Integrand size = 20, antiderivative size = 1058 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx =\text {Too large to display} \] Output:
-143401467550777247627940437025/73985542663511997461099839851260280832/(3- 2*x)^(9/2)-4611053278117143010907562317585/7250583181024175751187784305423 507521536/(3-2*x)^(7/2)-405965372440630510720926890227/2071595194578335928 910795515835287863296/(3-2*x)^(5/2)-4986681479187781853417316522775/870069 98172290109014253411665082090258432/(3-2*x)^(3/2)-927027754781476746208047 620505/58004665448193406009502274443388060172288/(3-2*x)^(1/2)-39481943432 91401740321996415/202881463139404195937734623232/(3-2*x)^(37/2)-3046882292 62620222736480811/537361713180043545997243056128/(3-2*x)^(35/2)+2124315846 756567455653862925/1688851098565851144562763890688/(3-2*x)^(33/2)+47657515 074514118796095929535/66632852434325399703658138959872/(3-2*x)^(31/2)+3491 1619993974714062172751985/124667917457770102671360389021696/(3-2*x)^(29/2) +149066309808794760843017404825/1624981820656451683095663001731072/(3-2*x) ^(27/2)+15848613964169066543734380171/601845118761648771516912222863360/(3 -2*x)^(25/2)+11155168222970774232376891145/1685166332532616560247354224017 408/(3-2*x)^(23/2)+14011818498091020272474956375/1011099799519569936148412 5344104448/(3-2*x)^(21/2)-13056959628363355534285785425/106924014357253562 723941220352/(3-2*x)^(39/2)+5/595601664*(751303+1831285*x)/(3-2*x)^(39/2)/ (2*x^2+x+1)^16+1/25015269888*(184959785+429411497*x)/(3-2*x)^(39/2)/(2*x^2 +x+1)^15+1/4902992898048*(41652915209+92630823167*x)/(3-2*x)^(39/2)/(2*x^2 +x+1)^14+1/297448235814912*(2871555518177+6100156355517*x)/(3-2*x)^(39/...
Result contains complex when optimal does not.
Time = 36.09 (sec) , antiderivative size = 1242, normalized size of antiderivative = 1.17 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx =\text {Too large to display} \] Input:
Integrate[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]
Output:
-1/150276832468*(393*Sqrt[3 - 2*x] + 287*(3 - 2*x)^(3/2))/(14 - 7*(3 - 2*x ) + (3 - 2*x)^2)^19 - (-4226921*Sqrt[3 - 2*x] + 1313129*(3 - 2*x)^(3/2))/( 75739523563872*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^18) - (-3401932701*Sqrt[3 - 2*x] + 760755809*(3 - 2*x)^(3/2))/(36052013216403072*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^17) - (5*(-146490500023*Sqrt[3 - 2*x] + 16144709919*(3 - 2*x )^(3/2)))/(16151301920948576256*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^16) - (97 45709632283*Sqrt[3 - 2*x] - 4557912048927*(3 - 2*x)^(3/2))/(45223645378656 0135168*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^15) - (435856117815771*Sqrt[3 - 2 *x] - 123609208162571*(3 - 2*x)^(3/2))/(9330352099175345946624*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^14) - (127435522656997631*Sqrt[3 - 2*x] - 3127030241 4674811*(3 - 2*x)^(3/2))/(3396248164099825924571136*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^13) + (5*(-1540359167602841319*Sqrt[3 - 2*x] + 3420265577570880 31*(3 - 2*x)^(3/2)))/(380379794379180503551967232*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^12) + (5*(-21084628139481190687*Sqrt[3 - 2*x] + 41586699245502578 27*(3 - 2*x)^(3/2)))/(13017441852087510566000656384*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^11) - (1633293973597342712581*Sqrt[3 - 2*x] - 23708074415419338 4005*(3 - 2*x)^(3/2))/(728976743716900591696036757504*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^10) - (7350432513431022017155*Sqrt[3 - 2*x] + 513156431847137 6538977*(3 - 2*x)^(3/2))/(61234046472219649702467087630336*(14 - 7*(3 - 2* x) + (3 - 2*x)^2)^9) - (-113207386492327172550771*Sqrt[3 - 2*x] + 43421...
