Optimal. Leaf size=78 \[ \frac {4 \left ((x-1)^3\right )^{3/4} \left (1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^9-8805988591725 x^8+3131067556500 x^7+9260757242646 x^6+4070651298324 x^5-2008108342110 x^4-2834315032620 x^3-1158885626660 x^2+32327777464 x+1308401597431\right )}{1179090487575 (x-1)^2} \]
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Rubi [B] time = 1.00, antiderivative size = 248, normalized size of antiderivative = 3.18, number of steps used = 53, number of rules used = 6, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {6742, 2067, 15, 30, 2081, 43} \begin {gather*} -\frac {324 (1-x)^{13}}{49 \sqrt [4]{(x-1)^3}}+\frac {96 (1-x)^{12}}{\sqrt [4]{(x-1)^3}}-\frac {25488 (1-x)^{11}}{41 \sqrt [4]{(x-1)^3}}+\frac {87312 (1-x)^{10}}{37 \sqrt [4]{(x-1)^3}}-\frac {191416 (1-x)^9}{33 \sqrt [4]{(x-1)^3}}+\frac {278928 (1-x)^8}{29 \sqrt [4]{(x-1)^3}}-\frac {271528 (1-x)^7}{25 \sqrt [4]{(x-1)^3}}+\frac {57648 (1-x)^6}{7 \sqrt [4]{(x-1)^3}}-\frac {68820 (1-x)^5}{17 \sqrt [4]{(x-1)^3}}+\frac {16032 (1-x)^4}{13 \sqrt [4]{(x-1)^3}}+\frac {144 (1-x)^2}{5 \sqrt [4]{(x-1)^3}}-\frac {4 (1-x)}{\sqrt [4]{(x-1)^3}}+\frac {2104}{9} \left ((x-1)^3\right )^{3/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rule 43
Rule 2067
Rule 2081
Rule 6742
Rubi steps
\begin {align*} \int \frac {\left (-1-2 x+x^2+3 x^3\right )^4}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx &=\int \left (\frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {8 x}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {20 x^2}{\sqrt [4]{-1+3 x-3 x^2+x^3}}-\frac {4 x^3}{\sqrt [4]{-1+3 x-3 x^2+x^3}}-\frac {98 x^4}{\sqrt [4]{-1+3 x-3 x^2+x^3}}-\frac {116 x^5}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {122 x^6}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {316 x^7}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {37 x^8}{\sqrt [4]{-1+3 x-3 x^2+x^3}}-\frac {312 x^9}{\sqrt [4]{-1+3 x-3 x^2+x^3}}-\frac {162 x^{10}}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {108 x^{11}}{\sqrt [4]{-1+3 x-3 x^2+x^3}}+\frac {81 x^{12}}{\sqrt [4]{-1+3 x-3 x^2+x^3}}\right ) \, dx\\ &=-\left (4 \int \frac {x^3}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx\right )+8 \int \frac {x}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+20 \int \frac {x^2}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+37 \int \frac {x^8}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+81 \int \frac {x^{12}}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx-98 \int \frac {x^4}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+108 \int \frac {x^{11}}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx-116 \int \frac {x^5}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+122 \int \frac {x^6}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx-162 \int \frac {x^{10}}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx-312 \int \frac {x^9}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+316 \int \frac {x^7}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx+\int \frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3}} \, dx\\ &=-\left (4 \operatorname {Subst}\left (\int \frac {(1+x)^3}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )\right )+8 \operatorname {Subst}\left (\int \frac {1+x}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+20 \operatorname {Subst}\left (\int \frac {(1+x)^2}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+37 \operatorname {Subst}\left (\int \frac {(1+x)^8}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+81 \operatorname {Subst}\left (\int \frac {(1+x)^{12}}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )-98 \operatorname {Subst}\left (\int \frac {(1+x)^4}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+108 \operatorname {Subst}\left (\int \frac {(1+x)^{11}}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )-116 \operatorname {Subst}\left (\int \frac {(1+x)^5}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+122 \operatorname {Subst}\left (\int \frac {(1+x)^6}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )-162 \operatorname {Subst}\left (\int \frac {(1+x)^{10}}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )-312 \operatorname {Subst}\left (\int \frac {(1+x)^9}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+316 \operatorname {Subst}\left (\int \frac {(1+x)^7}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )+\operatorname {Subst}\left (\int \frac {1}{\sqrt [4]{x^3}} \, dx,x,-1+x\right )\\ &=\frac {(-1+x)^{3/4} \operatorname {Subst}\left (\int \frac {1}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (4 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^3}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (8 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {1+x}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (20 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^2}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (37 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^8}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (81 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^{12}}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (98 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^4}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (108 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^{11}}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (116 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^5}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (122 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^6}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (162 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^{10}}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (312 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^9}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (316 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \frac {(1+x)^7}{x^{3/4}} \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}\\ &=-\frac {4 (1-x)}{\sqrt [4]{(-1+x)^3}}-\frac {\left (4 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+3 \sqrt [4]{x}+3 x^{5/4}+x^{9/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (8 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+\sqrt [4]{x}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (20 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+2 \sqrt [4]{x}+x^{5/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (37 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+8 \sqrt [4]{x}+28 x^{5/4}+56 x^{9/4}+70 x^{13/4}+56 x^{17/4}+28 x^{21/4}+8 x^{25/4}+x^{29/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (81 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+12 \sqrt [4]{x}+66 x^{5/4}+220 x^{9/4}+495 x^{13/4}+792 x^{17/4}+924 x^{21/4}+792 x^{25/4}+495 x^{29/4}+220 x^{33/4}+66 x^{37/4}+12 x^{41/4}+x^{45/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (98 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+4 \sqrt [4]{x}+6 x^{5/4}+4 x^{9/4}+x^{13/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (108 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+11 \sqrt [4]{x}+55 x^{5/4}+165 x^{9/4}+330 x^{13/4}+462 x^{17/4}+462 x^{21/4}+330 x^{25/4}+165 x^{29/4}+55 x^{33/4}+11 x^{37/4}+x^{41/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (116 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+5 \sqrt [4]{x}+10 x^{5/4}+10 x^{9/4}+5 x^{13/4}+x^{17/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (122 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+6 \sqrt [4]{x}+15 x^{5/4}+20 x^{9/4}+15 x^{13/4}+6 x^{17/4}+x^{21/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (162 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+10 \sqrt [4]{x}+45 x^{5/4}+120 x^{9/4}+210 x^{13/4}+252 x^{17/4}+210 x^{21/4}+120 x^{25/4}+45 