2*log(sqrt(x - 4) - 1)","B",0
1016,1,458,0,20.990708," ","integrate(1/x/(x^2+3*x+3)/(x^3+3*x^2+3*x+3)^(1/3),x, algorithm=""fricas"")","-\frac{1}{54} \cdot 3^{\frac{2}{3}} \log\left(\frac{3 \cdot 3^{\frac{2}{3}} {\left(7 \, x^{4} + 28 \, x^{3} + 42 \, x^{2} + 30 \, x + 9\right)} {\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{2}{3}} + 3^{\frac{1}{3}} {\left(31 \, x^{6} + 186 \, x^{5} + 465 \, x^{4} + 666 \, x^{3} + 603 \, x^{2} + 324 \, x + 81\right)} + 9 \, {\left(5 \, x^{5} + 25 \, x^{4} + 50 \, x^{3} + 54 \, x^{2} + 33 \, x + 9\right)} {\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{1}{3}}}{x^{6} + 6 \, x^{5} + 15 \, x^{4} + 18 \, x^{3} + 9 \, x^{2}}\right) + \frac{1}{27} \cdot 3^{\frac{2}{3}} \log\left(\frac{2 \cdot 3^{\frac{2}{3}} {\left(x^{3} + 3 \, x^{2} + 3 \, x\right)} - 9 \cdot 3^{\frac{1}{3}} {\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{1}{3}} {\left(x^{2} + 2 \, x + 1\right)} + 9 \, {\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{2}{3}} {\left(x + 1\right)}}{x^{3} + 3 \, x^{2} + 3 \, x}\right) - \frac{1}{9} \cdot 3^{\frac{1}{6}} \arctan\left(\frac{3^{\frac{1}{6}} {\left(12 \cdot 3^{\frac{2}{3}} {\left(7 \, x^{7} + 49 \, x^{6} + 147 \, x^{5} + 240 \, x^{4} + 225 \, x^{3} + 117 \, x^{2} + 27 \, x\right)} {\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{2}{3}} - 3^{\frac{1}{3}} {\left(127 \, x^{9} + 1143 \, x^{8} + 4572 \, x^{7} + 11070 \, x^{6} + 18414 \, x^{5} + 22032 \, x^{4} + 18900 \, x^{3} + 11178 \, x^{2} + 4131 \, x + 729\right)} - 18 \, {\left(31 \, x^{8} + 248 \, x^{7} + 868 \, x^{6} + 1782 \, x^{5} + 2400 \, x^{4} + 2196 \, x^{3} + 1332 \, x^{2} + 486 \, x + 81\right)} {\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{1}{3}}\right)}}{3 \, {\left(251 \, x^{9} + 2259 \, x^{8} + 9036 \, x^{7} + 21546 \, x^{6} + 34398 \, x^{5} + 38556 \, x^{4} + 30348 \, x^{3} + 16038 \, x^{2} + 5103 \, x + 729\right)}}\right)"," ",0,"-1/54*3^(2/3)*log((3*3^(2/3)*(7*x^4 + 28*x^3 + 42*x^2 + 30*x + 9)*(x^3 + 3*x^2 + 3*x + 3)^(2/3) + 3^(1/3)*(31*x^6 + 186*x^5 + 465*x^4 + 666*x^3 + 603*x^2 + 324*x + 81) + 9*(5*x^5 + 25*x^4 + 50*x^3 + 54*x^2 + 33*x + 9)*(x^3 + 3*x^2 + 3*x + 3)^(1/3))/(x^6 + 6*x^5 + 15*x^4 + 18*x^3 + 9*x^2)) + 1/27*3^(2/3)*log((2*3^(2/3)*(x^3 + 3*x^2 + 3*x) - 9*3^(1/3)*(x^3 + 3*x^2 + 3*x + 3)^(1/3)*(x^2 + 2*x + 1) + 9*(x^3 + 3*x^2 + 3*x + 3)^(2/3)*(x + 1))/(x^3 + 3*x^2 + 3*x)) - 1/9*3^(1/6)*arctan(1/3*3^(1/6)*(12*3^(2/3)*(7*x^7 + 49*x^6 + 147*x^5 + 240*x^4 + 225*x^3 + 117*x^2 + 27*x)*(x^3 + 3*x^2 + 3*x + 3)^(2/3) - 3^(1/3)*(127*x^9 + 1143*x^8 + 4572*x^7 + 11070*x^6 + 18414*x^5 + 22032*x^4 + 18900*x^3 + 11178*x^2 + 4131*x + 729) - 18*(31*x^8 + 248*x^7 + 868*x^6 + 1782*x^5 + 2400*x^4 + 2196*x^3 + 1332*x^2 + 486*x + 81)*(x^3 + 3*x^2 + 3*x + 3)^(1/3))/(251*x^9 + 2259*x^8 + 9036*x^7 + 21546*x^6 + 34398*x^5 + 38556*x^4 + 30348*x^3 + 16038*x^2 + 5103*x + 729))","B",0
1017,1,289,0,11.268032," ","integrate((-x^2+1)/(x^2-x+1)/(-x^3+1)^(2/3),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{4^{\frac{1}{6}} \sqrt{3} {\left(2 \cdot 4^{\frac{2}{3}} {\left(x^{5} - x^{4} - 3 \, x^{3} + 3 \, x^{2} + x - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4 \, {\left(x^{4} - 4 \, x^{3} + 5 \, x^{2} - 4 \, x + 1\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(x^{6} - 7 \, x^{5} + 10 \, x^{4} - 7 \, x^{3} + 10 \, x^{2} - 7 \, x + 1\right)}\right)}}{6 \, {\left(3 \, x^{6} - 9 \, x^{5} + 6 \, x^{4} - x^{3} + 6 \, x^{2} - 9 \, x + 3\right)}}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \log\left(\frac{2 \cdot 4^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{2} - 3 \, x + 1\right)} - 4^{\frac{2}{3}} {\left(x^{4} - 3 \, x^{2} + 1\right)} - 8 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{2} - x\right)}}{x^{4} - 2 \, x^{3} + 3 \, x^{2} - 2 \, x + 1}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \log\left(-\frac{4^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} {\left(x - 1\right)} - 4^{\frac{1}{3}} {\left(x^{2} - x + 1\right)} - 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2} - x + 1}\right)"," ",0,"-1/6*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*sqrt(3)*(2*4^(2/3)*(x^5 - x^4 - 3*x^3 + 3*x^2 + x - 1)*(-x^3 + 1)^(1/3) + 4*(x^4 - 4*x^3 + 5*x^2 - 4*x + 1)*(-x^3 + 1)^(2/3) + 4^(1/3)*(x^6 - 7*x^5 + 10*x^4 - 7*x^3 + 10*x^2 - 7*x + 1))/(3*x^6 - 9*x^5 + 6*x^4 - x^3 + 6*x^2 - 9*x + 3)) - 1/24*4^(2/3)*log((2*4^(1/3)*(-x^3 + 1)^(2/3)*(x^2 - 3*x + 1) - 4^(2/3)*(x^4 - 3*x^2 + 1) - 8*(-x^3 + 1)^(1/3)*(x^2 - x))/(x^4 - 2*x^3 + 3*x^2 - 2*x + 1)) + 1/12*4^(2/3)*log(-(4^(2/3)*(-x^3 + 1)^(1/3)*(x - 1) - 4^(1/3)*(x^2 - x + 1) - 2*(-x^3 + 1)^(2/3))/(x^2 - x + 1))","B",0
1018,1,51,0,1.297256," ","integrate(x^2/(x^4+1)/(x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \arctan\left(\frac{\sqrt{x^{4} - 1} x}{x^{2} + 1}\right) + \frac{1}{8} \, \log\left(\frac{x^{4} + 2 \, x^{2} + 2 \, \sqrt{x^{4} - 1} x - 1}{x^{4} + 1}\right)"," ",0,"1/4*arctan(sqrt(x^4 - 1)*x/(x^2 + 1)) + 1/8*log((x^4 + 2*x^2 + 2*sqrt(x^4 - 1)*x - 1)/(x^4 + 1))","A",0