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 |
| \(\displaystyle \frac {1}{133} \left (\frac {1}{252} \left (\frac {15}{238} \left (\frac {1}{224} \left (\frac {1}{210} \left (\frac {3}{196} \left (\frac {1}{26} \left (\frac {5}{168} \left (\frac {9}{154} \left (\frac {1}{140} \left (\frac {1}{126} \left (\frac {919498192874055581221 x+691833601144925854831}{112 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^8}-\frac {69}{112} \left (\frac {65}{98} \left (\frac {1}{12} \left (\frac {57}{70} \int \frac {8543790507285537502259-10426142448623187379187 x}{(3-2 x)^{41/2} \left (2 x^2+x+1\right )^5}dx-\frac {2599313568802265110081-10426142448623187379187 x}{70 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^5}\right )-\frac {298281884944522225747 x+908287136092467468517}{84 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^6}\right )-\frac {908287136092467468517 x+919498192874055581221}{98 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^7}\right )\right )+\frac {9477172618423641847 x+6063974149878048635}{126 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^9}\right )+\frac {78752911037377255 x+45187921585208601}{140 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{10}}\right )+\frac {5020880176134289 x+2656658801194921}{154 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{11}}\right )+\frac {156274047129113 x+77559130805859}{168 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{12}}\right )+\frac {6100156355517 x+2871555518177}{182 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{13}}\right )+\frac {92630823167 x+41652915209}{196 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{14}}\right )+\frac {429411497 x+184959785}{210 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{15}}\right )+\frac {1831285 x+751303}{224 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{16}}\right )+\frac {107329 x+40657}{238 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{17}}\right )+\frac {373 x+113}{252 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{18}}\right )+\frac {x}{133 (3-2 x)^{39/2} \left (2 x^2+x+1\right )^{19}}\) |
Input:
Int[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]
Output:
$Aborted
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 = 8.08 (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 | \(\text {Expression too large to display}\) | \(820\) |
Input:
int(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x,method=_RETURNVERBOSE)
Output:
115/5908552821163231304184823545856*((x-3/2)^19*(x^2+1/2*x+1/2)^19*(1/2*(7 +2*14^(1/2))^(1/2)*(62541562556792464940960784209*14^(1/2)-234044028404883 307655877091262)*(ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(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)+112855552756005864755762319018)*( arctan((2*(3-2*x)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))+arcta n((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))))*(3-2*x)^ (1/2)+225711105512011729511524638036*(-7+2*14^(1/2))^(1/2)*(35128571782045 484630026117801687570244083874053171/4517315819499287681645418200730380459 26298694451200*x+183212802026248860514288501929804345458085916920873773/57 83192372047452224012626430522535438601263513600*x^17-339692530351150840696 302021012775910383197972648611749049/2202191462005902744802141372856060473 890706135449600*x^20+16088554099632166662170276395247605557702557286910897 24699/17617531696047221958417130982848483791125649083596800*x^19+330991985 1041151721938329104326989773026441469925012281/135519474584978630449362546 02191141377788960833536*x^21-410719388838590997785308221509211987369317097 087246119213/1101095731002951372401070686428030236945353067724800*x^22+625 318899982989425383877400685785463778432122219115569133/1101095731002951372 401070686428030236945353067724800*x^23-27406709657651230963424691464485550 30280367060674320773/3329926605855699714922592801697672087536350003200*...
Leaf count of result is larger than twice the leaf count of optimal. 1986 vs. \(2 (821) = 1642\).
Time = 0.32 (sec) , antiderivative size = 1986, normalized size of antiderivative = 1.88 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Too large to display} \] Input:
integrate(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x, algorithm="fricas")
Output:
-1/336864077912586356135291702496114974019074478550548480*(47704745152350* sqrt(1/2)*(549755813888*x^58 - 11269994184704*x^57 + 107064944754688*x^56 - 630638638006272*x^55 + 2618521301286912*x^54 - 8342252417974272*x^53 + 2 1849572376576000*x^52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188583312363618304*x^49 + 323261995581177856*x^48 - 517079841212727296*x^ 47 + 778117896260812800*x^46 - 1105641165387988992*x^45 + 1491287028233404 416*x^44 - 1919929663119949824*x^43 + 2363050939901804544*x^42 - 278627402 0645928960*x^41 + 3161145685194047488*x^40 - 3453753931369283584*x^39 + 36 34098467102523392*x^38 - 3697893960325791744*x^37 + 3640651752731836416*x^ 36 - 3461798212247617536*x^35 + 3194540251789393920*x^34 - 286154457949529 7024*x^33 + 2477632938217930752*x^32 - 2088430257127768064*x^31 + 17127610 05459316736*x^30 - 1355447485390974976*x^29 + 1048940886155151360*x^28 - 7 90511024135089152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^25 + 282845069599813728*x^24 - 186113897194906128*x^23 + 123982890381352520* x^22 - 78116367732251996*x^21 + 46488580159296898*x^20 - 29591055660829971 *x^19 + 16200795673453545*x^18 - 8941894120163277*x^17 + 5578893209169441* x^16 - 2296849711499532*x^15 + 1448289882400788*x^14 - 756896247319212*x^1 3 + 182213447974992*x^12 - 240797810407770*x^11 + 25549234281774*x^10 - 26 500281727302*x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354811164 *x^6 + 3755740313808*x^5 + 1820618017974*x^4 + 463742325333*x^3 + 13985...
Timed out. \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Timed out} \] Input:
integrate(1/(3-2*x)**(41/2)/(2*x**2+x+1)**20,x)
Output:
Timed out
\[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\int { \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{20} {\left (-2 \, x + 3\right )}^{\frac {41}{2}}} \,d x } \] Input:
integrate(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x, algorithm="maxima")
Output:
integrate(1/((2*x^2 + x + 1)^20*(-2*x + 3)^(41/2)), x)
Time = 0.93 (sec) , antiderivative size = 1410, normalized size of antiderivative = 1.33 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Too large to display} \] Input:
integrate(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x, algorithm="giac")
Output:
-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 = 0.68 (sec) , antiderivative size = 1017, normalized size of antiderivative = 0.96 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx=\text {Too large to display} \] Input:
int(1/((3 - 2*x)^(41/2)*(x + 2*x^2 + 1)^20),x)
Output:
((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 = 0.59 (sec) , antiderivative size = 21074, normalized size of antiderivative = 19.92 \[ \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx =\text {Too large to display} \] Input:
int(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x)
Output:
( - 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 -...