x^{29/4}+10 x^{33/4}+x^{37/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}-\frac {\left (312 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+9 \sqrt [4]{x}+36 x^{5/4}+84 x^{9/4}+126 x^{13/4}+126 x^{17/4}+84 x^{21/4}+36 x^{25/4}+9 x^{29/4}+x^{33/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}+\frac {\left (316 (-1+x)^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{x^{3/4}}+7 \sqrt [4]{x}+21 x^{5/4}+35 x^{9/4}+35 x^{13/4}+21 x^{17/4}+7 x^{21/4}+x^{25/4}\right ) \, dx,x,-1+x\right )}{\sqrt [4]{(-1+x)^3}}\\ &=-\frac {4 (1-x)}{\sqrt [4]{(-1+x)^3}}+\frac {144 (1-x)^2}{5 \sqrt [4]{(-1+x)^3}}+\frac {16032 (1-x)^4}{13 \sqrt [4]{(-1+x)^3}}-\frac {68820 (1-x)^5}{17 \sqrt [4]{(-1+x)^3}}+\frac {57648 (1-x)^6}{7 \sqrt [4]{(-1+x)^3}}-\frac {271528 (1-x)^7}{25 \sqrt [4]{(-1+x)^3}}+\frac {278928 (1-x)^8}{29 \sqrt [4]{(-1+x)^3}}-\frac {191416 (1-x)^9}{33 \sqrt [4]{(-1+x)^3}}+\frac {87312 (1-x)^{10}}{37 \sqrt [4]{(-1+x)^3}}-\frac {25488 (1-x)^{11}}{41 \sqrt [4]{(-1+x)^3}}+\frac {96 (1-x)^{12}}{\sqrt [4]{(-1+x)^3}}-\frac {324 (1-x)^{13}}{49 \sqrt [4]{(-1+x)^3}}+\frac {2104}{9} \left ((-1+x)^3\right )^{3/4}\\ \end {align*}
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Mathematica [A] time = 0.10, size = 156, normalized size = 2.00 \begin {gather*} \frac {4 \left (\frac {81}{49} (x-1)^{49/4}+24 (x-1)^{45/4}+\frac {6372}{41} (x-1)^{41/4}+\frac {21828}{37} (x-1)^{37/4}+\frac {47854}{33} (x-1)^{33/4}+\frac {69732}{29} (x-1)^{29/4}+\frac {67882}{25} (x-1)^{25/4}+\frac {14412}{7} (x-1)^{21/4}+\frac {17205}{17} (x-1)^{17/4}+\frac {4008}{13} (x-1)^{13/4}+\frac {526}{9} (x-1)^{9/4}+\frac {36}{5} (x-1)^{5/4}+\sqrt [4]{x-1}\right ) (x-1)^{3/4}}{\sqrt [4]{(x-1)^3}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 5.08, size = 138, normalized size = 1.77 \begin {gather*} \frac {4 \left (1179090487575 \sqrt [4]{-1+x}+8489451510540 (-1+x)^{5/4}+68911288496050 (-1+x)^{9/4}+363522667246200 (-1+x)^{13/4}+1193308931689875 (-1+x)^{17/4}+2427578872418700 (-1+x)^{21/4}+3201560819102646 (-1+x)^{25/4}+2835184064813100 (-1+x)^{29/4}+1709824127042850 (-1+x)^{33/4}+695599653048300 (-1+x)^{37/4}+183247916751900 (-1+x)^{41/4}+28298171701800 (-1+x)^{45/4}+1949108765175 (-1+x)^{49/4}\right ) \left ((-1+x)^3\right )^{3/4}}{1179090487575 (-1+x)^{9/4}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 87, normalized size = 1.12 \begin {gather*} \frac {4 \, {\left (1949108765175 \, x^{12} + 4908866519700 \, x^{11} + 609206533650 \, x^{10} - 9283999210200 \, x^{9} - 8805988591725 \, x^{8} + 3131067556500 \, x^{7} + 9260757242646 \, x^{6} + 4070651298324 \, x^{5} - 2008108342110 \, x^{4} - 2834315032620 \, x^{3} - 1158885626660 \, x^{2} + 32327777464 \, x + 1308401597431\right )} {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}^{\frac {3}{4}}}{1179090487575 \, {\left (x^{2} - 2 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (3 \, x^{3} + x^{2} - 2 \, x - 1\right )}^{4}}{{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}^{\frac {1}{4}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 73, normalized size = 0.94
method | result | size |
risch | \(\frac {4 \left (-1+x \right ) \left (1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^{9}-8805988591725 x^{8}+3131067556500 x^{7}+9260757242646 x^{6}+4070651298324 x^{5}-2008108342110 x^{4}-2834315032620 x^{3}-1158885626660 x^{2}+32327777464 x +1308401597431\right )}{1179090487575 \left (\left (-1+x \right )^{3}\right )^{\frac {1}{4}}}\) | \(73\) |
gosper | \(\frac {4 \left (-1+x \right ) \left (1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^{9}-8805988591725 x^{8}+3131067556500 x^{7}+9260757242646 x^{6}+4070651298324 x^{5}-2008108342110 x^{4}-2834315032620 x^{3}-1158885626660 x^{2}+32327777464 x +1308401597431\right )}{1179090487575 \left (x^{3}-3 x^{2}+3 x -1\right )^{\frac {1}{4}}}\) | \(81\) |
