Optimal. Leaf size=36 \[ \frac {x}{-4-\frac {3}{x}+x-\left (5-x-\frac {x}{4+\frac {\log ^2(16)}{x^2}}\right )^2} \]
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Rubi [F]
time = 5.82, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1350000000 x^4-156250000 x^5-5864000000 x^3 \left (1+\frac {875 \log ^2(16)}{46912}\right )-24708960000 x^2 \left (1+\frac {14875 \log ^2(16)}{411816}\right )-102057574400 x \left (1+\frac {125 \log ^2(16) \left (1368832+3625 \log ^2(16)\right )}{4082302976}\right )-411920265216 \left (1+\frac {625 \log ^2(16) \left (4001792+24375 \log ^2(16)\right )}{51490033152}\right )}{9765625 \left (216 x^6-25 x^7-3 \log ^4(16)-29 x \log ^4(16)-48 x^4 \left (1-\frac {49 \log ^2(16)}{24}\right )-24 x^2 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right )-232 x^3 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right )-464 x^5 \left (1+\frac {5 \log ^2(16)}{232}\right )\right )}+\frac {-1235760795648 \log ^4(16) \left (1+\frac {625 \log ^2(16) \left (4001792+24375 \log ^2(16)\right )}{51490033152}\right )-12251860414464 x \log ^4(16) \left (1+\frac {625 \log ^2(16) \left (948948224+5803125 \log ^2(16)\right )}{12251860414464}\right )+40434032685056 x^6 \left (1-\frac {125 \log ^2(16) \left (-4604686592-35300000 \log ^2(16)+15625 \log ^4(16)\right )}{10108508171264}\right )-196029766631424 x^5 \left (1-\frac {5 \log ^2(16) \left (-948025732096-5311226000 \log ^2(16)+671875 \log ^4(16)\right )}{98014883315712}\right )-98014883315712 x^3 \log ^2(16) \left (1-\frac {\log ^2(16) \left (-4768179906816-28650360000 \log ^2(16)+2734375 \log ^4(16)\right )}{98014883315712}\right )-9886086365184 x^2 \log ^2(16) \left (1-\frac {\log ^2(16) \left (508555669888+45222830000 \log ^2(16)+364453125 \log ^4(16)\right )}{4943043182592}\right )-19772172730368 x^4 \left (1+\frac {\log ^2(16) \left (-3784345902592-234209966400 \log ^2(16)-1788100000 \log ^4(16)+390625 \log ^6(16)\right )}{4943043182592}\right )}{9765625 \left (216 x^6-25 x^7-3 \log ^4(16)-29 x \log ^4(16)-48 x^4 \left (1-\frac {49 \log ^2(16)}{24}\right )-24 x^2 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right )-232 x^3 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right )-464 x^5 \left (1+\frac {5 \log ^2(16)}{232}\right )\right )^2}\right ) \, dx\\ &=\frac {\int \frac {-1350000000 x^4-156250000 x^5-5864000000 x^3 \left (1+\frac {875 \log ^2(16)}{46912}\right )-24708960000 x^2 \left (1+\frac {14875 \log ^2(16)}{411816}\right )-102057574400 x \left (1+\frac {125 \log ^2(16) \left (1368832+3625 \log ^2(16)\right )}{4082302976}\right )-411920265216 \left (1+\frac {625 \log ^2(16) \left (4001792+24375 \log ^2(16)\right )}{51490033152}\right )}{216 x^6-25 x^7-3 \log ^4(16)-29 x \log ^4(16)-48 x^4 \left (1-\frac {49 \log ^2(16)}{24}\right )-24 x^2 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right )-232 x^3 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right )-464 x^5 \left (1+\frac {5 \log ^2(16)}{232}\right )} \, dx}{9765625}+\frac {\int \frac {-1235760795648 \log ^4(16) \left (1+\frac {625 \log ^2(16) \left (4001792+24375 \log ^2(16)\right )}{51490033152}\right )-12251860414464 x \log ^4(16) \left (1+\frac {625 \log ^2(16) \left (948948224+5803125 \log ^2(16)\right )}{12251860414464}\right )+40434032685056 x^6 \left (1-\frac {125 \log ^2(16) \left (-4604686592-35300000 \log ^2(16)+15625 \log ^4(16)\right )}{10108508171264}\right )-196029766631424 x^5 \left (1-\frac {5 \log ^2(16) \left (-948025732096-5311226000 \log ^2(16)+671875 \log ^4(16)\right )}{98014883315712}\right )-98014883315712 x^3 \log ^2(16) \left (1-\frac {\log ^2(16) \left (-4768179906816-28650360000 \log ^2(16)+2734375 \log ^4(16)\right )}{98014883315712}\right )-9886086365184 x^2 \log ^2(16) \left (1-\frac {\log ^2(16) \left (508555669888+45222830000 \log ^2(16)+364453125 \log ^4(16)\right )}{4943043182592}\right )-19772172730368 x^4 \left (1+\frac {\log ^2(16) \left (-3784345902592-234209966400 \log ^2(16)-1788100000 \log ^4(16)+390625 \log ^6(16)\right )}{4943043182592}\right )}{\left (216 x^6-25 x^7-3 \log ^4(16)-29 x \log ^4(16)-48 x^4 \left (1-\frac {49 \log ^2(16)}{24}\right )-24 x^2 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right )-232 x^3 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right )-464 x^5 \left (1+\frac {5 \log ^2(16)}{232}\right )\right )^2} \, dx}{9765625}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(99\) vs. \(2(36)=72\).
