Optimal. Leaf size=407 \[ -\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128}-\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128}+\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256} \]
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Rubi [A]
time = 0.42, antiderivative size = 407, normalized size of antiderivative = 1.00, number of steps
used = 19, number of rules used = 9, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.450, Rules used = {754, 836, 842,
840, 1183, 648, 632, 210, 642} \begin {gather*} \frac {x}{28 (3-2 x)^{9/2} \left (2 x^2+x+1\right )^4}+\frac {5 (4377 x+3049)}{153664 (3-2 x)^{9/2} \left (2 x^2+x+1\right )}+\frac {3049 x+1387}{32928 (3-2 x)^{9/2} \left (2 x^2+x+1\right )^2}+\frac {73 x+23}{1176 (3-2 x)^{9/2} \left (2 x^2+x+1\right )^3}-\frac {38225}{240945152 \sqrt {3-2 x}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {19255}{395136 (3-2 x)^{9/2}}+\frac {5 \sqrt {\frac {1}{2} \left (40815066112 \sqrt {14}-149046503977\right )} \log \left (-2 x-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (40815066112 \sqrt {14}-149046503977\right )} \log \left (-2 x+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{6746464256}+\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {2 \sqrt {14}-7}}\right )}{3373232128}-\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \tan ^{-1}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{3373232128} \end {gather*}
Antiderivative was successfully verified.
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Rule 210
Rule 632
Rule 642
Rule 648
Rule 754
Rule 836
Rule 840
Rule 842
Rule 1183
Rubi steps
\begin {align*} \int \frac {1}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^5} \, dx &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {1}{784} \int \frac {700-644 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^4} \, dx\\ &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {\int \frac {325752-543704 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^3} \, dx}{460992}\\ &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {\int \frac {54660480-250993680 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^2} \, dx}{180708864}\\ &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-25503229920-55488454560 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )} \, dx}{35418937344}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-93048930240-434943647040 x}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )} \, dx}{991730245632}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {125495852160-2981857603200 x}{(3-2 x)^{7/2} \left (1+x+2 x^2\right )} \, dx}{27768446877696}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {6967682023680-17389162210560 x}{(3-2 x)^{5/2} \left (1+x+2 x^2\right )} \, dx}{777516512575488}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {90519780610560-76464245168640 x}{(3-2 x)^{3/2} \left (1+x+2 x^2\right )} \, dx}{21770462352113664}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {877086735221760-96706348569600 x}{\sqrt {3-2 x} \left (1+x+2 x^2\right )} \, dx}{609572945859182592}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\text {Subst}\left (\int \frac {-1464054424734720-96706348569600 x^2}{28-14 x^2+2 x^4} \, dx,x,\sqrt {3-2 x}\right )}{304786472929591296}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\text {Subst}\left (\int \frac {-1464054424734720 \sqrt {7+2 \sqrt {14}}-\left (-1464054424734720+96706348569600 \sqrt {14}\right ) x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1219145891718365184 \sqrt {14 \left (7+2 \sqrt {14}\right )}}+\frac {\text {Subst}\left (\int \frac {-1464054424734720 \sqrt {7+2 \sqrt {14}}+\left (-1464054424734720+96706348569600 \sqrt {14}\right ) x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1219145891718365184 \sqrt {14 \left (7+2 \sqrt {14}\right )}}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}-\frac {\left (5 \left (107030+115739 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{13492928512}-\frac {\left (5 \left (107030+115739 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{13492928512}+\frac {\left (5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )}\right ) \text {Subst}\left (\int \frac {-\sqrt {7+2 \sqrt {14}}+2 x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{6746464256}-\frac {\left (5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )}\right ) \text {Subst}\left (\int \frac {\sqrt {7+2 \sqrt {14}}+2 x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{6746464256}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}+\frac {\left (5 \left (107030+115739 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{7-2 \sqrt {14}-x^2} \, dx,x,-\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}\right )}{6746464256}+\frac {\left (5 \left (107030+115739 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{7-2 \sqrt {14}-x^2} \, dx,x,\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}\right )}{6746464256}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {5 \sqrt {298093007954+81630132224 \sqrt {14}} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{6746464256}-\frac {5 \sqrt {298093007954+81630132224 \sqrt {14}} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{6746464256}+\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 4.10, size = 178, normalized size = 0.44 \begin {gather*} \frac {-\frac {14 \left (40289347-429812744 x+135202154 x^2-1073855156 x^3+1627773523 x^4-1470758860 x^5+2888625656 x^6-3106712560 x^7+2343370048 x^8-2443779648 x^9+1873554048 x^{10}-677249280 x^{11}+88070400 x^{12}\right )}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}-45 \sqrt {149046503977+12577271771 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1-\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )-45 \sqrt {149046503977-12577271771 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1+\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )}{30359089152} \end {gather*}
Antiderivative was successfully verified.
