3.16.13 \(\int \frac {e^{-5-x} (14876160-14876160 x-5963520 x^2-838656 x^3-75776 x^4-3584 x^5+256 x^6)}{3376772100+2382858660 x+744859249 x^2+142613992 x^3+19810676 x^4+1973216 x^5+118070 x^6+3128 x^7-160 x^8-36 x^9+x^{10}} \, dx\)

Optimal. Leaf size=34 \[ \frac {e^{-5-x} x}{(30-x) \left (1+x+\left (2+\frac {1}{16} (3+x)^2\right )^2\right )} \]

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Rubi [F]  time = 2.35, 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^{-5-x} \left (14876160-14876160 x-5963520 x^2-838656 x^3-75776 x^4-3584 x^5+256 x^6\right )}{3376772100+2382858660 x+744859249 x^2+142613992 x^3+19810676 x^4+1973216 x^5+118070 x^6+3128 x^7-160 x^8-36 x^9+x^{10}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-5 - x)*(14876160 - 14876160*x - 5963520*x^2 - 838656*x^3 - 75776*x^4 - 3584*x^5 + 256*x^6))/(33767721
00 + 2382858660*x + 744859249*x^2 + 142613992*x^3 + 19810676*x^4 + 1973216*x^5 + 118070*x^6 + 3128*x^7 - 160*x
^8 - 36*x^9 + x^10),x]

[Out]

(7680*E^(-5 - x))/(1264577*(30 - x)) + (73502114816*Defer[Int][E^(-5 - x)/(1937 + 748*x + 118*x^2 + 12*x^3 + x
^4)^2, x])/1264577 + (22762243072*Defer[Int][(E^(-5 - x)*x)/(1937 + 748*x + 118*x^2 + 12*x^3 + x^4)^2, x])/126
4577 + (2689723392*Defer[Int][(E^(-5 - x)*x^2)/(1937 + 748*x + 118*x^2 + 12*x^3 + x^4)^2, x])/1264577 + (15653
5808*Defer[Int][(E^(-5 - x)*x^3)/(1937 + 748*x + 118*x^2 + 12*x^3 + x^4)^2, x])/1264577 - (26675968*Defer[Int]
[E^(-5 - x)/(1937 + 748*x + 118*x^2 + 12*x^3 + x^4), x])/1264577 - (11136000*Defer[Int][(E^(-5 - x)*x)/(1937 +
748*x + 118*x^2 + 12*x^3 + x^4), x])/1264577 - (330240*Defer[Int][(E^(-5 - x)*x^2)/(1937 + 748*x + 118*x^2 +
12*x^3 + x^4), x])/1264577 - (7680*Defer[Int][(E^(-5 - x)*x^3)/(1937 + 748*x + 118*x^2 + 12*x^3 + x^4), x])/12
64577

