Integrand size = 20, antiderivative size = 1058 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx =\text {Too large to display} \]
149066309808794760843017404825/1624981820656451683095663001731072/(3-2*x)^ (27/2)+15848613964169066543734380171/601845118761648771516912222863360/(3- 2*x)^(25/2)+11155168222970774232376891145/16851663325326165602473542240174 08/(3-2*x)^(23/2)+14011818498091020272474956375/10110997995195699361484125 344104448/(3-2*x)^(21/2)-13056959628363355534285785425/1069240143572535627 23941220352/(3-2*x)^(39/2)-304688229262620222736480811/5373617131800435459 97243056128/(3-2*x)^(35/2)+2124315846756567455653862925/168885109856585114 4562763890688/(3-2*x)^(33/2)+47657515074514118796095929535/666328524343253 99703658138959872/(3-2*x)^(31/2)+34911619993974714062172751985/12466791745 7770102671360389021696/(3-2*x)^(29/2)-3948194343291401740321996415/2028814 63139404195937734623232/(3-2*x)^(37/2)-101190274412779618678573275245/3963 511214116714149701777134888943616/(3-2*x)^(15/2)-4605031904169582830874393 37135/34350430522344855964082068502370844672/(3-2*x)^(13/2)-22116195887909 11794826342607495/406920484649315986036049119181931544576/(3-2*x)^(11/2)+1 73441368149804378661935869705/896508488907352010051592447177261056/(3-2*x) ^(19/2)-22724090823469905152713519545/160427834857105096535548122126457241 6/(3-2*x)^(17/2)-927027754781476746208047620505/58004665448193406009502274 443388060172288/(3-2*x)^(1/2)-405965372440630510720926890227/2071595194578 335928910795515835287863296/(3-2*x)^(5/2)-4986681479187781853417316522775/ 87006998172290109014253411665082090258432/(3-2*x)^(3/2)-461105327811714...
Result contains complex when optimal does not.
Time = 17.33 (sec) , antiderivative size = 1100, normalized size of antiderivative = 1.04 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx =\text {Too large to display} \]
x/(133*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^19) + ((44296 + 146216*x)/(3528*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^18) + ((223125616 + 589021552*x)/(3332*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^17) + ((865861681440 + 2110519336800*x)/(3136 *(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^16) + ((2984274342235200 + 6928434268875 840*x)/(2940*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^15) + ((9408813737133390720 + 20924013532366815360*x)/(2744*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14) + ((2 7243065619141593598720 + 57873497074462503141120*x)/(2548*(3 - 2*x)^(39/2) *(1 + x + 2*x^2)^13) + ((72110377354780278913835520 + 14529534294868310616 4016640*x)/(2352*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^12) + ((1729014581089328 96335179801600 + 326770416680301421681066214400*x)/(2156*(3 - 2*x)^(39/2)* (1 + x + 2*x^2)^11) + ((370557652515461812186329087129600 + 64580296723188 6306826540424448000*x)/(1960*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^10) + ((6961 75598675973438759010577554944000 + 1088028437838790621809440473088716800*x )/(1764*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^9) + ((11119650634712440154892481 63496668569600 + 1477884081820868038735185945420330393600*x)/(1568*(3 - 2* x)^(39/2)*(1 + x + 2*x^2)^8) + ((14276360230389585254181896232760391602176 00 + 1410229454280293592108580217248432347955200*x)/(1372*(3 - 2*x)^(39/2) *(1 + x + 2*x^2)^7) + ((1283308803395067168818807997696073436639232000 + 4 21439161286999121770135584246204836237312000*x)/(1176*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + ((359909043739097249991695788946258930146664448000 - ...
