Integrand size = 20, antiderivative size = 648 \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx =\text {Too large to display} \]
4718120139975/351733660450816/(3-2*x)^(19/2)-815900548375/629418129227776/ (3-2*x)^(17/2)-3029508823715/1555033025150976/(3-2*x)^(15/2)-1351574302182 5/13476952884641792/(3-2*x)^(13/2)-5846828446875/14513641568075776/(3-2*x) ^(11/2)-37283626871975/261245548225363968/(3-2*x)^(9/2)-132355162272575/28 44673747342852096/(3-2*x)^(7/2)-11557581705725/812763927812243456/(3-2*x)^ (5/2)-46601678385075/11378694989371408384/(3-2*x)^(3/2)+1/63*x/(3-2*x)^(19 /2)/(2*x^2+x+1)^9+1/7056*(53+173*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^8+1/691488* (8477+21409*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^7+5/6453888*(21409+47471*x)/(3-2 *x)^(19/2)/(2*x^2+x+1)^6+41/90354432*(47471+92875*x)/(3-2*x)^(19/2)/(2*x^2 +x+1)^5+41/5059848192*(3436375+5677637*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^4+451 /10119696384*(811091+998691*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^3+451/2833514987 52*(28962039+14627273*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^2+11275/3966920982528* (14627273-35058731*x)/(3-2*x)^(19/2)/(2*x^2+x+1)-24229218097975/2275738997 8742816768/(3-2*x)^(1/2)+11275/1274413838809597739008*ln(3-2*x+14^(1/2)-(3 -2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(9756589235-2148932869*14^(1/2))*(-14+4* 14^(1/2))^(1/2)-11275/1274413838809597739008*ln(3-2*x+14^(1/2)+(3-2*x)^(1/ 2)*(7+2*14^(1/2))^(1/2))*(9756589235-2148932869*14^(1/2))*(-14+4*14^(1/2)) ^(1/2)+11275/637206919404798869504*arctan((-2*(3-2*x)^(1/2)+(7+2*14^(1/2)) ^(1/2))/(-7+2*14^(1/2))^(1/2))*(9756589235+2148932869*14^(1/2))*(14+4*14^( 1/2))^(1/2)-11275/637206919404798869504*arctan((2*(3-2*x)^(1/2)+(7+2*14...
Result contains complex when optimal does not.
Time = 16.41 (sec) , antiderivative size = 610, normalized size of antiderivative = 0.94 \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx =\text {Too large to display} \]
x/(63*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^9) + ((20776 + 67816*x)/(1568*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + ((46521776 + 117492592*x)/(1372*(3 - 2*x) ^(19/2)*(1 + x + 2*x^2)^7) + ((74020332960 + 164128134240*x)/(1176*(3 - 2* x)^(19/2)*(1 + x + 2*x^2)^6) + ((94209549053760 + 184316990760000*x)/(980* (3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + ((95476201213680000 + 15774739736793 4080*x)/(784*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^4) + ((72879297583985544960 + 89735798552133000960*x)/(588*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^3) + ((364 32734212165998389760 + 18400346379541577848320*x)/(392*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^2) + ((6440121232839552246912000 - 1543571914665913655846400 0*x)/(196*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (39479926882545221954112000/ (19*(3 - 2*x)^(19/2)) + (-908021664138480966930240000/(17*(3 - 2*x)^(17/2) ) + (-19105520493023248582746201600/(3 - 2*x)^(15/2) + (-26849557435537239 465884310720000/(13*(3 - 2*x)^(13/2)) + (-15099442385859879653927412000000 0/(3 - 2*x)^(11/2) + (-8237718113587514139784976619840000/(3 - 2*x)^(9/2) + (-338389312036560466460044072847040000/(3 - 2*x)^(7/2) + (-1013530552857 6510550836394515648960000/(3 - 2*x)^(5/2) + (-2043343757384956488128059567 91073600000/(3 - 2*x)^(3/2) + (-2230994866519889796828561036406228800000/S qrt[3 - 2*x] + ((Sqrt[(7 - I*Sqrt[7])/2]*(-3123392813127845715559985450968 7203200000 - (71750597240923349846054347713013891200000*I)*Sqrt[7])*ArcTan h[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[7 - I*Sqrt[7]]])/(-14 + (2*I)*Sqrt[7]) +...