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Mathics [F(-1)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.89, size = 415, normalized size = 1.02
method | result | size |
derivativedivides | \(\frac {1}{151263 \left (3-2 x \right )^{\frac {9}{2}}}+\frac {5}{235298 \left (3-2 x \right )^{\frac {7}{2}}}+\frac {19}{470596 \left (3-2 x \right )^{\frac {5}{2}}}+\frac {185}{2823576 \left (3-2 x \right )^{\frac {3}{2}}}+\frac {505}{3294172 \sqrt {3-2 x}}+\frac {\frac {567651623 \sqrt {3-2 x}}{32}-\frac {6194606411 \left (3-2 x \right )^{\frac {3}{2}}}{192}+\frac {9801432515 \left (3-2 x \right )^{\frac {5}{2}}}{384}-\frac {8763772549 \left (3-2 x \right )^{\frac {7}{2}}}{768}+\frac {149630663 \left (3-2 x \right )^{\frac {9}{2}}}{48}-\frac {200063633 \left (3-2 x \right )^{\frac {11}{2}}}{384}+\frac {18969965 \left (3-2 x \right )^{\frac {13}{2}}}{384}-\frac {526135 \left (3-2 x \right )^{\frac {15}{2}}}{256}}{6588344 \left (\left (3-2 x \right )^{2}-7+14 x \right )^{4}}+\frac {5 \left (-146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}+569986 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{13492928512}+\frac {5 \left (-115739 \sqrt {14}+\frac {\left (-146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}+569986 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128 \sqrt {-7+2 \sqrt {14}}}+\frac {5 \left (146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-569986 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{13492928512}+\frac {5 \left (-115739 \sqrt {14}-\frac {\left (146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-569986 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128 \sqrt {-7+2 \sqrt {14}}}\) | \(415\) |
default | \(\frac {1}{151263 \left (3-2 x \right )^{\frac {9}{2}}}+\frac {5}{235298 \left (3-2 x \right )^{\frac {7}{2}}}+\frac {19}{470596 \left (3-2 x \right )^{\frac {5}{2}}}+\frac {185}{2823576 \left (3-2 x \right )^{\frac {3}{2}}}+\frac {505}{3294172 \sqrt {3-2 x}}+\frac {\frac {567651623 \sqrt {3-2 x}}{32}-\frac {6194606411 \left (3-2 x \right )^{\frac {3}{2}}}{192}+\frac {9801432515 \left (3-2 x \right )^{\frac {5}{2}}}{384}-\frac {8763772549 \left (3-2 x \right )^{\frac {7}{2}}}{768}+\frac {149630663 \left (3-2 x \right )^{\frac {9}{2}}}{48}-\frac {200063633 \left (3-2 x \right )^{\frac {11}{2}}}{384}+\frac {18969965 \left (3-2 x \right )^{\frac {13}{2}}}{384}-\frac {526135 \left (3-2 x \right )^{\frac {15}{2}}}{256}}{6588344 \left (\left (3-2 x \right )^{2}-7+14 x \right )^{4}}+\frac {5 \left (-146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}+569986 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{13492928512}+\frac {5 \left (-115739 \sqrt {14}+\frac {\left (-146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}+569986 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128 \sqrt {-7+2 \sqrt {14}}}+\frac {5 \left (146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-569986 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{13492928512}+\frac {5 \left (-115739 \sqrt {14}-\frac {\left (146319 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-569986 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128 \sqrt {-7+2 \sqrt {14}}}\) | \(415\) |
trager | \(\text {Expression too large to display}\) | \(509\) |
risch | \(-\frac {88070400 x^{12}-677249280 x^{11}+1873554048 x^{10}-2443779648 x^{9}+2343370048 x^{8}-3106712560 x^{7}+2888625656 x^{6}-1470758860 x^{5}+1627773523 x^{4}-1073855156 x^{3}+135202154 x^{2}-429812744 x +40289347}{2168506368 \left (2 x^{2}+x +1\right )^{4} \sqrt {3-2 x}\, \left (2 x -3\right )^{4}}-\frac {731595 \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}\, \sqrt {14}}{13492928512}+\frac {1424965 \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{6746464256}-\frac {731595 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right ) \sqrt {14}}{6746464256 \sqrt {-7+2 \sqrt {14}}}+\frac {1424965 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right )}{3373232128 \sqrt {-7+2 \sqrt {14}}}-\frac {578695 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \sqrt {14}}{3373232128 \sqrt {-7+2 \sqrt {14}}}+\frac {731595 \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}\, \sqrt {14}}{13492928512}-\frac {1424965 \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{6746464256}-\frac {731595 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right ) \sqrt {14}}{6746464256 \sqrt {-7+2 \sqrt {14}}}+\frac {1424965 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right )}{3373232128 \sqrt {-7+2 \sqrt {14}}}-\frac {578695 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \sqrt {14}}{3373232128 \sqrt {-7+2 \sqrt {14}}}\) | \(536\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 957 vs.