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {1}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{20}} \, dx\) |
| \(\Big \downarrow \) 1165 |
| \(\displaystyle \frac {\int \frac {28 (130-113 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{19}}dx}{3724}+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \int \frac {130-113 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{19}}dx+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {\int \frac {14 (33336-40657 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{18}}dx}{3528}+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \int \frac {33336-40657 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{18}}dx+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {\int \frac {210 (539991-751303 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{17}}dx}{3332}+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \int \frac {539991-751303 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{17}}dx+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {\int \frac {14 (122225856-184959785 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{16}}dx}{3136}+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \int \frac {122225856-184959785 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{16}}dx+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {\int \frac {14 (25488953979-41652915209 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{15}}dx}{2940}+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \int \frac {25488953979-41652915209 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{15}}dx+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {\int \frac {42 (1614300418670-2871555518177 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{14}}dx}{2744}+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \int \frac {1614300418670-2871555518177 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{14}}dx+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {\int \frac {98 (39357458161627-77559130805859 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{13}}dx}{2548}+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \int \frac {39357458161627-77559130805859 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{13}}dx+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {\int \frac {70 (1182110687469684-2656658801194921 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{12}}dx}{2352}+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \int \frac {1182110687469684-2656658801194921 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{12}}dx+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {\int \frac {126 (16782494726084327-45187921585208601 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{11}}dx}{2156}+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \int \frac {16782494726084327-45187921585208601 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{11}}dx+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {\int \frac {14 (1706599234272796606-6063974149878048635 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{10}}dx}{1960}+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \int \frac {1706599234272796606-6063974149878048635 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^{10}}dx+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {\int \frac {14 (113832295864564863195-691833601144925854831 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^9}dx}{1764}+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \int \frac {113832295864564863195-691833601144925854831 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^9}dx+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {\int -\frac {966 (919498192874055581221 x+5605528390794056352)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^8}dx}{1568}+\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \int \frac {919498192874055581221 x+5605528390794056352}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^8}dx\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {\int \frac {910 (908287136092467468517 x+305002625573972621385)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^7}dx}{1372}-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {65}{98} \int \frac {908287136092467468517 x+305002625573972621385}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^7}dx-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {65}{98} \left (\frac {\int \frac {98 (2599313568802265110081 x+6512728008712726244634)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^6}dx}{1176}-\frac {298281884944522225747 x+908287136092467468517}{84 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^6}\right )-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {65}{98} \left (\frac {1}{12} \int \frac {2599313568802265110081 x+6512728008712726244634}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^6}dx-\frac {298281884944522225747 x+908287136092467468517}{84 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^6}\right )-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {65}{98} \left (\frac {1}{12} \left (\frac {1}{980} \int \frac {798 (8543790507285537502259-10426142448623187379187 x)}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^5}dx-\frac {2599313568802265110081-10426142448623187379187 x}{70 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^5}\right )-\frac {298281884944522225747 x+908287136092467468517}{84 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^6}\right )-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {65}{98} \left (\frac {1}{12} \left (\frac {57}{70} \int \frac {8543790507285537502259-10426142448623187379187 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^5}dx-\frac {2599313568802265110081-10426142448623187379187 x}{70 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^5}\right )-\frac {298281884944522225747 x+908287136092467468517}{84 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^6}\right )-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
3.1.49.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_S ymbol] :> Simp[(d + e*x)^(m + 1)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e) *x)*((a + b*x + c*x^2)^(p + 1)/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^ 2))), x] + Simp[1/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)) Int[(d + e*x)^m*Simp[b*c*d*e*(2*p - m + 2) + b^2*e^2*(m + p + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3) - c*e*(2*c*d - b*e)*(m + 2*p + 4)*x, x]*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, m}, x] && LtQ[p, -1] && IntQuadraticQ[a, b, c, d, e, m, p, x]
Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c _.)*(x_)^2)^(p_), x_Symbol] :> Simp[(d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2 *a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x)*((a + b*x + c*x^2)^(p + 1)/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))), x] + Simp[1/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)) Int[(d + e*x)^m *(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d* m + b*e*m) - b*d*(3*c*d - b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, m}, x] && LtQ[p, -1] && (IntegerQ[m] || IntegerQ[p] || IntegersQ[2*m, 2*p] )
Time = 7.41 (sec) , antiderivative size = 502, normalized size of antiderivative = 0.47
| method | result | size |
| pseudoelliptic | \(\text {Expression too large to display}\) | \(502\) |
| trager | \(\text {Expression too large to display}\) | \(733\) |
| risch | \(\text {Expression too large to display}\) | \(761\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(820\) |
| default | \(\text {Expression too large to display}\) | \(820\) |
115/5908552821163231304184823545856/(3-2*x)^(39/2)/(-7+2*14^(1/2))^(1/2)*( (x-3/2)^19*(1/2*(7+2*14^(1/2))^(1/2)*(62541562556792464940960784209*14^(1/ 2)-234044028404883307655877091262)*(ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*1 4^(1/2))^(1/2))-ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2)))*(-7 +2*14^(1/2))^(1/2)+(30297118912219360725028693061*14^(1/2)+112855552756005 864755762319018)*(arctan((2*(3-2*x)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^( 1/2))^(1/2))+arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2)) ^(1/2))))*(x^2+1/2*x+1/2)^19*(3-2*x)^(1/2)+225711105512011729511524638036* (-7+2*14^(1/2))^(1/2)*(440996520277951008903098744562486494852026613994907 /44191133016840857755226917181058069710181394022400*x^6+351285717820454846 30026117801687570244083874053171/45173158194992876816454182007303804592629 8694451200*x+210574562552165591334786629936646706654271617680629/188221492 47913698673522575836376585246929112268800*x^5+3283584831830973024106759848 20102893536081023906041/11293289548748219204113545501825951148157467361280 0*x^4+26422837290755407889965256858972508931537804132765/18069263277997150 726581672802921521837051947778048*x^3+102588617441827054856799965258821391 64879327899743/41066507449993524378594710915730731447845335859200*x^2-3396 92530351150840696302021012775910383197972648611749049/22021914620059027448 02141372856060473890706135449600*x^20-522812506810746872215164433461641835 72170004539439383783/92723851031827483991669110436044651532240258334720...
