Optimal. Leaf size=27 \[ \frac {3}{4+\frac {256 e^{20} \left (6+\frac {6}{25+x}\right )^4}{81 x^4}} \]
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Rubi [F] time = 3.50, 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 {e^{20} \left (548371200000000 x^3+172947840000000 x^4+23828513280000 x^5+1873311897600 x^6+91912863744 x^7+2882018304 x^8+56398848 x^9+629760 x^{10}+3072 x^{11}\right )}{152587890625 x^8+48828125000 x^9+6835937500 x^{10}+546875000 x^{11}+27343750 x^{12}+875000 x^{13}+17500 x^{14}+200 x^{15}+x^{16}+e^{40} \left (218971048064843776+67375707096875008 x+9069806724579328 x^2+697677440352256 x^3+33542184632320 x^4+1032067219456 x^5+19847446528 x^6+218103808 x^7+1048576 x^8\right )+e^{20} \left (365580800000000 x^4+114736128000000 x^5+15753287680000 x^6+1235891404800 x^7+60596226048 x^8+1901371392 x^9+37285888 x^{10}+417792 x^{11}+2048 x^{12}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{20} \int \frac {548371200000000 x^3+172947840000000 x^4+23828513280000 x^5+1873311897600 x^6+91912863744 x^7+2882018304 x^8+56398848 x^9+629760 x^{10}+3072 x^{11}}{152587890625 x^8+48828125000 x^9+6835937500 x^{10}+546875000 x^{11}+27343750 x^{12}+875000 x^{13}+17500 x^{14}+200 x^{15}+x^{16}+e^{40} \left (218971048064843776+67375707096875008 x+9069806724579328 x^2+697677440352256 x^3+33542184632320 x^4+1032067219456 x^5+19847446528 x^6+218103808 x^7+1048576 x^8\right )+e^{20} \left (365580800000000 x^4+114736128000000 x^5+15753287680000 x^6+1235891404800 x^7+60596226048 x^8+1901371392 x^9+37285888 x^{10}+417792 x^{11}+2048 x^{12}\right )} \, dx\\ &=e^{20} \int \left (\frac {12 \left (-21632 e^{10} \left (53+8 e^5\right )+52 \left (8125+5300 e^5-1312 e^{10}-256 e^{15}\right ) x+\left (33825+21824 e^5-96 e^{10}-256 e^{15}\right ) x^2+\left (677+432 e^5+32 e^{10}\right ) x^3\right )}{e^{10} \left (21632 e^{10}-208 e^5 \left (25-8 e^5\right ) x+\left (625-408 e^5+32 e^{10}\right ) x^2+2 \left (25-4 e^5\right ) x^3+x^4\right )^2}+\frac {3 \left (-2 \left (325-212 e^5-32 e^{10}\right )-4 \left (13-2 e^5\right ) x-x^2\right )}{2 e^{15} \left (21632 e^{10}-208 e^5 \left (25-8 e^5\right ) x+\left (625-408 e^5+32 e^{10}\right ) x^2+2 \left (25-4 e^5\right ) x^3+x^4\right )}+\frac {12 \left (-21632 e^{10} \left (53-8 e^5\right )+52 \left (8125-5300 e^5-1312 e^{10}+256 e^{15}\right ) x+\left (33825-21824 e^5-96 e^{10}+256 e^{15}\right ) x^2+\left (677-432 e^5+32 e^{10}\right ) x^3\right )}{e^{10} \left (21632 e^{10}+208 e^5 \left (25+8 e^5\right ) x+\left (625+408 e^5+32 e^{10}\right ) x^2+2 \left (25+4 e^5\right ) x^3+x^4\right )^2}+\frac {3 \left (2 \left (325+212 e^5-32 e^{10}\right )+4 \left (13+2 e^5\right ) x+x^2\right )}{2 e^{15} \left (21632 e^{10}+208 e^5 \left (25+8 e^5\right ) x+\left (625+408 e^5+32 e^{10}\right ) x^2+2 \left (25+4 e^5\right ) x^3+x^4\right )}\right ) \, dx\\ &=\frac {1}{2} \left (3 e^5\right ) \int \frac {-2 \left (325-212 e^5-32 e^{10}\right )-4 \left (13-2 e^5\right ) x-x^2}{21632 e^{10}-208 e^5 \left (25-8 e^5\right ) x+\left (625-408 e^5+32 e^{10}\right ) x^2+2 \left (25-4 e^5\right ) x^3+x^4} \, dx+\frac {1}{2} \left (3 e^5\right ) \int \frac {2 \left (325+212 e^5-32 e^{10}\right )+4 \left (13+2 e^5\right ) x+x^2}{21632 e^{10}+208 e^5 \left (25+8 e^5\right ) x+\left (625+408 e^5+32 e^{10}\right ) x^2+2 \left (25+4 e^5\right ) x^3+x^4} \, dx+\left (12 e^{10}\right ) \int \frac {-21632 e^{10} \left (53+8 e^5\right )+52 \left (8125+5300 e^5-1312 e^{10}-256 e^{15}\right ) x+\left (33825+21824 e^5-96 e^{10}-256 e^{15}\right ) x^2+\left (677+432 e^5+32 e^{10}\right ) x^3}{\left (21632 e^{10}-208 e^5 \left (25-8 e^5\right ) x+\left (625-408 e^5+32 e^{10}\right ) x^2+2 \left (25-4 e^5\right ) x^3+x^4\right )^2} \, dx+\left (12 e^{10}\right ) \int \frac {-21632 e^{10} \left (53-8 e^5\right )+52 \left (8125-5300 e^5-1312 e^{10}+256 e^{15}\right ) x+\left (33825-21824 e^5-96 e^{10}+256 e^{15}\right ) x^2+\left (677-432 e^5+32 e^{10}\right ) x^3}{\left (21632 e^{10}+208 e^5 \left (25+8 e^5\right ) x+\left (625+408 e^5+32 e^{10}\right ) x^2+2 \left (25+4 e^5\right ) x^3+x^4\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 32, normalized size = 1.19 \begin {gather*} -\frac {768 e^{20} (26+x)^4}{x^4 (25+x)^4+1024 e^{20} (26+x)^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 70, normalized size = 2.59 \begin {gather*} -\frac {768 \, {\left (x^{4} + 104 \, x^{3} + 4056 \, x^{2} + 70304 \, x + 456976\right )} e^{20}}{x^{8} + 100 \, x^{7} + 3750 \, x^{6} + 62500 \, x^{5} + 390625 \, x^{4} + 1024 \, {\left (x^{4} + 104 \, x^{3} + 4056 \, x^{2} + 70304 \, x + 456976\right )} e^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [B] time = 1.56, size = 81, normalized size = 3.00
method | result | size |
risch | \(\frac {{\mathrm e}^{20} \left (-\frac {3}{4} x^{4}-78 x^{3}-3042 x^{2}-52728 x -342732\right )}{x^{4} {\mathrm e}^{20}+\frac {x^{8}}{1024}+104 x^{3} {\mathrm e}^{20}+\frac {25 x^{7}}{256}+4056 x^{2} {\mathrm e}^{20}+\frac {1875 x^{6}}{512}+70304 x \,{\mathrm e}^{20}+\frac {15625 x^{5}}{256}+456976 \,{\mathrm e}^{20}+\frac {390625 x^{4}}{1024}}\) | \(81\) |
gosper | \(-\frac {768 \left (x +26\right ) \left (x^{3}+78 x^{2}+2028 x +17576\right ) {\mathrm e}^{20}}{1024 x^{4} {\mathrm e}^{20}+x^{8}+106496 x^{3} {\mathrm e}^{20}+100 x^{7}+4153344 x^{2} {\mathrm e}^{20}+3750 x^{6}+71991296 x \,{\mathrm e}^{20}+62500 x^{5}+467943424 \,{\mathrm e}^{20}+390625 x^{4}}\) | \(89\) |
norman | \(\frac {-53993472 x \,{\mathrm e}^{20}-3115008 x^{2} {\mathrm e}^{20}-79872 x^{3} {\mathrm e}^{20}-768 x^{4} {\mathrm e}^{20}-350957568 \,{\mathrm e}^{20}}{1024 x^{4} {\mathrm e}^{20}+x^{8}+106496 x^{3} {\mathrm e}^{20}+100 x^{7}+4153344 x^{2} {\mathrm e}^{20}+3750 x^{6}+71991296 x \,{\mathrm e}^{20}+62500 x^{5}+467943424 \,{\mathrm e}^{20}+390625 x^{4}}\) | \(109\) |
default | \(384 \,{\mathrm e}^{20} \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{16}+200 \textit {\_Z}^{15}+17500 \textit {\_Z}^{14}+875000 \textit {\_Z}^{13}+\left (2048 \,{\mathrm e}^{20}+27343750\right ) \textit {\_Z}^{12}+\left (417792 \,{\mathrm e}^{20}+546875000\right ) \textit {\_Z}^{11}+\left (37285888 \,{\mathrm e}^{20}+6835937500\right ) \textit {\_Z}^{10}+\left (1901371392 \,{\mathrm e}^{20}+48828125000\right ) \textit {\_Z}^{9}+\left (1048576 \,{\mathrm e}^{40}+60596226048 \,{\mathrm e}^{20}+152587890625\right ) \textit {\_Z}^{8}+\left (218103808 \,{\mathrm e}^{40}+1235891404800 \,{\mathrm e}^{20}\right ) \textit {\_Z}^{7}+\left (19847446528 \,{\mathrm e}^{40}+15753287680000 \,{\mathrm e}^{20}\right ) \textit {\_Z}^{6}+\left (1032067219456 \,{\mathrm e}^{40}+114736128000000 \,{\mathrm e}^{20}\right ) \textit {\_Z}^{5}+\left (33542184632320 \,{\mathrm e}^{40}+365580800000000 \,{\mathrm e}^{20}\right ) \textit {\_Z}^{4}+697677440352256 \,{\mathrm e}^{40} \textit {\_Z}^{3}+9069806724579328 \textit {\_Z}^{2} {\mathrm e}^{40}+67375707096875008 \,{\mathrm e}^{40} \textit {\_Z} +218971048064843776 \,{\mathrm e}^{40}\right )}{\sum }\frac {\left (\textit {\_R}^{11}+205 \textit {\_R}^{10}+18359 \textit {\_R}^{9}+938157 \textit {\_R}^{8}+29919552 \textit {\_R}^{7}+609802050 \textit {\_R}^{6}+7756677500 \textit {\_R}^{5}+56298125000 \textit {\_R}^{4}+178506250000 \textit {\_R}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{41015625 \textit {\_R}^{11}+1421875 \textit {\_R}^{12}+30625 \textit {\_R}^{13}+375 \textit {\_R}^{14}+2 \textit {\_R}^{15}+152587890625 \textit {\_R}^{7}+54931640625 \textit {\_R}^{8}+751953125 \textit {\_R}^{10}+8544921875 \textit {\_R}^{9}+182790400000000 \textit {\_R}^{3} {\mathrm e}^{20}+261629040132096 \textit {\_R}^{2} {\mathrm e}^{40}+1048576 \,{\mathrm e}^{40} \textit {\_R}^{7}+60596226048 \,{\mathrm e}^{20} \textit {\_R}^{7}+1081404979200 \,{\mathrm e}^{20} \textit {\_R}^{6}+574464 \,{\mathrm e}^{20} \textit {\_R}^{10}+14885584896 \,{\mathrm e}^{40} \textit {\_R}^{5}+46607360 \,{\mathrm e}^{20} \textit {\_R}^{9}+645042012160 \,{\mathrm e}^{40} \textit {\_R}^{4}+16771092316160 \,{\mathrm e}^{40} \textit {\_R}^{3}+2267451681144832 \,{\mathrm e}^{40} \textit {\_R} +3072 \,{\mathrm e}^{20} \textit {\_R}^{11}+190840832 \,{\mathrm e}^{40} \textit {\_R}^{6}+71710080000000 \textit {\_R}^{4} {\mathrm e}^{20}+2139042816 \textit {\_R}^{8} {\mathrm e}^{20}+11814965760000 \textit {\_R}^{5} {\mathrm e}^{20}+8421963387109376 \,{\mathrm e}^{40}}\right )\) | \(372\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.45, size = 76, normalized size = 2.81 \begin {gather*} -\frac {768 \, {\left (x^{4} + 104 \, x^{3} + 4056 \, x^{2} + 70304 \, x + 456976\right )} e^{20}}{x^{8} + 100 \, x^{7} + 3750 \, x^{6} + 62500 \, x^{5} + x^{4} {\left (1024 \, e^{20} + 390625\right )} + 106496 \, x^{3} e^{20} + 4153344 \, x^{2} e^{20} + 71991296 \, x e^{20} + 467943424 \, e^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.57, size = 63, normalized size = 2.33 \begin {gather*} -\frac {768\,{\mathrm {e}}^{20}\,{\left (x+26\right )}^4}{x^8+100\,x^7+3750\,x^6+62500\,x^5+\left (1024\,{\mathrm {e}}^{20}+390625\right )\,x^4+106496\,{\mathrm {e}}^{20}\,x^3+4153344\,{\mathrm {e}}^{20}\,x^2+71991296\,{\mathrm {e}}^{20}\,x+467943424\,{\mathrm {e}}^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 17.57, size = 95, normalized size = 3.52 \begin {gather*} \frac {- 768 x^{4} e^{20} - 79872 x^{3} e^{20} - 3115008 x^{2} e^{20} - 53993472 x e^{20} - 350957568 e^{20}}{x^{8} + 100 x^{7} + 3750 x^{6} + 62500 x^{5} + x^{4} \left (390625 + 1024 e^{20}\right ) + 106496 x^{3} e^{20} + 4153344 x^{2} e^{20} + 71991296 x e^{20} + 467943424 e^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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