trager | \(\frac {4 \left (1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^{9}-8805988591725 x^{8}+3131067556500 x^{7}+9260757242646 x^{6}+4070651298324 x^{5}-2008108342110 x^{4}-2834315032620 x^{3}-1158885626660 x^{2}+32327777464 x +1308401597431\right ) \left (x^{3}-3 x^{2}+3 x -1\right )^{\frac {3}{4}}}{1179090487575 \left (-1+x \right )^{2}}\) | \(83\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 540, normalized size = 6.92 \begin {gather*} \frac {108 \, {\left (729183975 \, x^{13} + 48612265 \, x^{12} + 56911920 \, x^{11} + 67679040 \, x^{10} + 82035200 \, x^{9} + 101836800 \, x^{8} + 130351104 \, x^{7} + 173801472 \, x^{6} + 245366784 \, x^{5} + 377487360 \, x^{4} + 671088640 \, x^{3} + 1610612736 \, x^{2} + 12884901888 \, x - 17179869184\right )}}{11910004925 \, {\left (x - 1\right )}^{\frac {3}{4}}} + \frac {48 \, {\left (48612265 \, x^{12} + 3556995 \, x^{11} + 4229940 \, x^{10} + 5127200 \, x^{9} + 6364800 \, x^{8} + 8146944 \, x^{7} + 10862592 \, x^{6} + 15335424 \, x^{5} + 23592960 \, x^{4} + 41943040 \, x^{3} + 100663296 \, x^{2} + 805306368 \, x - 1073741824\right )}}{243061325 \, {\left (x - 1\right )}^{\frac {3}{4}}} - \frac {648 \, {\left (13042315 \, x^{11} + 1057485 \, x^{10} + 1281800 \, x^{9} + 1591200 \, x^{8} + 2036736 \, x^{7} + 2715648 \, x^{6} + 3833856 \, x^{5} + 5898240 \, x^{4} + 10485760 \, x^{3} + 25165824 \, x^{2} + 201326592 \, x - 268435456\right )}}{534734915 \, {\left (x - 1\right )}^{\frac {3}{4}}} - \frac {96 \, {\left (1762475 \, x^{10} + 160225 \, x^{9} + 198900 \, x^{8} + 254592 \, x^{7} + 339456 \, x^{6} + 479232 \, x^{5} + 737280 \, x^{4} + 1310720 \, x^{3} + 3145728 \, x^{2} + 25165824 \, x - 33554432\right )}}{5016275 \, {\left (x - 1\right )}^{\frac {3}{4}}} + \frac {148 \, {\left (480675 \, x^{9} + 49725 \, x^{8} + 63648 \, x^{7} + 84864 \, x^{6} + 119808 \, x^{5} + 184320 \, x^{4} + 327680 \, x^{3} + 786432 \, x^{2} + 6291456 \, x - 8388608\right )}}{15862275 \, {\left (x - 1\right )}^{\frac {3}{4}}} + \frac {1264 \, {\left (16575 \, x^{8} + 1989 \, x^{7} + 2652 \, x^{6} + 3744 \, x^{5} + 5760 \, x^{4} + 10240 \, x^{3} + 24576 \, x^{2} + 196608 \, x - 262144\right )}}{480675 \, {\left (x - 1\right )}^{\frac {3}{4}}} + \frac {488 \, {\left (4641 \, x^{7} + 663 \, x^{6} + 936 \, x^{5} + 1440 \, x^{4} + 2560 \, x^{3} + 6144 \, x^{2} + 49152 \, x - 65536\right )}}{116025 \, {\left (x - 1\right )}^{\frac {3}{4}}} - \frac {464 \, {\left (663 \, x^{6} + 117 \, x^{5} + 180 \, x^{4} + 320 \, x^{3} + 768 \, x^{2} + 6144 \, x - 8192\right )}}{13923 \, {\left (x - 1\right )}^{\frac {3}{4}}} - \frac {392 \, {\left (195 \, x^{5} + 45 \, x^{4} + 80 \, x^{3} + 192 \, x^{2} + 1536 \, x - 2048\right )}}{3315 \, {\left (x - 1\right )}^{\frac {3}{4}}} - \frac {16 \, {\left (15 \, x^{4} + 5 \, x^{3} + 12 \, x^{2} + 96 \, x - 128\right )}}{195 \, {\left (x - 1\right )}^{\frac {3}{4}}} + \frac {16 \, {\left (5 \, x^{3} + 3 \, x^{2} + 24 \, x - 32\right )}}{9 \, {\left (x - 1\right )}^{\frac {3}{4}}} + \frac {32 \, {\left (x^{2} + 3 \, x - 4\right )}}{5 \, {\left (x - 1\right )}^{\frac {3}{4}}} + 4 \, {\left (x - 1\right )}^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.90, size = 86, normalized size = 1.10 \begin {gather*} \frac {{\left (x^3-3\,x^2+3\,x-1\right )}^{3/4}\,\left (\frac {324\,x^{12}}{49}+\frac {816\,x^{11}}{49}+\frac {4152\,x^{10}}{2009}-\frac {2341152\,x^9}{74333}-\frac {73280188\,x^8}{2452989}+\frac {755612080\,x^7}{71136681}+\frac {7981691224\,x^6}{254059575}+\frac {24558982192\,x^5}{1778417025}-\frac {41191965992\,x^4}{6046617885}-\frac {755817342032\,x^3}{78606032505}-\frac {927108501328\,x^2}{235818097515}+\frac {129311109856\,x}{1179090487575}+\frac {5233606389724}{1179090487575}\right )}{x^2-2\,x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (3 x^{3} + x^{2} - 2 x - 1\right )^{4}}{\sqrt [4]{\left (x - 1\right )^{3}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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