Result contains complex when optimal does not.
Time = 2.04 (sec) , antiderivative size = 1905, normalized size of antiderivative = 1.80 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Too large to display} \]
1/336864077912586356135291702496114974019074478550548480*(207411935445*(54 9755813888*x^58 - 11269994184704*x^57 + 107064944754688*x^56 - 63063863800 6272*x^55 + 2618521301286912*x^54 - 8342252417974272*x^53 + 21849572376576 000*x^52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188583312363 618304*x^49 + 323261995581177856*x^48 - 517079841212727296*x^47 + 77811789 6260812800*x^46 - 1105641165387988992*x^45 + 1491287028233404416*x^44 - 19 19929663119949824*x^43 + 2363050939901804544*x^42 - 2786274020645928960*x^ 41 + 3161145685194047488*x^40 - 3453753931369283584*x^39 + 363409846710252 3392*x^38 - 3697893960325791744*x^37 + 3640651752731836416*x^36 - 34617982 12247617536*x^35 + 3194540251789393920*x^34 - 2861544579495297024*x^33 + 2 477632938217930752*x^32 - 2088430257127768064*x^31 + 1712761005459316736*x ^30 - 1355447485390974976*x^29 + 1048940886155151360*x^28 - 79051102413508 9152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^25 + 2828450695 99813728*x^24 - 186113897194906128*x^23 + 123982890381352520*x^22 - 781163 67732251996*x^21 + 46488580159296898*x^20 - 29591055660829971*x^19 + 16200 795673453545*x^18 - 8941894120163277*x^17 + 5578893209169441*x^16 - 229684 9711499532*x^15 + 1448289882400788*x^14 - 756896247319212*x^13 + 182213447 974992*x^12 - 240797810407770*x^11 + 25549234281774*x^10 - 26500281727302* x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354811164*x^6 + 375574 0313808*x^5 + 1820618017974*x^4 + 463742325333*x^3 + 139858796529*x^2 +...
Timed out. \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Timed out} \]
\[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\int { \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{20} {\left (-2 \, x + 3\right )}^{\frac {41}{2}}} \,d x } \]
Time = 1.09 (sec) , antiderivative size = 1410, normalized size of antiderivative = 1.33 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Too large to display} \]
-115/363805261691069042491598265308929913400590336*sqrt(7)*(24183332733429 828161949068361*14^(3/4)*sqrt(7)*(sqrt(14) + 4)*sqrt(-2*sqrt(14) + 8) + 80 61110911143276053983022787*14^(3/4)*sqrt(7)*(sqrt(14) - 4)*sqrt(-2*sqrt(14 ) + 8) - 56427776378002932377881159509*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt (14) + 4) - 169283329134008797133643478527*14^(3/4)*sqrt(2*sqrt(14) + 8)*( sqrt(14) - 4) + 242376951297754885800229544488*14^(1/4)*sqrt(7)*sqrt(-2*sq rt(14) + 8) - 1696638659084284200601606811416*14^(1/4)*sqrt(2*sqrt(14) + 8 ))*arctan(1/28*14^(3/4)*(14^(1/4)*sqrt(1/2)*sqrt(sqrt(14) + 4) + 2*sqrt(-2 *x + 3))/sqrt(-1/8*sqrt(14) + 1/2)) - 115/36380526169106904249159826530892 9913400590336*sqrt(7)*(24183332733429828161949068361*14^(3/4)*sqrt(7)*(sqr t(14) + 4)*sqrt(-2*sqrt(14) + 8) + 8061110911143276053983022787*14^(3/4)*s qrt(7)*(sqrt(14) - 4)*sqrt(-2*sqrt(14) + 8) - 5642777637800293237788115950 9*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) + 4) - 1692833291340087971336434 78527*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 242376951297754885800 229544488*14^(1/4)*sqrt(7)*sqrt(-2*sqrt(14) + 8) - 16966386590842842006016 06811416*14^(1/4)*sqrt(2*sqrt(14) + 8))*arctan(-1/28*14^(3/4)*(14^(1/4)*sq rt(1/2)*sqrt(sqrt(14) + 4) - 2*sqrt(-2*x + 3))/sqrt(-1/8*sqrt(14) + 1/2)) - 115/727610523382138084983196530617859826801180672*sqrt(7)*(8061110911143 276053983022787*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(14) + 4) + 241 83332733429828161949068361*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(...