time = 0.39, size = 99, normalized size = 2.75 \begin {gather*} -\frac {x^2 \left (4 x^2+\log ^2(16)\right )^2}{-216 x^6+25 x^7+3 \log ^4(16)+29 x \log ^4(16)+x^4 \left (48-98 \log ^2(16)\right )+x^3 \log ^2(16) \left (232+\log ^2(16)\right )+2 x^5 \left (232+5 \log ^2(16)\right )+x^2 \left (24 \log ^2(16)-11 \log ^4(16)\right )} \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. \(115\) vs.
\(2(37)=74\).
time = 0.58, size = 116, normalized size = 3.22
| method | result | size |
| gosper | \(-\frac {16 x^{2} \left (16 \ln \left (2\right )^{4}+8 x^{2} \ln \left (2\right )^{2}+x^{4}\right )}{256 x^{3} \ln \left (2\right )^{4}+160 x^{5} \ln \left (2\right )^{2}+25 x^{7}-2816 x^{2} \ln \left (2\right )^{4}-1568 x^{4} \ln \left (2\right )^{2}-216 x^{6}+7424 x \ln \left (2\right )^{4}+3712 x^{3} \ln \left (2\right )^{2}+464 x^{5}+768 \ln \left (2\right )^{4}+384 x^{2} \ln \left (2\right )^{2}+48 x^{4}}\) | \(115\) |
| risch | \(\frac {-x^{2} \ln \left (2\right )^{4}-\frac {x^{4} \ln \left (2\right )^{2}}{2}-\frac {x^{6}}{16}}{x^{3} \ln \left (2\right )^{4}+\frac {5 x^{5} \ln \left (2\right )^{2}}{8}+\frac {25 x^{7}}{256}-11 x^{2} \ln \left (2\right )^{4}-\frac {49 x^{4} \ln \left (2\right )^{2}}{8}-\frac {27 x^{6}}{32}+29 x \ln \left (2\right )^{4}+\frac {29 x^{3} \ln \left (2\right )^{2}}{2}+\frac {29 x^{5}}{16}+3 \ln \left (2\right )^{4}+\frac {3 x^{2} \ln \left (2\right )^{2}}{2}+\frac {3 x^{4}}{16}}\) | \(115\) |
| default | \(\frac {-x^{2} \ln \left (2\right )^{4}-\frac {x^{4} \ln \left (2\right )^{2}}{2}-\frac {x^{6}}{16}}{x^{3} \ln \left (2\right )^{4}+\frac {5 x^{5} \ln \left (2\right )^{2}}{8}+\frac {25 x^{7}}{256}-11 x^{2} \ln \left (2\right )^{4}-\frac {49 x^{4} \ln \left (2\right )^{2}}{8}-\frac {27 x^{6}}{32}+29 x \ln \left (2\right )^{4}+\frac {29 x^{3} \ln \left (2\right )^{2}}{2}+\frac {29 x^{5}}{16}+3 \ln \left (2\right )^{4}+\frac {3 x^{2} \ln \left (2\right )^{2}}{2}+\frac {3 x^{4}}{16}}\) | \(116\) |
| norman | \(\frac {-16 x^{6}-128 x^{4} \ln \left (2\right )^{2}-256 x^{2} \ln \left (2\right )^{4}}{256 x^{3} \ln \left (2\right )^{4}+160 x^{5} \ln \left (2\right )^{2}+25 x^{7}-2816 x^{2} \ln \left (2\right )^{4}-1568 x^{4} \ln \left (2\right )^{2}-216 x^{6}+7424 x \ln \left (2\right )^{4}+3712 x^{3} \ln \left (2\right )^{2}+464 x^{5}+768 \ln \left (2\right )^{4}+384 x^{2} \ln \left (2\right )^{2}+48 x^{4}}\) | \(116\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 112 vs.
