Optimal. Leaf size=1058 \[ \text{result too large to display} \]
[Out]
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Rubi [A] time = 2.48972, antiderivative size = 1058, normalized size of antiderivative = 1., number of steps used = 49, number of rules used = 9, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.45, Rules used = {740, 822, 828, 826, 1169, 634, 618, 204, 628} \[ \text{result too large to display} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 740
Rule 822
Rule 828
Rule 826
Rule 1169
Rule 634
Rule 618
Rule 204
Rule 628
Rubi steps
\begin{align*} \int \frac{1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{\int \frac{3640-3164 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{19}} \, dx}{3724}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{\int \frac{13067712-15937544 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{18}} \, dx}{13138272}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{\int \frac{44452059120-61847262960 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{17}} \, dx}{43776722304}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{\int \frac{140862854522880-213162453016800 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{16}} \, dx}{137283801145344}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{\int \frac{411257135544050880-672058124080956480 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{15}} \, dx}{403614375367311360}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{\int \frac{1093943980547175340800-1945933258510113828480 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{14}} \, dx}{1107517846007902371840}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{\int \frac{2613748771210815258935040-5150741239627162779559680 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{13}} \, dx}{2821955471628135243448320}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{\int \frac{5495319948977447333781657600-12350104150638064023941414400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{12}} \, dx}{6637239269269374092590448640}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{\int \frac{9830189811300874808578976332800-26468403751104415156166363366400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{11}} \, dx}{14309887864544770543625007267840}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{\int \frac{13994744255814899394658210554777600-49726828476855245625643612682496000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{10}} \, dx}{28047380214507750265505014244966400}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{\int \frac{13068536369629429401640635068702208000-79426075962231715392089154535476326400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^9} \, dx}{49475578698391671468350845128120729600}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{\int \frac{-621663169952319046771764500985957580800-101974001645639894672727830234002797158400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^8} \, dx}{77577707399078140862374125160893304012800}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{\int \frac{-30781058646716715966024014766066735728640000-91664914528219083487057714121148102617088000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^7} \, dx}{106436614551535209263177299720745613105561600}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{\int \frac{-64412327323696265886549616069250637895016448000-25707788838506946427978270639018495010476032000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^6} \, dx}{125169458712605406093496504471596841012140441600}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}+\frac{\int \frac{-67430989462987479984124242299597562667894677504000+82287258915490697105406527276587259062086377472000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^5} \, dx}{122666069538353297971626574382164904191897632768000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}+\frac{\int \frac{-12641043879585143204616228153551645061449995714560000+161124734478367517548652018811830529223223793500160000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^4} \, dx}{96170198518068985609755234315617284886447744090112000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}+\frac{\int \frac{68068541213694880932350653701675675390158594756935680000+127875080054950933515108749931588600071440916461486080000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^3} \, dx}{56548076728624563538536077777582963513231273524985856000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{\int \frac{85414151041513293818778811305636762456175069081725173760000-5205061494636461860243311207210532946592052023002726400000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^2} \, dx}{22166846077620828907106142488812521697186659221794455552000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{6724421340577980732010378947094366406252347332593730846720000-101043150693578590411737736011809849211032817167024064430080000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )} \, dx}{4344701831213682465792803927807254252648585207471713288192000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{255881672111781026679558503600374629672084412994797975633920000-579361218799159619542384900282481629641187513671769463193600000 x}{(3-2 x)^{39/2} \left (1+x+2 x^2\right )} \, dx}{121651651273983109042198509978603119074160385809207972069376000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{3205775814492567452521237829367960296659050331301922731458560000-2452640624347833610536075387293391259158787430051424876625920000 x}{(3-2 x)^{37/2} \left (1+x+2 x^2\right )} \, dx}{3406246235671527053181558279400887334076490802657823217942528000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{30551487764636206841242053409530464891589977510518231604920320000-1892740488116731853131501006288506368316523255100858333921280000 x}{(3-2 x)^{35/2} \left (1+x+2 x^2\right )} \, dx}{95374894598802757489083631823224845354141742474419050102390784000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{248197383093323118436199429288820731869352866594347569507205120000+110849508129844436246179207600390821356460770511467776416153600000 x}{(3-2 x)^{33/2} \left (1+x+2 x^2\right )} \, dx}{2670497048766477209694341691050295669915968789283733402866941952000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{1763880048486896074997237019109784212241901391731845003225333760000+1657886581152359091221872962757627855616176089446196936525742080000 x}{(3-2 x)^{31/2} \left (1+x+2 x^2\right )} \, dx}{74773917365461361871441567349408278757647126099944535280274374656000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{10795267225590450417534150227363017986702858954962366152751185920000+17002839680861738847320185852984903982664662103604561632055787520000 x}{(3-2 x)^{29/2} \left (1+x+2 x^2\right )} \, dx}{2093669686232918132400363885783431805214119530798446987847682490368000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{52356458443000125645632830112934335928293547432489805957897912320000+145198106987532234754057716027361495842799408441476834403339468800000 x}{(3-2 x)^{27/2} \left (1+x+2 x^2\right )} \, dx}{58622751214521707707210188801936090545995346862356515659735109730304000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{128455453568936535656947208848751695740749562576964778856504360960000+1080614475697193911106877616615906318769970640378820230251628462080000 x}{(3-2 x)^{25/2} \left (1+x+2 x^2\right )} \, dx}{1641437034006607815801885286454210535287869712145982438472583072448512000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{11155168222970774232376891145}{1685166332532616560247354224017408 (3-2 x)^{23/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-1133585322842895536958177562441799071613944780141922229651222036480000+6997508668458909609269054535090444695582822092580780496935788216320000 x}{(3-2 x)^{23/2} \left (1+x+2 x^2\right )} \, dx}{45960236952185018842452788020717894988060351940087508277232326028558336000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{11155168222970774232376891145}{1685166332532616560247354224017408 (3-2 x)^{23/2}}+\frac{14011818498091020272474956375}{10110997995195699361484125344104448 (3-2 x)^{21/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-23063699919660983514203529569715281964077202426296938831081352724480000+37450710719381875507781616960775471887041153434916994063009841152000000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )} \, dx}{1286886634661180527588678064580101059665689854322450231762505128799633408000}\\ \end{align*}
Mathematica [C] time = 6.17009, size = 1100, normalized size = 1.04 \[ \text{result too large to display} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.08, size = 989, normalized size = 0.9 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{20}{\left (-2 \, x + 3\right )}^{\frac{41}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{20}{\left (-2 \, x + 3\right )}^{\frac{41}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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