3.37.58 \(\int \frac {e^{20} (548371200000000 x^3+172947840000000 x^4+23828513280000 x^5+1873311897600 x^6+91912863744 x^7+2882018304 x^8+56398848 x^9+629760 x^{10}+3072 x^{11})}{152587890625 x^8+48828125000 x^9+6835937500 x^{10}[phone] x^{11}[phone] x^{12}+875000 x^{13}+17500 x^{14}+200 x^{15}+x^{16}+e^{40} (218971048064843776+67375707096875008 x+9069806724579328 x^2+697677440352256 x^3+33542184632320 x^4+1032067219456 x^5+19847446528 x^6+218103808 x^7+1048576 x^8)+e^{20} (365580800000000 x^4+114736128000000 x^5+15753287680000 x^6+1235891404800 x^7+60596226048 x^8+1901371392 x^9+37285888 x^{10}+417792 x^{11}+2048 x^{12})} \, dx\)

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}[phone] x^{11}[phone] 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.

[In]

Int[(E^20*(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*(218971048064843776
+ 67375707096875008*x + 9069806724579328*x^2 + 697677440352256*x^3 + 33542184632320*x^4 + 1032067219456*x^5 +
19847446528*x^6 + 218103808*x^7 + 1048576*x^8) + E^20*(365580800000000*x^4 + 114736128000000*x^5 + 1575328768
0000*x^6 + 1235891404800*x^7 + 60596226048*x^8 + 1901371392*x^9 + 37285888*x^10 + 417792*x^11 + 2048*x^12)),x]

[Out]

(-3*E^10*(677 + 432*E^5 + 32*E^10))/(21632*E^10 - 208*E^5*(25 - 8*E^5)*x + (625 - 408*E^5 + 32*E^10)*x^2 + 2*(
25 - 4*E^5)*x^3 + x^4) - (3*E^10*(677 - 432*E^5 + 32*E^10))/(21632*E^10 + 208*E^5*(25 + 8*E^5)*x + (625 + 408*
E^5 + 32*E^10)*x^2 + 2*(25 + 4*E^5)*x^3 + x^4) + (3*E^5*Defer[Int][x^2/(-21632*E^10 + 208*E^5*(25 - 8*E^5)*x -
(625 - 408*E^5 + 32*E^10)*x^2 - 2*(25 - 4*E^5)*x^3 - x^4), x])/2 + 624*E^15*(16925 - 16664*E^5 - 5984*E^10 -
256*E^15)*Defer[Int][(21632*E^10 - 208*E^5*(25 - 8*E^5)*x + (625 - 408*E^5 + 32*E^10)*x^2 + 2*(25 - 4*E^5)*x^3
+ x^4)^(-2), x] + 6*E^10*(421875 + 557416*E^5 - 1856*E^10 - 27392*E^15 - 1024*E^20)*Defer[Int][x/(21632*E^10
- 208*E^5*(25 - 8*E^5)*x + (625 - 408*E^5 + 32*E^10)*x^2 + 2*(25 - 4*E^5)*x^3 + x^4)^2, x] + 6*E^10*(16875 + 1
9372*E^5 + 2592*E^10 - 128*E^15)*Defer[Int][x^2/(21632*E^10 - 208*E^5*(25 - 8*E^5)*x + (625 - 408*E^5 + 32*E^1
0)*x^2 + 2*(25 - 4*E^5)*x^3 + x^4)^2, x] - 3*E^5*(325 - 212*E^5 - 32*E^10)*Defer[Int][(21632*E^10 - 208*E^5*(2
5 - 8*E^5)*x + (625 - 408*E^5 + 32*E^10)*x^2 + 2*(25 - 4*E^5)*x^3 + x^4)^(-1), x] - 6*E^5*(13 - 2*E^5)*Defer[I
nt][x/(21632*E^10 - 208*E^5*(25 - 8*E^5)*x + (625 - 408*E^5 + 32*E^10)*x^2 + 2*(25 - 4*E^5)*x^3 + x^4), x] - 6
24*E^15*(16925 + 16664*E^5 - 5984*E^10 + 256*E^15)*Defer[Int][(21632*E^10 + 208*E^5*(25 + 8*E^5)*x + (625 + 40
8*E^5 + 32*E^10)*x^2 + 2*(25 + 4*E^5)*x^3 + x^4)^(-2), x] + 6*E^10*(421875 - 557416*E^5 - 1856*E^10 + 27392*E^
15 - 1024*E^20)*Defer[Int][x/(21632*E^10 + 208*E^5*(25 + 8*E^5)*x + (625 + 408*E^5 + 32*E^10)*x^2 + 2*(25 + 4*
E^5)*x^3 + x^4)^2, x] + 6*E^10*(16875 - 19372*E^5 + 2592*E^10 + 128*E^15)*Defer[Int][x^2/(21632*E^10 + 208*E^5
*(25 + 8*E^5)*x + (625 + 408*E^5 + 32*E^10)*x^2 + 2*(25 + 4*E^5)*x^3 + x^4)^2, x] + 3*E^5*(325 + 212*E^5 - 32*
E^10)*Defer[Int][(21632*E^10 + 208*E^5*(25 + 8*E^5)*x + (625 + 408*E^5 + 32*E^10)*x^2 + 2*(25 + 4*E^5)*x^3 + x
^4)^(-1), x] + 6*E^5*(13 + 2*E^5)*Defer[Int][x/(21632*E^10 + 208*E^5*(25 + 8*E^5)*x + (625 + 408*E^5 + 32*E^10
)*x^2 + 2*(25 + 4*E^5)*x^3 + x^4), x] + (3*E^5*Defer[Int][x^2/(21632*E^10 + 208*E^5*(25 + 8*E^5)*x + (625 + 40
8*E^5 + 32*E^10)*x^2 + 2*(25 + 4*E^5)*x^3 + x^4), x])/2