\(2 (37) = 74\).
time = 0.29, size = 112, normalized size = 3.11 \begin {gather*} -\frac {16 \, {\left (x^{6} + 8 \, x^{4} \log \left (2\right )^{2} + 16 \, x^{2} \log \left (2\right )^{4}\right )}}{25 \, x^{7} + 16 \, {\left (10 \, \log \left (2\right )^{2} + 29\right )} x^{5} - 216 \, x^{6} - 16 \, {\left (98 \, \log \left (2\right )^{2} - 3\right )} x^{4} + 7424 \, x \log \left (2\right )^{4} + 128 \, {\left (2 \, \log \left (2\right )^{4} + 29 \, \log \left (2\right )^{2}\right )} x^{3} + 768 \, \log \left (2\right )^{4} - 128 \, {\left (22 \, \log \left (2\right )^{4} - 3 \, \log \left (2\right )^{2}\right )} x^{2}} \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. 93 vs.
\(2 (37) = 74\).
time = 0.41, size = 93, normalized size = 2.58 \begin {gather*} -\frac {16 \, {\left (x^{6} + 8 \, x^{4} \log \left (2\right )^{2} + 16 \, x^{2} \log \left (2\right )^{4}\right )}}{25 \, x^{7} - 216 \, x^{6} + 464 \, x^{5} + 256 \, {\left (x^{3} - 11 \, x^{2} + 29 \, x + 3\right )} \log \left (2\right )^{4} + 48 \, x^{4} + 32 \, {\left (5 \, x^{5} - 49 \, x^{4} + 116 \, x^{3} + 12 \, x^{2}\right )} \log \left (2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 109 vs.
\(2 (26) = 52\).
time = 29.81, size = 109, normalized size = 3.03 \begin {gather*} \frac {- 16 x^{6} - 128 x^{4} \log {\left (2 \right )}^{2} - 256 x^{2} \log {\left (2 \right )}^{4}}{25 x^{7} - 216 x^{6} + x^{5} \cdot \left (160 \log {\left (2 \right )}^{2} + 464\right ) + x^{4} \cdot \left (48 - 1568 \log {\left (2 \right )}^{2}\right ) + x^{3} \cdot \left (256 \log {\left (2 \right )}^{4} + 3712 \log {\left (2 \right )}^{2}\right ) + x^{2} \left (- 2816 \log {\left (2 \right )}^{4} + 384 \log {\left (2 \right )}^{2}\right ) + 7424 x \log {\left (2 \right )}^{4} + 768 \log {\left (2 \right )}^{4}} \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. 114 vs.
\(2 (37) = 74\).
time = 0.77, size = 114, normalized size = 3.17 \begin {gather*} -\frac {16 \, {\left (x^{6} + 8 \, x^{4} \log \left (2\right )^{2} + 16 \, x^{2} \log \left (2\right )^{4}\right )}}{25 \, x^{7} + 160 \, x^{5} \log \left (2\right )^{2} + 256 \, x^{3} \log \left (2\right )^{4} - 216 \, x^{6} - 1568 \, x^{4} \log \left (2\right )^{2} - 2816 \, x^{2} \log \left (2\right )^{4} + 464 \, x^{5} + 3712 \, x^{3} \log \left (2\right )^{2} + 7424 \, x \log \left (2\right )^{4} + 48 \, x^{4} + 384 \, x^{2} \log \left (2\right )^{2} + 768 \, \log \left (2\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.60, size = 102, normalized size = 2.83 \begin {gather*} -\frac {16\,x^2\,{\left (x^2+4\,{\ln \left (2\right )}^2\right )}^2}{25\,x^7-216\,x^6+\left (160\,{\ln \left (2\right )}^2+464\right )\,x^5+\left (48-1568\,{\ln \left (2\right )}^2\right )\,x^4+\left (3712\,{\ln \left (2\right )}^2+256\,{\ln \left (2\right )}^4\right )\,x^3+\left (384\,{\ln \left (2\right )}^2-2816\,{\ln \left (2\right )}^4\right )\,x^2+7424\,{\ln \left (2\right )}^4\,x+768\,{\ln \left (2\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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