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.
| \(\displaystyle \int \frac {1}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^{10}} \, dx\) |
| \(\Big \downarrow \) 1165 |
| \(\displaystyle \frac {\int \frac {28 (60-53 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^9}dx}{1764}+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \int \frac {60-53 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^9}dx+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {\int \frac {14 (6466-8477 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^8}dx}{1568}+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \int \frac {6466-8477 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^8}dx+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {\int \frac {630 (13031-21409 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^7}dx}{1372}+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \int \frac {13031-21409 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^7}dx+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {\int \frac {574 (22702-47471 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^6}dx}{1176}+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \int \frac {22702-47471 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^6}dx+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{980} \int \frac {14 (1120631-3436375 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^5}dx+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \int \frac {1120631-3436375 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^5}dx+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {1}{784} \int \frac {3234 (93800-811091 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^4}dx+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \int \frac {93800-811091 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^4}dx+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{588} \int -\frac {14 (28962039 x+7167383)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^3}dx+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}-\frac {1}{42} \int \frac {28962039 x+7167383}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^3}dx\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {1}{392} \int \frac {350 (14627273 x+24843002)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^2}dx\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \int \frac {14627273 x+24843002}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )^2}dx\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1235 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {1}{196} \int \frac {42 (158887401-245411117 x)}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )}dx-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \int \frac {158887401-245411117 x}{(3-2 x)^{21/2} \left (2 x^2+x+1\right )}dx-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1198 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{28} \int \frac {2 (880960721-418458549 x)}{(3-2 x)^{19/2} \left (2 x^2+x+1\right )}dx-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \int \frac {880960721-418458549 x}{(3-2 x)^{19/2} \left (2 x^2+x+1\right )}dx-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1198 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{28} \int \frac {14 (72363685 x+563185919)}{(3-2 x)^{17/2} \left (2 x^2+x+1\right )}dx+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \int \frac {72363685 x+563185919}{(3-2 x)^{17/2} \left (2 x^2+x+1\right )}dx+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1198 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{28} \int \frac {2 (1343462893 x+2180379991)}{(3-2 x)^{15/2} \left (2 x^2+x+1\right )}dx+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \int \frac {1343462893 x+2180379991}{(3-2 x)^{15/2} \left (2 x^2+x+1\right )}dx+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1198 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{28} \int \frac {14 (1198735523 x+1054008153)}{(3-2 x)^{13/2} \left (2 x^2+x+1\right )}dx+\frac {1198735523}{26 (3-2 x)^{13/2}}\right )+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{2} \int \frac {1198735523 x+1054008153}{(3-2 x)^{13/2} \left (2 x^2+x+1\right )}dx+\frac {1198735523}{26 (3-2 x)^{13/2}}\right )+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1198 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{28} \int \frac {2 (5704222875 