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}[phone] x^{11}[phone] 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.

[In]

Integrate[(E^20*(548371200000000*x^3 + 172947840000000*x^4 + 23828513280000*x^5 + 1873311897600*x^6 + 91912863
744*x^7 + 2882018304*x^8 + 56398848*x^9 + 629760*x^10 + 3072*x^11))/(152587890625*x^8 + 48828125000*x^9 + 6835
937500*x^10 + 546875000*x^11 + 27343750*x^12 + 875000*x^13 + 17500*x^14 + 200*x^15 + x^16 + E^40*(218971048064
843776 + 67375707096875008*x + 9069806724579328*x^2 + 697677440352256*x^3 + 33542184632320*x^4 + 1032067219456
*x^5 + 19847446528*x^6 + 218103808*x^7 + 1048576*x^8) + E^20*(365580800000000*x^4 + 114736128000000*x^5 + 1575
3287680000*x^6 + 1235891404800*x^7 + 60596226048*x^8 + 1901371392*x^9 + 37285888*x^10 + 417792*x^11 + 2048*x^1
2)),x]

[Out]

(-768*E^20*(26 + x)^4)/(x^4*(25 + x)^4 + 1024*E^20*(26 + x)^4)

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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.

[In]

integrate((3072*x^11+629760*x^10+56398848*x^9+2882018304*x^8+91912863744*x^7+1873311897600*x^6+23828513280000*
x^5+172947840000000*x^4+548371200000000*x^3)*exp(5)^4/((1048576*x^8+218103808*x^7+19847446528*x^6+103206721945
6*x^5+33542184632320*x^4+697677440352256*x^3+9069806724579328*x^2+67375707096875008*x+218971048064843776)*exp(
5)^8+(2048*x^12+417792*x^11+37285888*x^10+1901371392*x^9+60596226048*x^8+1235891404800*x^7+15753287680000*x^6+
114736128000000*x^5+365580800000000*x^4)*exp(5)^4+x^16+200*x^15+17500*x^14+875000*x^13+27343750*x^12+546875000
*x^11+6835937500*x^10+48828125000*x^9+152587890625*x^8),x, algorithm="fricas")

[Out]

-768*(x^4 + 104*x^3 + 4056*x^2 + 70304*x + 456976)*e^20/(x^8 + 100*x^7 + 3750*x^6 + 62500*x^5 + 390625*x^4 + 1
024*(x^4 + 104*x^3 + 4056*x^2 + 70304*x + 456976)*e^20)

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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.

[In]

integrate((3072*x^11+629760*x^10+56398848*x^9+2882018304*x^8+91912863744*x^7+1873311897600*x^6+23828513280000*
x^5+172947840000000*x^4+548371200000000*x^3)*exp(5)^4/((1048576*x^8+218103808*x^7+19847446528*x^6+103206721945
6*x^5+33542184632320*x^4+697677440352256*x^3+9069806724579328*x^2+67375707096875008*x+218971048064843776)*exp(
5)^8+(2048*x^12+417792*x^11+37285888*x^10+1901371392*x^9+60596226048*x^8+1235891404800*x^7+15753287680000*x^6+
114736128000000*x^5+365580800000000*x^4)*exp(5)^4+x^16+200*x^15+17500*x^14+875000*x^13+27343750*x^12+546875000
*x^11+6835937500*x^10+48828125000*x^9+152587890625*x^8),x, algorithm="giac")

