Optimal. Leaf size=378 \[ -\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {63043297-29625922 x}{41160000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {31 (7434109-3088870 x)}{411600000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}+\frac {\sqrt {\frac {1}{70} \left (151363871237318045+110320475741093888 \sqrt {2}\right )} \tan ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (151363871237318045+110320475741093888 \sqrt {2}\right )}} \left (308108167+312239803 \sqrt {2}+\left (932587773+620347970 \sqrt {2}\right ) x\right )}{\sqrt {3-2 x+x^2}}\right )}{137200000000}-\frac {\sqrt {\frac {1}{70} \left (-151363871237318045+110320475741093888 \sqrt {2}\right )} \tanh ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (-151363871237318045+110320475741093888 \sqrt {2}\right )}} \left (308108167-312239803 \sqrt {2}+\left (932587773-620347970 \sqrt {2}\right ) x\right )}{\sqrt {3-2 x+x^2}}\right )}{137200000000} \]
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Rubi [A]
time = 0.49, antiderivative size = 378, normalized size of antiderivative = 1.00, number of steps
used = 14, number of rules used = 6, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.261, Rules used = {988, 1074,
1049, 1043, 212, 210} \begin {gather*} \frac {\sqrt {\frac {1}{70} \left (151363871237318045+110320475741093888 \sqrt {2}\right )} \text {ArcTan}\left (\frac {\sqrt {\frac {5}{7 \left (151363871237318045+110320475741093888 \sqrt {2}\right )}} \left (\left (932587773+620347970 \sqrt {2}\right ) x+312239803 \sqrt {2}+308108167\right )}{\sqrt {x^2-2 x+3}}\right )}{137200000000}-\frac {63043297-29625922 x}{41160000000 \left (x^2-2 x+3\right )^{3/2}}-\frac {31 (7434109-3088870 x)}{411600000000 \sqrt {x^2-2 x+3}}+\frac {3 (8233 x+8822)}{343000 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )}+\frac {8878 x+5485}{117600 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^2}-\frac {30316369-15043110 x}{6860000000 \left (x^2-2 x+3\right )^{5/2}}+\frac {67 x+28}{1050 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^3}-\frac {4878869-2578034 x}{411600000 \left (x^2-2 x+3\right )^{7/2}}-\frac {1-10 x}{280 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^4}-\frac {3450497-2004270 x}{123480000 \left (x^2-2 x+3\right )^{9/2}}-\frac {\sqrt {\frac {1}{70} \left (110320475741093888 \sqrt {2}-151363871237318045\right )} \tanh ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (110320475741093888 \sqrt {2}-151363871237318045\right )}} \left (\left (932587773-620347970 \sqrt {2}\right ) x-312239803 \sqrt {2}+308108167\right )}{\sqrt {x^2-2 x+3}}\right )}{137200000000} \end {gather*}
Antiderivative was successfully verified.
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Rule 210
Rule 212
Rule 988
Rule 1043
Rule 1049
Rule 1074
Rubi steps
\begin {align*} \int \frac {1}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )^5} \, dx &=-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}-\frac {\int \frac {-1235+1335 x-800 x^2}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )^4} \, dx}{1400}\\ &=-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}-\frac {\int \frac {-1015350+1334900 x-1313200 x^2}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )^3} \, dx}{1470000}\\ &=-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}-\frac {\int \frac {-333716250+619001250 x-932190000 x^2}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )^2} \, dx}{1029000000}\\ &=-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {127736962500-7441875000 x-259339500000 x^2}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )} \, dx}{360150000000}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {32819267250000+52489111500000 x-168358680000000 x^2}{\left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )} \, dx}{648270000000000}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-4101557985000000+36919386630000000 x-68214779640000000 x^2}{\left (3-2 x+x^2\right )^{7/2} \left (1+x+2 x^2\right )} \, dx}{907578000000000000}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-6061741906500000000+12245707845000000000 x-15921627624000000000 x^2}{\left (3-2 x+x^2\right )^{5/2} \left (1+x+2 x^2\right )} \, dx}{907578000000000000000}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {63043297-29625922 x}{41160000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-1654460252550000000000+1868769331380000000000 