x+3017297089)}{(3-2 x)^{11/2} \left (2 x^2+x+1\right )}dx+\frac {5704222875}{154 (3-2 x)^{11/2}}\right )+\frac {1198735523}{26 (3-2 x)^{13/2}}\right )+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \int \frac {5704222875 x+3017297089}{(3-2 x)^{11/2} \left (2 x^2+x+1\right )}dx+\frac {5704222875}{154 (3-2 x)^{11/2}}\right )+\frac {1198735523}{26 (3-2 x)^{13/2}}\right )+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 1198 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{28} \int \frac {14 (3306751829 x+909280783)}{(3-2 x)^{9/2} \left (2 x^2+x+1\right )}dx+\frac {3306751829}{18 (3-2 x)^{9/2}}\right )+\frac {5704222875}{154 (3-2 x)^{11/2}}\right )+\frac {1198735523}{26 (3-2 x)^{13/2}}\right )+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{63} \left (\frac {1}{112} \left (\frac {45}{98} \left (\frac {41}{84} \left (\frac {1}{70} \left (\frac {33}{8} \left (\frac {1}{42} \left (\frac {14627273 x+28962039}{28 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}-\frac {25}{28} \left (\frac {3}{14} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{2} \left (\frac {1}{14} \left (\frac {1}{2} \int \frac {3306751829 x+909280783}{(3-2 x)^{9/2} \left (2 x^2+x+1\right )}dx+\frac {3306751829}{18 (3-2 x)^{9/2}}\right )+\frac {5704222875}{154 (3-2 x)^{11/2}}\right )+\frac {1198735523}{26 (3-2 x)^{13/2}}\right )+\frac {1343462893}{210 (3-2 x)^{15/2}}\right )+\frac {72363685}{34 (3-2 x)^{17/2}}\right )-\frac {418458549}{266 (3-2 x)^{19/2}}\right )-\frac {14627273-35058731 x}{14 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}\right )\right )+\frac {998691 x+811091}{42 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}\right )+\frac {5677637 x+3436375}{56 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}\right )+\frac {92875 x+47471}{70 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}\right )+\frac {47471 x+21409}{84 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}\right )+\frac {21409 x+8477}{98 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}\right )+\frac {173 x+53}{112 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}\right )+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}\) |
3.1.48.3.1 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), x_Symbol] :> Simp[(e*f - d*g)*((d + e*x)^(m + 1)/((m + 1)*(c *d^2 - b*d*e + a*e^2))), x] + Simp[1/(c*d^2 - b*d*e + a*e^2) Int[(d + e*x )^(m + 1)*(Simp[c*d*f - f*b*e + a*e*g - c*(e*f - d*g)*x, x]/(a + b*x + c*x^ 2)), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && FractionQ[m] && LtQ[m, -1 ]
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 = 3.78 (sec) , antiderivative size = 352, normalized size of antiderivative = 0.54
| method | result | size |
| pseudoelliptic | \(\frac {\frac {11275 \left (x -\frac {3}{2}\right )^{9} \left (\sqrt {7+2 \sqrt {14}}\, \left (18352320711 \sqrt {14}-69111417106\right ) \left (\ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )-\ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )\right ) \sqrt {-7+2 \sqrt {14}}+2 \left (9756589235 \sqrt {14}+30085060166\right ) \left (\arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )+\arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )\right )\right ) \left (x^{2}+\frac {1}{2} x +\frac {1}{2}\right )^{9} \sqrt {3-2 x}}{4861502986181632}+\frac {24229218097975 \sqrt {-7+2 \sqrt {14}}\, \left (-\frac {9651082208977600419673}{266701338819682697216} x^{6}+\frac {22855828001615591421921}{26670133881968269721600} x +\frac {1836651529138911112693463}{120015602468857213747200} x^{5}-\frac {134998393682507368342493}{40005200822952404582400} x^{4}+\frac {996043194154916251217}{175461407118212300800} x^{3}+\frac {847930065890931816713}{1818418219225109299200} x^{2}-\frac {465471892878599}{515743888560} x^{20}-\frac {38014370445393391293}{31762259291597120} x^{18}-\frac {299208867441559564523}{254098074332776960} x^{16}-\frac {20254438577741909746663}{81311383786488627200} x^{10}-\frac {1129001874807303405453}{2032784594662215680} x^{12}-\frac {10928359993529274103333}{11434413344974963200} x^{14}+\frac {193096157908388472533}{152458844599666176} x^{17}+\frac {271924352600651293}{257184285761920} x^{19}+\frac {3324327068969447}{4916758404272} x^{21}-\frac {63047885074067}{141829569354} x^{22}+\frac {21065437682057}{77361583284} x^{23}-\frac {1216492052933}{8595731476} x^{24}+\frac {112774755927521146576673}{650491070291909017600} x^{9}+\frac {12198896895542543585363}{28698135454054809600} x^{11}+\frac {21932125545555763373243}{30491768919933235200} x^{13}+\frac {297725881275469254209863}{6667533470492067430400} x^{7}-\frac {221517107732330809366211}{1951473210875727052800} x^{8}+\frac {442803288917}{8595731476} x^{25}+\frac {144203782903185201071}{133735828596198400} x^{15}-\frac {23473582374}{2148932869} x^{26}+x^{27}-\frac {542713011130261972193}{26670133881968269721600}\right )}{86812553324672}}{\left (2 x^{2}+x +1\right )^{9} \sqrt {-7+2 \sqrt {14}}\, \left (3-2 x \right )^{\frac {19}{2}}}\) | \(352\) |