[Out]

Timed out

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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	\(-\frac {768 \left (x +26\right ) \left (x^{3}+78 x^{2}+2028 x +17576\right ) {\mathrm e}^{20}}{1024 x^{4} {\mathrm e}^{20}+x^{8}+106496 x^{3} {\mathrm e}^{20}+100 x^{7}+4153344 x^{2} {\mathrm e}^{20}+3750 x^{6}[phone] x \,{\mathrm e}^{20}+62500 x^{5}[phone] \,{\mathrm e}^{20}+390625 x^{4}}\)	\(89\)
norman	\(\frac {-53993472 x \,{\mathrm e}^{20}-3115008 x^{2} {\mathrm e}^{20}-79872 x^{3} {\mathrm e}^{20}-768 x^{4} {\mathrm e}^{20}-350957568 \,{\mathrm e}^{20}}{1024 x^{4} {\mathrm e}^{20}+x^{8}+106496 x^{3} {\mathrm e}^{20}+100 x^{7}+4153344 x^{2} {\mathrm e}^{20}+3750 x^{6}[phone] x \,{\mathrm e}^{20}+62500 x^{5}[phone] \,{\mathrm e}^{20}+390625 x^{4}}\)	\(109\)
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}[phone]\right ) \textit {\_Z}^{12}+\left (417792 \,{\mathrm e}^{20}[phone]\right ) \textit {\_Z}^{11}+\left (37285888 \,{\mathrm e}^{20}[phone]\right ) \textit {\_Z}^{10}+\left (1901371392 \,{\mathrm e}^{20}[phone]\right ) \textit {\_Z}^{9}+\left (1048576 \,{\mathrm e}^{40}[phone] \,{\mathrm e}^{20}[phone]\right ) \textit {\_Z}^{8}+\left (218103808 \,{\mathrm e}^{40}[phone] \,{\mathrm e}^{20}\right ) \textit {\_Z}^{7}+\left (19847446528 \,{\mathrm e}^{40}[phone] \,{\mathrm e}^{20}\right ) \textit {\_Z}^{6}+\left (1032067219456 \,{\mathrm e}^{40}[phone] \,{\mathrm e}^{20}\right ) \textit {\_Z}^{5}+\left (33542184632320 \,{\mathrm e}^{40}[phone] \,{\mathrm e}^{20}\right ) \textit {\_Z}^{4}[phone] \,{\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}[phone] \textit {\_R}^{7}[phone] \textit {\_R}^{6}[phone] \textit {\_R}^{5}[phone] \textit {\_R}^{4}[phone] \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}[phone] \textit {\_R}^{7}[phone] \textit {\_R}^{8}[phone] \textit {\_R}^{10}[phone] \textit {\_R}^{9}[phone] \textit {\_R}^{3} {\mathrm e}^{20}[phone] \textit {\_R}^{2} {\mathrm e}^{40}+1048576 \,{\mathrm e}^{40} \textit {\_R}^{7}[phone] \,{\mathrm e}^{20} \textit {\_R}^{7}[phone] \,{\mathrm e}^{20} \textit {\_R}^{6}+574464 \,{\mathrm e}^{20} \textit {\_R}^{10}[phone] \,{\mathrm e}^{40} \textit {\_R}^{5}[phone] \,{\mathrm e}^{20} \textit {\_R}^{9}[phone] \,{\mathrm e}^{40} \textit {\_R}^{4}[phone] \,{\mathrm e}^{40} \textit {\_R}^{3}+2267451681144832 \,{\mathrm e}^{40} \textit {\_R} +3072 \,{\mathrm e}^{20} \textit {\_R}^{11}[phone] \,{\mathrm e}^{40} \textit {\_R}^{6}[phone] \textit {\_R}^{4} {\mathrm e}^{20}[phone] \textit {\_R}^{8} {\mathrm e}^{20}[phone] \textit {\_R}^{5} {\mathrm e}^{20}+8421963387109376 \,{\mathrm e}^{40}}\right )\)	\(372\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3072*x^11+629760*x^10+56398848*x^9+2882018304*x^8+91912863744*x^7+1873311897600*x^6+23828513280000*x^5+17
2947840000000*x^4+548371200000000*x^3)*exp(5)^4/((1048576*x^8+218103808*x^7+19847446528*x^6+1032067219456*x^5+
33542184632320*x^4+697677440352256*x^3+9069806724579328*x^2+67375707096875008*x+218971048064843776)*exp(5)^8+(
2048*x^12+417792*x^11+37285888*x^10+1901371392*x^9+60596226048*x^8+1235891404800*x^7+15753287680000*x^6+114736
128000000*x^5+365580800000000*x^4)*exp(5)^4+x^16+200*x^15+17500*x^14+875000*x^13+27343750*x^12+546875000*x^11+
6835937500*x^10+48828125000*x^9+152587890625*x^8),x,method=_RETURNVERBOSE)