x-1567803792240000000000 x^2}{\left (3-2 x+x^2\right )^{3/2} \left (1+x+2 x^2\right )} \, dx}{544546800000000000000000}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {63043297-29625922 x}{41160000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {31 (7434109-3088870 x)}{411600000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {-105286925935800000000000+71284514842800000000000 x}{\sqrt {3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{108909360000000000000000000}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {63043297-29625922 x}{41160000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {31 (7434109-3088870 x)}{411600000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {\int \frac {3969000000000000 \left (222438197-132636591 \sqrt {2}\right )-3969000000000000 \left (42834985-89801606 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{1089093600000000000000000000 \sqrt {2}}+\frac {\int \frac {3969000000000000 \left (222438197+132636591 \sqrt {2}\right )-3969000000000000 \left (42834985+89801606 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{1089093600000000000000000000 \sqrt {2}}\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {63043297-29625922 x}{41160000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {31 (7434109-3088870 x)}{411600000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}-\frac {1}{7} \left (101250 \left (220640951482187776-151363871237318045 \sqrt {2}\right )\right ) \text {Subst}\left (\int \frac {1}{-110270727000000000000000000000000 \left (151363871237318045-110320475741093888 \sqrt {2}\right )-5 x^2} \, dx,x,\frac {3969000000000000 \left (308108167-312239803 \sqrt {2}\right )+3969000000000000 \left (932587773-620347970 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2}}\right )-\frac {1}{7} \left (101250 \left (220640951482187776+151363871237318045 \sqrt {2}\right )\right ) \text {Subst}\left (\int \frac {1}{-110270727000000000000000000000000 \left (151363871237318045+110320475741093888 \sqrt {2}\right )-5 x^2} \, dx,x,\frac {3969000000000000 \left (308108167+312239803 \sqrt {2}\right )+3969000000000000 \left (932587773+620347970 \sqrt {2}\right ) x}{\sqrt {3-2 x+x^2}}\right )\\ &=-\frac {3450497-2004270 x}{123480000 \left (3-2 x+x^2\right )^{9/2}}-\frac {4878869-2578034 x}{411600000 \left (3-2 x+x^2\right )^{7/2}}-\frac {30316369-15043110 x}{6860000000 \left (3-2 x+x^2\right )^{5/2}}-\frac {63043297-29625922 x}{41160000000 \left (3-2 x+x^2\right )^{3/2}}-\frac {31 (7434109-3088870 x)}{411600000000 \sqrt {3-2 x+x^2}}-\frac {1-10 x}{280 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}+\frac {28+67 x}{1050 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^3}+\frac {5485+8878 x}{117600 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^2}+\frac {3 (8822+8233 x)}{343000 \left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )}+\frac {\sqrt {\frac {1}{70} \left (151363871237318045+110320475741093888 \sqrt {2}\right )} \tan ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (151363871237318045+110320475741093888 \sqrt {2}\right )}} \left (308108167+312239803 \sqrt {2}+\left (932587773+620347970 \sqrt {2}\right ) x\right )}{\sqrt {3-2 x+x^2}}\right )}{137200000000}-\frac {\sqrt {\frac {1}{70} \left (-151363871237318045+110320475741093888 \sqrt {2}\right )} \tanh ^{-1}\left (\frac {\sqrt {\frac {5}{7 \left (-151363871237318045+110320475741093888 \sqrt {2}\right )}} \left (308108167-312239803 \sqrt {2}+\left (932587773-620347970 \sqrt {2}\right ) x\right )}{\sqrt {3-2 x+x^2}}\right )}{137200000000}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 2.67, size = 733, normalized size = 1.94 \begin {gather*} \frac {\frac {-53205422447+261702502714 x-266966654968 x^2+1002897791524 x^3-1409335257371 x^4+2503427226914 x^5-3359813871472 x^6+4591320676952 x^7-5134334619701 x^8+5380603084494 x^9-4915797913008 x^{10}+3999656132532 x^{11}-2679143870481 x^{12}+1459208021718 x^{13}-606785954952 x^{14}+188603773872 x^{15}-38639385552 x^{16}+4596238560 x^{17}}{\left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )^4}-49392 \text {RootSum}\left [14+7 \text {$\#$1}-5 \text {$\#$1}^2-\text {$\#$1}^3+\text {$\#$1}^4\&,\frac {-6014 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right )-10727 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}+3229 