| derivativedivides | \(\frac {\frac {9364999706478908741137 \left (3-2 x \right )^{\frac {5}{2}}}{2048}-\frac {23851905772903279054347 \left (3-2 x \right )^{\frac {7}{2}}}{4096}+\frac {192983613795383541041317 \left (3-2 x \right )^{\frac {9}{2}}}{36864}-\frac {57758421475348449750643 \left (3-2 x \right )^{\frac {11}{2}}}{16384}+\frac {60333035869584695411551 \left (3-2 x \right )^{\frac {13}{2}}}{32768}-\frac {149770885083493978040723 \left (3-2 x \right )^{\frac {15}{2}}}{196608}+\frac {66256899944582155696811 \left (3-2 x \right )^{\frac {17}{2}}}{262144}+\frac {544765170330150812273 \sqrt {3-2 x}}{1024}-\frac {3476987783905860258979 \left (3-2 x \right )^{\frac {3}{2}}}{1536}+\frac {45406001689183688581 \left (3-2 x \right )^{\frac {25}{2}}}{131072}-\frac {43462358811134257841 \left (3-2 x \right )^{\frac {27}{2}}}{1179648}+\frac {192384852501874197 \left (3-2 x \right )^{\frac {29}{2}}}{65536}-\frac {1352841099712333 \left (3-2 x \right )^{\frac {31}{2}}}{8192}+\frac {4606702222670185 \left (3-2 x \right )^{\frac {33}{2}}}{786432}-\frac {25865320405815 \left (3-2 x \right )^{\frac {35}{2}}}{262144}-\frac {17729978841543630405471 \left (3-2 x \right )^{\frac {19}{2}}}{262144}+\frac {2869878271121283060373 \left (3-2 x \right )^{\frac {21}{2}}}{196608}-\frac {165574989211387894481 \left (3-2 x \right )^{\frac {23}{2}}}{65536}}{86812553324672 \left (\left (3-2 x \right )^{2}-7+14 x \right )^{9}}+\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}+\frac {11275 \left (-9756589235 \sqrt {14}-\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}-\frac {11275 \left (9756589235 \sqrt {14}+\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}+\frac {1}{5367029731 \left (3-2 x \right )^{\frac {19}{2}}}+\frac {5}{4802079233 \left (3-2 x \right )^{\frac {17}{2}}}+\frac {73}{23727920916 \left (3-2 x \right )^{\frac {15}{2}}}+\frac {165}{25705247659 \left (3-2 x \right )^{\frac {13}{2}}}+\frac {2365}{221460595216 \left (3-2 x \right )^{\frac {11}{2}}}+\frac {30349}{1993145356944 \left (3-2 x \right )^{\frac {9}{2}}}+\frac {854095}{43406276662336 \left (3-2 x \right )^{\frac {7}{2}}}+\frac {75933}{3100448333024 \left (3-2 x \right )^{\frac {5}{2}}}+\frac {8519225}{260437659974016 \left (3-2 x \right )^{\frac {3}{2}}}+\frac {891605}{12401793332096 \sqrt {3-2 x}}\) | \(550\) |
| default | \(\frac {\frac {9364999706478908741137 \left (3-2 x \right )^{\frac {5}{2}}}{2048}-\frac {23851905772903279054347 \left (3-2 x \right )^{\frac {7}{2}}}{4096}+\frac {192983613795383541041317 \left (3-2 x \right )^{\frac {9}{2}}}{36864}-\frac {57758421475348449750643 \left (3-2 x \right )^{\frac {11}{2}}}{16384}+\frac {60333035869584695411551 \left (3-2 x \right )^{\frac {13}{2}}}{32768}-\frac {149770885083493978040723 \left (3-2 x \right )^{\frac {15}{2}}}{196608}+\frac {66256899944582155696811 \left (3-2 x \right )^{\frac {17}{2}}}{262144}+\frac {544765170330150812273 \sqrt {3-2 x}}{1024}-\frac {3476987783905860258979 \left (3-2 x \right )^{\frac {3}{2}}}{1536}+\frac {45406001689183688581 \left (3-2 x \right )^{\frac {25}{2}}}{131072}-\frac {43462358811134257841 \left (3-2 x \right )^{\frac {27}{2}}}{1179648}+\frac {192384852501874197 \left (3-2 x \right )^{\frac {29}{2}}}{65536}-\frac {1352841099712333 \left (3-2 x \right )^{\frac {31}{2}}}{8192}+\frac {4606702222670185 \left (3-2 x \right )^{\frac {33}{2}}}{786432}-\frac {25865320405815 \left (3-2 x \right )^{\frac {35}{2}}}{262144}-\frac {17729978841543630405471 \left (3-2 x \right )^{\frac {19}{2}}}{262144}+\frac {2869878271121283060373 \left (3-2 x \right )^{\frac {21}{2}}}{196608}-\frac {165574989211387894481 \left (3-2 x \right )^{\frac {23}{2}}}{65536}}{86812553324672 \left (\left (3-2 x \right )^{2}-7+14 x \right )^{9}}+\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}+\frac {11275 \left (-9756589235 \sqrt {14}-\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}-\frac {11275 \left (9756589235 \sqrt {14}+\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}+\frac {1}{5367029731 \left (3-2 x \right )^{\frac {19}{2}}}+\frac {5}{4802079233 \left (3-2 x \right )^{\frac {17}{2}}}+\frac {73}{23727920916 \left (3-2 x \right )^{\frac {15}{2}}}+\frac {165}{25705247659 \left (3-2 x \right )^{\frac {13}{2}}}+\frac {2365}{221460595216 \left (3-2 x \right )^{\frac {11}{2}}}+\frac {30349}{1993145356944 \left (3-2 x \right )^{\frac {9}{2}}}+\frac {854095}{43406276662336 \left (3-2 x \right )^{\frac {7}{2}}}+\frac {75933}{3100448333024 \left (3-2 x \right )^{\frac {5}{2}}}+\frac {8519225}{260437659974016 \left (3-2 x \right )^{\frac {3}{2}}}+\frac {891605}{12401793332096 \sqrt {3-2 x}}\) | \(550\) |
| trager | \(\text {Expression too large to display}\) | \(584\) |
| risch | \(-\frac {240031204937714427494400 x^{27}-2621948941596237063782400 x^{26}+12365045055896811105484800 x^{25}-33969890064381284111155200 x^{24}+65360120291258796757811200 x^{23}-106701725825102321939251200 x^{22}+162290307223249502039654400 x^{21}-216634228326470609547509760 x^{20}+253788172995391086570485760 x^{19}-287279159180291305208156160 x^{18}+304010591010966811155955200 x^{17}-282644664539994827031006720 x^{16}+258819256815163249845447936 x^{15}-229408132984166521977166336 x^{14}+172649692294614969274168896 x^{13}-133312541377246386115890240 x^{12}+102031573634317834547976132 x^{11}-59791102681494117572149176 x^{10}+41613884937255303086792337 x^{9}-27246604251076689552043953 x^{8}+10718131725916893151555068 x^{7}-8685973988079840377705700 x^{6}+3673303058277822225386926 x^{5}-809990362095044210054958 x^{4}+1362587089603925431664856 x^{3}+111926768697602999806116 x^{2}+205702452014540322797289 x -4884417100172357749737}{860024524686669788479488 \left (2 x^{2}+x +1\right )^{9} \sqrt {3-2 x}\, \left (2 x -3\right )^{9}}+\frac {206922416016525 \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}\, \sqrt {14}}{1274413838809597739008}-\frac {389615613935075 \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{637206919404798869504}-\frac {206922416016525 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right ) \sqrt {14}}{637206919404798869504 \sqrt {-7+2 \sqrt {14}}}+\frac {389615613935075 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {110005543624625 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \sqrt {14}}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {206922416016525 \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}\, \sqrt {14}}{1274413838809597739008}+\frac {389615613935075 \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{637206919404798869504}-\frac {206922416016525 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right ) \sqrt {14}}{637206919404798869504 \sqrt {-7+2 \sqrt {14}}}+\frac {389615613935075 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {110005543624625 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \sqrt {14}}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}\) | \(611\) |
11275/4861502986181632*((x-3/2)^9*((7+2*14^(1/2))^(1/2)*(18352320711*14^(1 /2)-69111417106)*(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) +2*(9756589235*14^(1/2)+30085060166)*(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)^9*(3-2*x)^(1/2)+120340240664 *(-7+2*14^(1/2))^(1/2)*(-9651082208977600419673/266701338819682697216*x^6+ 22855828001615591421921/26670133881968269721600*x+183665152913891111269346 3/120015602468857213747200*x^5-134998393682507368342493/400052008229524045 82400*x^4+996043194154916251217/175461407118212300800*x^3+8479300658909318 16713/1818418219225109299200*x^2-465471892878599/515743888560*x^20-3801437 0445393391293/31762259291597120*x^18-299208867441559564523/254098074332776 960*x^16-20254438577741909746663/81311383786488627200*x^10-112900187480730 3405453/2032784594662215680*x^12-10928359993529274103333/11434413344974963 200*x^14+193096157908388472533/152458844599666176*x^17+271924352600651293/ 257184285761920*x^19+3324327068969447/4916758404272*x^21-63047885074067/14 1829569354*x^22+21065437682057/77361583284*x^23-1216492052933/8595731476*x ^24+112774755927521146576673/650491070291909017600*x^9+1219889689554254358 5363/28698135454054809600*x^11+21932125545555763373243/3049176891993323520 0*x^13+297725881275469254209863/6667533470492067430400*x^7-221517107732...