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {256 e^{-5-x} \left (58110-58110 x-23295 x^2-3276 x^3-296 x^4-14 x^5+x^6\right )}{\left (58110+20503 x+2792 x^2+242 x^3+18 x^4-x^5\right )^2} \, dx\\ &=256 \int \frac {e^{-5-x} \left (58110-58110 x-23295 x^2-3276 x^3-296 x^4-14 x^5+x^6\right )}{\left (58110+20503 x+2792 x^2+242 x^3+18 x^4-x^5\right )^2} \, dx\\ &=256 \int \left (\frac {30 e^{-5-x}}{1264577 (-30+x)^2}+\frac {30 e^{-5-x}}{1264577 (-30+x)}+\frac {4 e^{-5-x} \left (71779409+22228753 x+2626683 x^2+152867 x^3\right )}{1264577 \left (1937+748 x+118 x^2+12 x^3+x^4\right )^2}+\frac {e^{-5-x} \left (-104203-43500 x-1290 x^2-30 x^3\right )}{1264577 \left (1937+748 x+118 x^2+12 x^3+x^4\right )}\right ) \, dx\\ &=\frac {256 \int \frac {e^{-5-x} \left (-104203-43500 x-1290 x^2-30 x^3\right )}{1937+748 x+118 x^2+12 x^3+x^4} \, dx}{1264577}+\frac {1024 \int \frac {e^{-5-x} \left (71779409+22228753 x+2626683 x^2+152867 x^3\right )}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2} \, dx}{1264577}+\frac {7680 \int \frac {e^{-5-x}}{(-30+x)^2} \, dx}{1264577}+\frac {7680 \int \frac {e^{-5-x}}{-30+x} \, dx}{1264577}\\ &=\frac {7680 e^{-5-x}}{1264577 (30-x)}+\frac {7680 \text {Ei}(30-x)}{1264577 e^{35}}+\frac {256 \int \left (-\frac {104203 e^{-5-x}}{1937+748 x+118 x^2+12 x^3+x^4}-\frac {43500 e^{-5-x} x}{1937+748 x+118 x^2+12 x^3+x^4}-\frac {1290 e^{-5-x} x^2}{1937+748 x+118 x^2+12 x^3+x^4}-\frac {30 e^{-5-x} x^3}{1937+748 x+118 x^2+12 x^3+x^4}\right ) \, dx}{1264577}+\frac {1024 \int \left (\frac {71779409 e^{-5-x}}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2}+\frac {22228753 e^{-5-x} x}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2}+\frac {2626683 e^{-5-x} x^2}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2}+\frac {152867 e^{-5-x} x^3}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2}\right ) \, dx}{1264577}-\frac {7680 \int \frac {e^{-5-x}}{-30+x} \, dx}{1264577}\\ &=\frac {7680 e^{-5-x}}{1264577 (30-x)}-\frac {7680 \int \frac {e^{-5-x} x^3}{1937+748 x+118 x^2+12 x^3+x^4} \, dx}{1264577}-\frac {330240 \int \frac {e^{-5-x} x^2}{1937+748 x+118 x^2+12 x^3+x^4} \, dx}{1264577}-\frac {11136000 \int \frac {e^{-5-x} x}{1937+748 x+118 x^2+12 x^3+x^4} \, dx}{1264577}-\frac {26675968 \int \frac {e^{-5-x}}{1937+748 x+118 x^2+12 x^3+x^4} \, dx}{1264577}+\frac {156535808 \int \frac {e^{-5-x} x^3}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2} \, dx}{1264577}+\frac {2689723392 \int \frac {e^{-5-x} x^2}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2} \, dx}{1264577}+\frac {22762243072 \int \frac {e^{-5-x} x}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2} \, dx}{1264577}+\frac {73502114816 \int \frac {e^{-5-x}}{\left (1937+748 x+118 x^2+12 x^3+x^4\right )^2} \, dx}{1264577}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.52, size = 35, normalized size = 1.03 \begin {gather*} -\frac {256 e^{-5-x} x}{-58110-20503 x-2792 x^2-242 x^3-18 x^4+x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-5 - x)*(14876160 - 14876160*x - 5963520*x^2 - 838656*x^3 - 75776*x^4 - 3584*x^5 + 256*x^6))/(33
76772100 + 2382858660*x + 744859249*x^2 + 142613992*x^3 + 19810676*x^4 + 1973216*x^5 + 118070*x^6 + 3128*x^7 -
160*x^8 - 36*x^9 + x^10),x]

[Out]

(-256*E^(-5 - x)*x)/(-58110 - 20503*x - 2792*x^2 - 242*x^3 - 18*x^4 + x^5)

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fricas [A]  time = 0.84, size = 34, normalized size = 1.00 \begin {gather*} -\frac {256 \, x e^{\left (-x - 5\right )}}{x^{5} - 18 \, x^{4} - 242 \, x^{3} - 2792 \, x^{2} - 20503 \, x - 58110} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x^6-3584*x^5-75776*x^4-838656*x^3-5963520*x^2-14876160*x+14876160)/(x^10-36*x^9-160*x^8+3128*x^
7+118070*x^6+1973216*x^5+19810676*x^4+142613992*x^3+744859249*x^2+2382858660*x+3376772100)/exp(5+x),x, algorit
hm="fricas")