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}^2}{7-10 \text {$\#$1}-3 \text {$\#$1}^2+4 \text {$\#$1}^3}\&\right ]-56448 \text {RootSum}\left [14+7 \text {$\#$1}-5 \text {$\#$1}^2-\text {$\#$1}^3+\text {$\#$1}^4\&,\frac {73781 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right )-60407 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}+13104 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}^2}{7-10 \text {$\#$1}-3 \text {$\#$1}^2+4 \text {$\#$1}^3}\&\right ]-504 \text {RootSum}\left [14+7 \text {$\#$1}-5 \text {$\#$1}^2-\text {$\#$1}^3+\text {$\#$1}^4\&,\frac {275935046 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right )-208696097 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}+50007219 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}^2}{7-10 \text {$\#$1}-3 \text {$\#$1}^2+4 \text {$\#$1}^3}\&\right ]+1440 \text {RootSum}\left [14+7 \text {$\#$1}-5 \text {$\#$1}^2-\text {$\#$1}^3+\text {$\#$1}^4\&,\frac {3276009822 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right )-2447831621 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}+590084719 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}^2}{7-10 \text {$\#$1}-3 \text {$\#$1}^2+4 \text {$\#$1}^3}\&\right ]-18 \text {RootSum}\left [14+7 \text {$\#$1}-5 \text {$\#$1}^2-\text {$\#$1}^3+\text {$\#$1}^4\&,\frac {254137663854 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right )-189631531133 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}+45801521671 \log \left (-x+\sqrt {3-2 x+x^2}-\text {$\#$1}\right ) \text {$\#$1}^2}{7-10 \text {$\#$1}-3 \text {$\#$1}^2+4 \text {$\#$1}^3}\&\right ]}{1234800000000} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(21027\) vs.
\(2(298)=596\).
time = 1.52, size = 21028, normalized size = 55.63
method | result | size |
risch | \(\frac {4596238560 x^{17}-38639385552 x^{16}+188603773872 x^{15}-606785954952 x^{14}+1459208021718 x^{13}-2679143870481 x^{12}+3999656132532 x^{11}-4915797913008 x^{10}+5380603084494 x^{9}-5134334619701 x^{8}+4591320676952 x^{7}-3359813871472 x^{6}+2503427226914 x^{5}-1409335257371 x^{4}+1002897791524 x^{3}-266966654968 x^{2}+261702502714 x -53205422447}{1234800000000 \left (x^{2}-2 x +3\right )^{\frac {9}{2}} \left (2 x^{2}+x +1\right )^{4}}+\frac {\sqrt {4}\, \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}\, \sqrt {2}\, \left (9625722625 \sqrt {-6050+4280 \sqrt {2}}\, \arctan \left (\frac {\sqrt {-6050+4280 \sqrt {2}}\, \left (40 \sqrt {2}+57\right ) \left (\sqrt {2}-1+x \right )}{49 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}\, \left (\sqrt {2}+1-x \right )}\right ) \sqrt {-350+280 \sqrt {2}}\, \sqrt {2}+13664181884 \sqrt {-6050+4280 \sqrt {2}}\, \arctan \left (\frac {\sqrt {-6050+4280 \sqrt {2}}\, \left (40 \sqrt {2}+57\right ) \left (\sqrt {2}-1+x \right )}{49 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}\, \left (\sqrt {2}+1-x \right )}\right ) \sqrt {-350+280 \sqrt {2}}+456968008770 \arctanh \left (\frac {7 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}}{\sqrt {-350+280 \sqrt {2}}}\right ) \sqrt {2}-607941010600 \arctanh \left (\frac {7 \sqrt {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}}{\sqrt {-350+280 \sqrt {2}}}\right )\right )}{268912000000000 \sqrt {\frac {\frac {\left (\sqrt {2}-1+x \right )^{2}}{\left (\sqrt {2}+1-x \right )^{2}}+1}{\left (\frac {\sqrt {2}-1+x}{\sqrt {2}+1-x}+1\right )^{2}}}\, \left (\frac {\sqrt {2}-1+x}{\sqrt {2}+1-x}+1\right ) \sqrt {-350+280 \sqrt {2}}}\) | \(452\) |
trager | \(\text {Expression too large to display}\) | \(541\) |
default | \(\text {Expression too large to display}\) | \(21028\) |
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. 1873 vs.
\(2 (298) = 596\).
time = 1.13, size = 1873, normalized size = 4.96 \begin {gather*} \text {Too large to display} \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 {1}{\left (x^{2} - 2 x + 3\right )^{\frac {11}{2}} \left (2 x^{2} + x + 1\right )^{5}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] Result contains complex when optimal does not.
time = 34.88, size = 2509, normalized size = 6.64 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {1}{{\left (2\,x^2+x+1\right )}^5\,{\left (x^2-2\,x+3\right )}^{11/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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