Result contains complex when optimal does not.
Time = 0.28 (sec) , antiderivative size = 1005, normalized size of antiderivative = 1.55 \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Too large to display} \]
1/24080686691226754077425664*(37791*(524288*x^28 - 5505024*x^27 + 24772608 *x^26 - 64684032*x^25 + 119734272*x^24 - 194052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20 - 515594240*x^19 + 540503040*x^18 - 49658 1120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 248434368*x ^13 + 186495624*x^12 - 105219828*x^11 + 83621482*x^10 - 49793667*x^9 + 191 05065*x^8 - 20036484*x^7 + 5497632*x^6 - 2235114*x^5 + 3276126*x^4 + 73483 2*x^3 + 826686*x^2 + 137781*x + 59049)*sqrt(3882449493199924109118981875*I *sqrt(7) - 291499433615861543069724120625)*log(sqrt(3882449493199924109118 981875*I*sqrt(7) - 291499433615861543069724120625)*(18352320711*I*sqrt(7) - 9756589235) + 13827912344964974143078400*sqrt(-2*x + 3)) - 37791*(524288 *x^28 - 5505024*x^27 + 24772608*x^26 - 64684032*x^25 + 119734272*x^24 - 19 4052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20 - 51559424 0*x^19 + 540503040*x^18 - 496581120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 248434368*x^13 + 186495624*x^12 - 105219828*x^11 + 836 21482*x^10 - 49793667*x^9 + 19105065*x^8 - 20036484*x^7 + 5497632*x^6 - 22 35114*x^5 + 3276126*x^4 + 734832*x^3 + 826686*x^2 + 137781*x + 59049)*sqrt (3882449493199924109118981875*I*sqrt(7) - 291499433615861543069724120625)* log(sqrt(3882449493199924109118981875*I*sqrt(7) - 291499433615861543069724 120625)*(-18352320711*I*sqrt(7) + 9756589235) + 13827912344964974143078400 *sqrt(-2*x + 3)) - 37791*(524288*x^28 - 5505024*x^27 + 24772608*x^26 - ...
Timed out. \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Timed out} \]
\[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\int { \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{10} {\left (-2 \, x + 3\right )}^{\frac {21}{2}}} \,d x } \]
Leaf count of result is larger than twice the leaf count of optimal. 1000 vs. \(2 (491) = 982\).
Time = 0.76 (sec) , antiderivative size = 1000, normalized size of antiderivative = 1.54 \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Too large to display} \]
-11275/142734349946674946768896*sqrt(7)*(6446798607*14^(3/4)*sqrt(7)*(sqrt (14) + 4)*sqrt(-2*sqrt(14) + 8) + 2148932869*14^(3/4)*sqrt(7)*(sqrt(14) - 4)*sqrt(-2*sqrt(14) + 8) - 15042530083*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt (14) + 4) - 45127590249*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 780 52713880*14^(1/4)*sqrt(7)*sqrt(-2*sqrt(14) + 8) - 546368997160*14^(1/4)*sq rt(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)) - 11275/1427343499466 74946768896*sqrt(7)*(6446798607*14^(3/4)*sqrt(7)*(sqrt(14) + 4)*sqrt(-2*sq rt(14) + 8) + 2148932869*14^(3/4)*sqrt(7)*(sqrt(14) - 4)*sqrt(-2*sqrt(14) + 8) - 15042530083*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) + 4) - 45127590 249*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 78052713880*14^(1/4)*sq rt(7)*sqrt(-2*sqrt(14) + 8) - 546368997160*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)) - 11275/285468699893349893537792*sqrt(7) *(2148932869*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(14) + 4) + 644679 8607*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 45127590249*14 ^(3/4)*(sqrt(14) + 4)*sqrt(-2*sqrt(14) + 8) + 15042530083*14^(3/4)*(sqrt(1 4) - 4)*sqrt(-2*sqrt(14) + 8) + 78052713880*14^(1/4)*sqrt(7)*sqrt(2*sqrt(1 4) + 8) + 546368997160*14^(1/4)*sqrt(-2*sqrt(14) + 8))*log(14^(1/4)*sqrt(1 /2)*sqrt(-2*x + 3)*sqrt(sqrt(14) + 4) - 2*x + sqrt(14) + 3) + 11275/285...