[Out]

-256*x*e^(-x - 5)/(x^5 - 18*x^4 - 242*x^3 - 2792*x^2 - 20503*x - 58110)

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giac [A]  time = 0.22, size = 46, normalized size = 1.35 \begin {gather*} -\frac {256 \, x e^{\left (-x\right )}}{x^{5} e^{5} - 18 \, x^{4} e^{5} - 242 \, x^{3} e^{5} - 2792 \, x^{2} e^{5} - 20503 \, x e^{5} - 58110 \, e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x^6-3584*x^5-75776*x^4-838656*x^3-5963520*x^2-14876160*x+14876160)/(x^10-36*x^9-160*x^8+3128*x^
7+118070*x^6+1973216*x^5+19810676*x^4+142613992*x^3+744859249*x^2+2382858660*x+3376772100)/exp(5+x),x, algorit
hm="giac")

[Out]

-256*x*e^(-x)/(x^5*e^5 - 18*x^4*e^5 - 242*x^3*e^5 - 2792*x^2*e^5 - 20503*x*e^5 - 58110*e^5)

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maple [A]  time = 0.24, size = 35, normalized size = 1.03

method	result	size
gosper	\(-\frac {256 x \,{\mathrm e}^{-x -5}}{x^{5}-18 x^{4}-242 x^{3}-2792 x^{2}-20503 x -58110}\)	\(35\)
norman	\(-\frac {256 x \,{\mathrm e}^{-x -5}}{x^{5}-18 x^{4}-242 x^{3}-2792 x^{2}-20503 x -58110}\)	\(35\)
risch	\(-\frac {256 x \,{\mathrm e}^{-x -5}}{x^{5}-18 x^{4}-242 x^{3}-2792 x^{2}-20503 x -58110}\)	\(35\)
derivativedivides	\(-\frac {{\mathrm e}^{-x -5} \left (26457342630019 \left (5+x \right )^{4}-467179992899779 \left (5+x \right )^{3}+1958522171028850 \left (5+x \right )^{2}-2406902346252940-1670328791810852 x \right )}{59168734590373 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {\left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (10051224426811936963 \textit {\_R1}^{3}-18285891617927697815 \textit {\_R1}^{2}+34052872945814255368 \textit {\_R1} -61833367561959505900\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{299293683528360468884}+\frac {3135 \,{\mathrm e}^{-x -5} \left (15736448349 \left (5+x \right )^{4}-699186305165 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-224817712270196-53801779157404 x \right )}{236674938361492 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}-\frac {3135 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (19900896954526237 \textit {\_R1}^{3}-167751146659931449 \textit {\_R1}^{2}+1682313368734270232 \textit {\_R1} +372085206843856556\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{1197174734113441875536}-\frac {915 \,{\mathrm e}^{-x -5} \left (11259513079 \left (5+x \right )^{4}-451925961143 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-130620612678780-11143023707508 x \right )}{118337469180746 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {915 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (14222344132124471 \textit {\_R1}^{3}-59345193158847547 \textit {\_R1}^{2}+444683752509520712 \textit {\_R1} +1908188231637632292\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{598587367056720937768}-\frac {520 \,{\mathrm e}^{-x -5} \left (16116550627 \left (5+x \right )^{4}-864262432707 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-172851558611980-45289368173604 x \right )}{59168734590373 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {130 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (20104227034695459 \textit {\_R1}^{3}-366686691248384535 \textit {\_R1}^{2}+941690482768058824 \textit {\_R1} -3287487574324790508\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{74823420882090117221}-\frac {839 \,{\mathrm e}^{-x -5} \left (85625377873 \left (5+x \right )^{4}-3008699933217 \left (5+x \right )^{3}-2432668688810 \left (5+x \right )^{2}-154617390442660-15580521891628 x \right )}{118337469180746 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {839 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (112999361987759121 \textit {\_R1}^{3}+220768989492284547 \textit {\_R1}^{2}+2112501387415257560 \textit {\_R1} +1766867680363085820\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{598587367056720937768}+\frac {429 \,{\mathrm e}^{-x -5} \left (336595657661 \left (5+x \right )^{4}-16971403873037 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-82186468783860-97952653491868 x \right )}{236674938361492 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}-\frac {429 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (506187761381430397 \textit {\_R1}^{3}-3963717295453120057 \textit {\_R1}^{2}+2368936825845519576 \textit {\_R1} -16737830962654662228\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{1197174734113441875536}+\frac {22 \,{\mathrm e}^{-x -5} \left (1248895296807 \left (5+x \right )^{4}-787812502663 \left (5+x \right )^{3}-474766516574582 \left (5+x \right )^{2}-1449784438494780+30482178394316 x \right )}{59168734590373 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}-\frac {11 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (205882358313505639 \textit {\_R1}^{3}+18776492513037334453 \textit {\_R1}^{2}+1853977066436129416 \textit {\_R1} +61199126888932756964\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{149646841764180234442}\)	\(940\)