Time = 1.06 (sec) , antiderivative size = 1017, normalized size of antiderivative = 0.96 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Too large to display} \]
((64356352*(2*x - 3)^2)/38073 - (5767168*x)/1443 - (7517962240*(2*x - 3)^3 )/5444439 + (1357449428992*(2*x - 3)^4)/1181443263 - (34130408095744*(2*x - 3)^5)/34261854627 + (1965832636456960*(2*x - 3)^6)/2158496841501 - (9552 588571922432*(2*x - 3)^7)/10792484207505 + (69571472879183872*(2*x - 3)^8) /75547389452535 - (5204838729946112*(2*x - 3)^9)/5036492630169 + (32508205 2781755904*(2*x - 3)^10)/257635969158645 - (461538785202937088*(2*x - 3)^1 1)/272428464995505 + (17726678744562203264*(2*x - 3)^12)/6992330601551295 - (1432471149647610304*(2*x - 3)^13)/332968123883395 + (204346360124338870 4*(2*x - 3)^14)/241114848329355 - (96972768477343976816*(2*x - 3)^15)/4840 844262612435 + (10833870670122545927656*(2*x - 3)^16)/181389282075536535 - (44340157049832305729324*(2*x - 3)^17)/181389282075536535 + (691509778132 186261807282*(2*x - 3)^18)/423241658176251915 - (1357735833153708223970340 7*(2*x - 3)^19)/423241658176251915 + (509495943858959939640753039465067261 4981*(2*x - 3)^20)/203594616979243053623625646080 + (474753402737241482257 49886260884632526403*(2*x - 3)^21)/203594616979243053623625646080 + (54736 2406727667345868176230754600752341499*(2*x - 3)^22)/5182408432198914092237 74371840 + (1363217399168846741803250531443496167647559*(2*x - 3)^23)/4385 11482724523500112424468480 + (40035704814224807138997531075224002020138815 9*(2*x - 3)^24)/59856817391897457765345939947520 + (1678035321867106187517 78512174316524508553291*(2*x - 3)^25)/14964204347974364441336484986880 ...
Time = 0.49 (sec) , antiderivative size = 21074, normalized size of antiderivative = 19.92 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx =\text {Too large to display} \]
int(1/(sqrt( - 2*x + 3)*(1099511627776*x**60 - 21990232555520*x**59 + 2034 09651138560*x**58 - 1165482325442560*x**57 + 4713468909322240*x**56 - 1469 6622172667904*x**55 + 37975413636464640*x**54 - 85860863013027840*x**53 + 174954483485245440*x**52 - 325456214915809280*x**51 + 559335180095979520*x **50 - 899480999207895040*x**49 + 1362417946890076160*x**48 - 195024427572 7892480*x**47 + 2655050787339632640*x**46 - 3454213463394484224*x**45 + 42 97459244917063680*x**44 - 5129426764510003200*x**43 + 5899068289643970560* x**42 - 6532636198190448640*x**41 + 6975588688029810688*x**40 - 7215443384 918343680*x**39 + 7217508012240404480*x**38 - 6980838632089190400*x**37 + 6567934044063006720*x**36 - 5990347119448817664*x**35 + 528826154872995840 0*x**34 - 4560772155532902400*x**33 + 3814724692008796160*x**32 - 30865642 22450401280*x**31 + 2455195292378644480*x**30 - 1887528647506001920*x**29 + 1401931713076849920*x**28 - 1035508304991175680*x**27 + 7290669615357811 20*x**26 - 497756827982238720*x**25 + 344696953167612640*x**24 - 218363742 278057600*x**23 + 138843682967694320*x**22 - 90809898894615040*x**21 + 492 99115845374017*x**20 - 31274048227702980*x**19 + 18416687971629150*x**18 - 7956700333992900*x**17 + 6178623262471485*x**16 - 2362352323737168*x**15 + 1055820531031560*x**14 - 1056278420159760*x**13 - 7485893869230*x**12 - 268249139580600*x**11 + 50090355219636*x**10 + 18951434065800*x**9 + 56264 918185170*x**8 + 27866342669040*x**7 + 17786331160920*x**6 + 6503842982448 *x**5 + 2564077936365*x**4 + 643118011740*x**3 + 166590810270*x**2 + 23245 229340*x + 3486784401)),x)
( - 820106290170129967145447171095953091911999318235545600*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**57 + 1558201951323246937576349625082310874 6327987046475366400*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2 *sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**56 - 13 6342670740784107037930592194702201530369886656659456000*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**55 + 7362504220002341780048251978513918882639 97387945961062400*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*s qrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**54 - 2801 841883723113399629473669601130241449101170794351820800*sqrt(2*sqrt(14) - 7 )*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7 ))/sqrt(2*sqrt(14) - 7))*x**53 + 82419144462803992704429042981697480825108 59648395064115200*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*s qrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**52 - 2023 1548054548101683090925749291372929587761556265055027200*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**51 + 4376964934361511221918566466393319335736 1154238751703040000*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2 *sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**50 -...