1019,1,472,0,120.385500," ","integrate((-c*x^4+a)/(c*d*x^2+a*e)/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-c d^{3} e + b d^{2} e^{2} - a d e^{3}} \log\left(-\frac{c^{2} d^{2} e^{2} x^{8} - 2 \, {\left(3 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2} + 3 \, a c d e^{3}\right)} x^{6} + a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} - 8 \, b c d^{3} e - 8 \, a b d e^{3} + a^{2} e^{4} + 4 \, {\left(2 \, b^{2} + a c\right)} d^{2} e^{2}\right)} x^{4} - 2 \, {\left(3 \, a c d^{3} e - 4 \, a b d^{2} e^{2} + 3 \, a^{2} d e^{3}\right)} x^{2} + 4 \, {\left(c d e x^{5} + a d e x - {\left(c d^{2} - 2 \, b d e + a e^{2}\right)} x^{3}\right)} \sqrt{-c d^{3} e + b d^{2} e^{2} - a d e^{3}} \sqrt{c x^{4} + b x^{2} + a}}{c^{2} d^{2} e^{2} x^{8} + 2 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x^{6} + a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 4 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{4} + 2 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x^{2}}\right)}{4 \, {\left(c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)}}, \frac{\arctan\left(\frac{2 \, \sqrt{c d^{3} e - b d^{2} e^{2} + a d e^{3}} \sqrt{c x^{4} + b x^{2} + a} x}{c d e x^{4} + a d e - {\left(c d^{2} - 2 \, b d e + a e^{2}\right)} x^{2}}\right)}{2 \, \sqrt{c d^{3} e - b d^{2} e^{2} + a d e^{3}}}\right]"," ",0,"[-1/4*sqrt(-c*d^3*e + b*d^2*e^2 - a*d*e^3)*log(-(c^2*d^2*e^2*x^8 - 2*(3*c^2*d^3*e - 4*b*c*d^2*e^2 + 3*a*c*d*e^3)*x^6 + a^2*d^2*e^2 + (c^2*d^4 - 8*b*c*d^3*e - 8*a*b*d*e^3 + a^2*e^4 + 4*(2*b^2 + a*c)*d^2*e^2)*x^4 - 2*(3*a*c*d^3*e - 4*a*b*d^2*e^2 + 3*a^2*d*e^3)*x^2 + 4*(c*d*e*x^5 + a*d*e*x - (c*d^2 - 2*b*d*e + a*e^2)*x^3)*sqrt(-c*d^3*e + b*d^2*e^2 - a*d*e^3)*sqrt(c*x^4 + b*x^2 + a))/(c^2*d^2*e^2*x^8 + 2*(c^2*d^3*e + a*c*d*e^3)*x^6 + a^2*d^2*e^2 + (c^2*d^4 + 4*a*c*d^2*e^2 + a^2*e^4)*x^4 + 2*(a*c*d^3*e + a^2*d*e^3)*x^2))/(c*d^3*e - b*d^2*e^2 + a*d*e^3), 1/2*arctan(2*sqrt(c*d^3*e - b*d^2*e^2 + a*d*e^3)*sqrt(c*x^4 + b*x^2 + a)*x/(c*d*e*x^4 + a*d*e - (c*d^2 - 2*b*d*e + a*e^2)*x^2))/sqrt(c*d^3*e - b*d^2*e^2 + a*d*e^3)]","A",0
1020,1,1,0,0.783472," ","integrate(x+(-x^2+1)/(1+x),x, algorithm=""fricas"")","x"," ",0,"x","A",0
1021,1,73,0,0.647108," ","integrate(1/(1/x+(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} - 1\right)} \sqrt{-x^{2} + 1}}{3 \, {\left(x^{3} - x\right)}}\right) - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)*sqrt(-x^2 + 1)/(x^3 - x)) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