default	\(-\frac {{\mathrm e}^{-x -5} \left (26457342630019 \left (5+x \right )^{4}-467179992899779 \left (5+x \right )^{3}+1958522171028850 \left (5+x \right )^{2}-2406902346252940-1670328791810852 x \right )}{59168734590373 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {\left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (10051224426811936963 \textit {\_R1}^{3}-18285891617927697815 \textit {\_R1}^{2}+34052872945814255368 \textit {\_R1} -61833367561959505900\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{299293683528360468884}+\frac {3135 \,{\mathrm e}^{-x -5} \left (15736448349 \left (5+x \right )^{4}-699186305165 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-224817712270196-53801779157404 x \right )}{236674938361492 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}-\frac {3135 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (19900896954526237 \textit {\_R1}^{3}-167751146659931449 \textit {\_R1}^{2}+1682313368734270232 \textit {\_R1} +372085206843856556\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{1197174734113441875536}-\frac {915 \,{\mathrm e}^{-x -5} \left (11259513079 \left (5+x \right )^{4}-451925961143 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-130620612678780-11143023707508 x \right )}{118337469180746 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {915 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (14222344132124471 \textit {\_R1}^{3}-59345193158847547 \textit {\_R1}^{2}+444683752509520712 \textit {\_R1} +1908188231637632292\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{598587367056720937768}-\frac {520 \,{\mathrm e}^{-x -5} \left (16116550627 \left (5+x \right )^{4}-864262432707 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-172851558611980-45289368173604 x \right )}{59168734590373 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {130 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (20104227034695459 \textit {\_R1}^{3}-366686691248384535 \textit {\_R1}^{2}+941690482768058824 \textit {\_R1} -3287487574324790508\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{74823420882090117221}-\frac {839 \,{\mathrm e}^{-x -5} \left (85625377873 \left (5+x \right )^{4}-3008699933217 \left (5+x \right )^{3}-2432668688810 \left (5+x \right )^{2}-154617390442660-15580521891628 x \right )}{118337469180746 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}+\frac {839 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (112999361987759121 \textit {\_R1}^{3}+220768989492284547 \textit {\_R1}^{2}+2112501387415257560 \textit {\_R1} +1766867680363085820\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{598587367056720937768}+\frac {429 \,{\mathrm e}^{-x -5} \left (336595657661 \left (5+x \right )^{4}-16971403873037 \left (5+x \right )^{3}[phone] \left (5+x \right )^{2}-82186468783860-97952653491868 x \right )}{236674938361492 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}-\frac {429 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (506187761381430397 \textit {\_R1}^{3}-3963717295453120057 \textit {\_R1}^{2}+2368936825845519576 \textit {\_R1} -16737830962654662228\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{1197174734113441875536}+\frac {22 \,{\mathrm e}^{-x -5} \left (1248895296807 \left (5+x \right )^{4}-787812502663 \left (5+x \right )^{3}-474766516574582 \left (5+x \right )^{2}-1449784438494780+30482178394316 x \right )}{59168734590373 \left (\left (5+x \right )^{5}-43 \left (5+x \right )^{4}+368 \left (5+x \right )^{3}-3112 \left (5+x \right )^{2}-2560+1392 x \right )}-\frac {11 \left (\munderset {\textit {\_R1} =\RootOf \left (\textit {\_Z}^{4}-8 \textit {\_Z}^{3}+88 \textit {\_Z}^{2}-32 \textit {\_Z} +272\right )}{\sum }\frac {\left (205882358313505639 \textit {\_R1}^{3}+18776492513037334453 \textit {\_R1}^{2}+1853977066436129416 \textit {\_R1} +61199126888932756964\right ) {\mathrm e}^{-\textit {\_R1}} \expIntegralEi \left (1, 5+x -\textit {\_R1} \right )}{\textit {\_R1}^{3}-6 \textit {\_R1}^{2}+44 \textit {\_R1} -8}\right )}{149646841764180234442}\)	\(940\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((256*x^6-3584*x^5-75776*x^4-838656*x^3-5963520*x^2-14876160*x+14876160)/(x^10-36*x^9-160*x^8+3128*x^7+1180
70*x^6+1973216*x^5+19810676*x^4+142613992*x^3+744859249*x^2+2382858660*x+3376772100)/exp(5+x),x,method=_RETURN
VERBOSE)