Time = 0.61 (sec) , antiderivative size = 567, normalized size of antiderivative = 0.88 \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx=\text {Too large to display} \]
((184192*(2*x - 3)^2)/47481 - (18944*x)/2261 - (15552*(2*x - 3)^3)/4199 + (5666272*(2*x - 3)^4)/1440257 - (63490768*(2*x - 3)^5)/12962313 + (5334956 72*(2*x - 3)^6)/70572593 - (1111521492*(2*x - 3)^7)/70572593 + (7800732315 8*(2*x - 3)^8)/1482024453 - (250239440467*(2*x - 3)^9)/494008151 + (111869 3654785651073*(2*x - 3)^10)/453254454575104 + (1624300450152249301*(2*x - 3)^11)/97125954551808 + (35048653520674948897*(2*x - 3)^12)/90650890915020 8 + (95527511967437577915*(2*x - 3)^13)/1813017818300416 + (56406629997314 15610547*(2*x - 3)^14)/114220122552926208 + (1737142288764447500149*(2*x - 3)^15)/50764498912411648 + (12971210667229097601055*(2*x - 3)^16)/7107029 84773763072 + (32723441206946795665235*(2*x - 3)^17)/4264217908642578432 + (102645797034777710681325*(2*x - 3)^18)/39799367147330732032 + (146093178 7430200665315*(2*x - 3)^19)/2094703534070038528 + (687618468821894139745*( 2*x - 3)^20)/4528256169239642112 + (39968995676603847725*(2*x - 3)^21)/150 9418723079880704 + (5940132943613849875*(2*x - 3)^22)/1625527855624486912 + (5717978503620010375*(2*x - 3)^23)/14629750700620382208 + (1780569958183 25525*(2*x - 3)^24)/5689347494685704192 + (179665281323275*(2*x - 3)^25)/1 01595490976530432 + (1433237383402275*(2*x - 3)^26)/22757389978742816768 + (24229218097975*(2*x - 3)^27)/22757389978742816768 + 37120/2261)/(2066104 6784*(3 - 2*x)^(19/2) - 92974710528*(3 - 2*x)^(21/2) + 199231522560*(3 - 2 *x)^(23/2) - 270069397248*(3 - 2*x)^(25/2) + 259475340096*(3 - 2*x)^(27...
Time = 0.06 (sec) , antiderivative size = 10154, normalized size of antiderivative = 15.67 \[ \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx =\text {Too large to display} \]
int(1/(sqrt( - 2*x + 3)*(1048576*x**30 - 10485760*x**29 + 44564480*x**28 - 110100480*x**27 + 199557120*x**26 - 333053952*x**25 + 516096000*x**24 - 6 72399360*x**23 + 806952960*x**22 - 968704000*x**21 + 1014673408*x**20 - 96 8253440*x**19 + 979345920*x**18 - 852526080*x**17 + 662952960*x**16 - 6051 62496*x**15 + 428091600*x**14 - 272378400*x**13 + 248518760*x**12 - 121185 680*x**11 + 72037945*x**10 - 70761570*x**9 + 10063845*x**8 - 19009080*x**7 + 9814770*x**6 + 2510676*x**5 + 5664330*x**4 + 1837080*x**3 + 1082565*x** 2 + 196830*x + 59049)),x)
( - 4099829936255400031027200*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(1 4)*atan((2*sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))* x**27 + 36898469426298600279244800*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*s qrt(14)*atan((2*sqrt( - 2*x + 3) - sqrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**26 - 138369260348619751047168000*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**25 + 298262627862580352257228800*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**24 - 488904719898456453699993600*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**23 + 784092475308845255933952000*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**22 - 1132321780519538296069324800*sqrt(2*s qrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqrt( - 2*x + 3) - sqrt(2*s qrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**21 + 1326038745007605947535360000*s qrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqrt( - 2*x + 3) - s qrt(2*sqrt(14) + 7))/sqrt(2*sqrt(14) - 7))*x**20 - 15240797488815679662216 19200*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**19 + 1745726804810375 530399027200*sqrt(2*sqrt(14) - 7)*sqrt( - 2*x + 3)*sqrt(14)*atan((2*sqr...