1022,1,73,0,0.850317," ","integrate(x*(-x^2+1)^(1/2)/(x-x^3+(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} - 1\right)} \sqrt{-x^{2} + 1}}{3 \, {\left(x^{3} - x\right)}}\right) - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)*sqrt(-x^2 + 1)/(x^3 - x)) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
1023,1,31,0,0.743707," ","integrate((-x^4+1)^n/((x^3+x^2+x+1)^n),x, algorithm=""fricas"")","\frac{{\left(-x^{4} + 1\right)}^{n} {\left(x - 1\right)}}{{\left(x^{3} + x^{2} + x + 1\right)}^{n} {\left(n + 1\right)}}"," ",0,"(-x^4 + 1)^n*(x - 1)/((x^3 + x^2 + x + 1)^n*(n + 1))","A",0
1024,1,164,0,1.330990," ","integrate(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(28179280429056 \, c^{8} x^{8} + 6115295232000 \, b^{2} c^{6} x^{6} + 4076863488000 \, b^{3} c^{5} x^{5} + 179159040000 \, b^{4} c^{4} x^{4} + 486604800000 \, b^{5} c^{3} x^{3} + 112464000000 \, b^{6} c^{2} x^{2} + 3906640625 \, b^{8} + {\left(12230590464 \, c^{6} x^{6} + 1990656000 \, b^{2} c^{4} x^{4} + 1105920000 \, b^{3} c^{3} x^{3} + 38880000 \, b^{4} c^{2} x^{2} + 79200000 \, b^{5} c x + 12203125 \, b^{6}\right)} \sqrt{5308416 \, c^{4} x^{4} + 576000 \, b^{2} c^{2} x^{2} + 576000 \, b^{3} c x - 44375 \, b^{4}}\right)}{18432 \, c^{2}}"," ",0,"1/18432*log(28179280429056*c^8*x^8 + 6115295232000*b^2*c^6*x^6 + 4076863488000*b^3*c^5*x^5 + 179159040000*b^4*c^4*x^4 + 486604800000*b^5*c^3*x^3 + 112464000000*b^6*c^2*x^2 + 3906640625*b^8 + (12230590464*c^6*x^6 + 1990656000*b^2*c^4*x^4 + 1105920000*b^3*c^3*x^3 + 38880000*b^4*c^2*x^2 + 79200000*b^5*c*x + 12203125*b^6)*sqrt(5308416*c^4*x^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x - 44375*b^4))/c^2","A",0
1025,1,97,0,1.177303," ","integrate((1+4*x)/(64*x^4+64*x^3+64*x^2+120*x+9)^(1/2),x, algorithm=""fricas"")","\frac{1}{16} \, \log\left(-4096 \, x^{8} - 8192 \, x^{7} - 12288 \, x^{6} - 19456 \, x^{5} - 17024 \, x^{4} - 13440 \, x^{3} - 9280 \, x^{2} - {\left(512 \, x^{6} + 768 \, x^{5} + 960 \, x^{4} + 1280 \, x^{3} + 744 \, x^{2} + 444 \, x + 179\right)} \sqrt{64 \, x^{4} + 64 \, x^{3} + 64 \, x^{2} + 120 \, x + 9} - 2864 \, x - 921\right)"," ",0,"1/16*log(-4096*x^8 - 8192*x^7 - 12288*x^6 - 19456*x^5 - 17024*x^4 - 13440*x^3 - 9280*x^2 - (512*x^6 + 768*x^5 + 960*x^4 + 1280*x^3 + 744*x^2 + 444*x + 179)*sqrt(64*x^4 + 64*x^3 + 64*x^2 + 120*x + 9) - 2864*x - 921)","A",0