[Out]

-256*x/exp(5+x)/(x^5-18*x^4-242*x^3-2792*x^2-20503*x-58110)

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maxima [A]  time = 0.44, size = 46, normalized size = 1.35 \begin {gather*} -\frac {256 \, x e^{\left (-x\right )}}{x^{5} e^{5} - 18 \, x^{4} e^{5} - 242 \, x^{3} e^{5} - 2792 \, x^{2} e^{5} - 20503 \, x e^{5} - 58110 \, e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x^6-3584*x^5-75776*x^4-838656*x^3-5963520*x^2-14876160*x+14876160)/(x^10-36*x^9-160*x^8+3128*x^
7+118070*x^6+1973216*x^5+19810676*x^4+142613992*x^3+744859249*x^2+2382858660*x+3376772100)/exp(5+x),x, algorit
hm="maxima")

[Out]

-256*x*e^(-x)/(x^5*e^5 - 18*x^4*e^5 - 242*x^3*e^5 - 2792*x^2*e^5 - 20503*x*e^5 - 58110*e^5)

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mupad [B]  time = 0.24, size = 36, normalized size = 1.06 \begin {gather*} \frac {256\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-5}}{-x^5+18\,x^4+242\,x^3+2792\,x^2+20503\,x+58110} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(- x - 5)*(14876160*x + 5963520*x^2 + 838656*x^3 + 75776*x^4 + 3584*x^5 - 256*x^6 - 14876160))/(23828
58660*x + 744859249*x^2 + 142613992*x^3 + 19810676*x^4 + 1973216*x^5 + 118070*x^6 + 3128*x^7 - 160*x^8 - 36*x^
9 + x^10 + 3376772100),x)

[Out]

(256*x*exp(-x)*exp(-5))/(20503*x + 2792*x^2 + 242*x^3 + 18*x^4 - x^5 + 58110)

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sympy [A]  time = 0.15, size = 34, normalized size = 1.00 \begin {gather*} - \frac {256 x e^{- x - 5}}{x^{5} - 18 x^{4} - 242 x^{3} - 2792 x^{2} - 20503 x - 58110} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x**6-3584*x**5-75776*x**4-838656*x**3-5963520*x**2-14876160*x+14876160)/(x**10-36*x**9-160*x**8
+3128*x**7+118070*x**6+1973216*x**5+19810676*x**4+142613992*x**3+744859249*x**2+2382858660*x+3376772100)/exp(5
+x),x)

[Out]

-256*x*exp(-x - 5)/(x**5 - 18*x**4 - 242*x**3 - 2792*x**2 - 20503*x - 58110)

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