\(2 (298) = 596\).
time = 0.33, size = 957, normalized size = 2.35
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 795 vs.
\(2 (298) = 596\).
time = 0.27, size = 1277, normalized size = 3.14
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.47, size = 343, normalized size = 0.84 \begin {gather*} -\frac {\frac {272\,x}{441}-\frac {164\,{\left (2\,x-3\right )}^2}{441}+\frac {1966\,{\left (2\,x-3\right )}^3}{3087}-\frac {9091\,{\left (2\,x-3\right )}^4}{3087}-\frac {32070727\,{\left (2\,x-3\right )}^5}{5531904}-\frac {41014777\,{\left (2\,x-3\right )}^6}{11063808}-\frac {141921511\,{\left (2\,x-3\right )}^7}{154893312}+\frac {23262655\,{\left (2\,x-3\right )}^8}{309786624}+\frac {1571659\,{\left (2\,x-3\right )}^9}{15059072}+\frac {468427\,{\left (2\,x-3\right )}^{10}}{17210368}+\frac {394105\,{\left (2\,x-3\right )}^{11}}{120472576}+\frac {38225\,{\left (2\,x-3\right )}^{12}}{240945152}-\frac {520}{441}}{38416\,{\left (3-2\,x\right )}^{9/2}-76832\,{\left (3-2\,x\right )}^{11/2}+68600\,{\left (3-2\,x\right )}^{13/2}-35672\,{\left (3-2\,x\right )}^{15/2}+11809\,{\left (3-2\,x\right )}^{17/2}-2548\,{\left (3-2\,x\right )}^{19/2}+350\,{\left (3-2\,x\right )}^{21/2}-28\,{\left (3-2\,x\right )}^{23/2}+{\left (3-2\,x\right )}^{25/2}}+\frac {\mathrm {atan}\left (\frac {\sqrt {3-2\,x}\,\sqrt {-149046503977+\sqrt {7}\,12577271771{}\mathrm {i}}\,1572158971375{}\mathrm {i}}{391663056253676053933850624\,\left (-\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}-\frac {1572158971375\,\sqrt {7}\,\sqrt {3-2\,x}\,\sqrt {-149046503977+\sqrt {7}\,12577271771{}\mathrm {i}}}{391663056253676053933850624\,\left (-\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}\right )\,\sqrt {-149046503977+\sqrt {7}\,12577271771{}\mathrm {i}}\,5{}\mathrm {i}}{3373232128}-\frac {\mathrm {atan}\left (\frac {\sqrt {3-2\,x}\,\sqrt {-149046503977-\sqrt {7}\,12577271771{}\mathrm {i}}\,1572158971375{}\mathrm {i}}{391663056253676053933850624\,\left (\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}+\frac {1572158971375\,\sqrt {7}\,\sqrt {3-2\,x}\,\sqrt {-149046503977-\sqrt {7}\,12577271771{}\mathrm {i}}}{391663056253676053933850624\,\left (\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}\right )\,\sqrt {-149046503977-\sqrt {7}\,12577271771{}\mathrm {i}}\,5{}\mathrm {i}}{3373232128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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