[Out]

exp(20)*(-3/4*x^4-78*x^3-3042*x^2-52728*x-342732)/(x^4*exp(20)+1/1024*x^8+104*x^3*exp(20)+25/256*x^7+4056*x^2*
exp(20)+1875/512*x^6+70304*x*exp(20)+15625/256*x^5+456976*exp(20)+390625/1024*x^4)

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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.

[In]

integrate((3072*x^11+629760*x^10+56398848*x^9+2882018304*x^8+91912863744*x^7+1873311897600*x^6+23828513280000*
x^5+172947840000000*x^4+548371200000000*x^3)*exp(5)^4/((1048576*x^8+218103808*x^7+19847446528*x^6+103206721945
6*x^5+33542184632320*x^4+697677440352256*x^3+9069806724579328*x^2+67375707096875008*x+218971048064843776)*exp(
5)^8+(2048*x^12+417792*x^11+37285888*x^10+1901371392*x^9+60596226048*x^8+1235891404800*x^7+15753287680000*x^6+
114736128000000*x^5+365580800000000*x^4)*exp(5)^4+x^16+200*x^15+17500*x^14+875000*x^13+27343750*x^12+546875000
*x^11+6835937500*x^10+48828125000*x^9+152587890625*x^8),x, algorithm="maxima")

[Out]

-768*(x^4 + 104*x^3 + 4056*x^2 + 70304*x + 456976)*e^20/(x^8 + 100*x^7 + 3750*x^6 + 62500*x^5 + x^4*(1024*e^20
+ 390625) + 106496*x^3*e^20 + 4153344*x^2*e^20 + 71991296*x*e^20 + 467943424*e^20)

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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.

[In]

int((exp(20)*(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))/(exp(40)*(67375707096875008*x + 9069806724579
328*x^2 + 697677440352256*x^3 + 33542184632320*x^4 + 1032067219456*x^5 + 19847446528*x^6 + 218103808*x^7 + 104
8576*x^8 + 218971048064843776) + exp(20)*(365580800000000*x^4 + 114736128000000*x^5 + 15753287680000*x^6 + 123
5891404800*x^7 + 60596226048*x^8 + 1901371392*x^9 + 37285888*x^10 + 417792*x^11 + 2048*x^12) + 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),x)

[Out]

-(768*exp(20)*(x + 26)^4)/(467943424*exp(20) + 71991296*x*exp(20) + x^4*(1024*exp(20) + 390625) + 4153344*x^2*
exp(20) + 106496*x^3*exp(20) + 62500*x^5 + 3750*x^6 + 100*x^7 + x^8)

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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.

[In]

integrate((3072*x**11+629760*x**10+56398848*x**9+2882018304*x**8+91912863744*x**7+1873311897600*x**6+238285132
80000*x**5+172947840000000*x**4+548371200000000*x**3)*exp(5)**4/((1048576*x**8+218103808*x**7+19847446528*x**6
[phone]*x**5+33542184632320*x**4+697677440352256*x**3+9069806724579328*x**2+67375707096875008*x+2189710
48064843776)*exp(5)**8+(2048*x**12+417792*x**11+37285888*x**10+1901371392*x**9+60596226048*x**8+1235891404800*
x**7+15753287680000*x**6+114736128000000*x**5+365580800000000*x**4)*exp(5)**4+x**16+200*x**15+17500*x**14+8750
00*x**13+27343750*x**12+546875000*x**11+6835937500*x**10+48828125000*x**9+152587890625*x**8),x)

[Out]

(-768*x**4*exp(20) - 79872*x**3*exp(20) - 3115008*x**2*exp(20) - 53993472*x*exp(20) - 350957568*exp(20))/(x**8
+ 100*x**7 + 3750*x**6 + 62500*x**5 + x**4*(390625 + 1024*exp(20)) + 106496*x**3*exp(20) + 4153344*x**2*exp(2
0) + 71991296*x*exp(20) + 467943424*exp(20))

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