3.35.65 \(\int \frac {e^{\frac {1024 x^2+17408 x^3+114368 x^4+364256 x^5+578769 x^6+432496 x^7+151036 x^8+23566 x^9+1812 x^{10}+68 x^{11}+x^{12}}{256+4096 x+24832 x^2+68608 x^3+77920 x^4+17152 x^5+1552 x^6+64 x^7+x^8}} (4096+81920 x+693248 x^2+3407872 x^3+11917824 x^4+34328064 x^5+78478560 x^6+118319872 x^7+97752008 x^8+40329056 x^9+7831044 x^{10}+802040 x^{11}+45152 x^{12}+1328 x^{13}+16 x^{14})}{1024+20480 x+165120 x^2+675840 x^3+1434240 x^4+1383936 x^5+358560 x^6+42240 x^7+2580 x^8+80 x^9+x^{10}} \, dx\)

Optimal. Leaf size=26 \[ 4 e^{x^2 \left (2+x-\frac {25}{\left (16+\frac {4}{x}+x\right )^2}\right )^2} x \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((1024*x^2 + 17408*x^3 + 114368*x^4 + 364256*x^5 + 578769*x^6 + 432496*x^7 + 151036*x^8 + 23566*x^9 + 1
812*x^10 + 68*x^11 + x^12)/(256 + 4096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 +
x^8))*(4096 + 81920*x + 693248*x^2 + 3407872*x^3 + 11917824*x^4 + 34328064*x^5 + 78478560*x^6 + 118319872*x^7
+ 97752008*x^8 + 40329056*x^9 + 7831044*x^10 + 802040*x^11 + 45152*x^12 + 1328*x^13 + 16*x^14))/(1024 + 20480
*x + 165120*x^2 + 675840*x^3 + 1434240*x^4 + 1383936*x^5 + 358560*x^6 + 42240*x^7 + 2580*x^8 + 80*x^9 + x^10),
x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.18, size = 44, normalized size = 1.69 \begin {gather*} 4 e^{\frac {x^2 \left (32+272 x+631 x^2+328 x^3+34 x^4+x^5\right )^2}{\left (4+16 x+x^2\right )^4}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((1024*x^2 + 17408*x^3 + 114368*x^4 + 364256*x^5 + 578769*x^6 + 432496*x^7 + 151036*x^8 + 23566*x
^9 + 1812*x^10 + 68*x^11 + x^12)/(256 + 4096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64
*x^7 + x^8))*(4096 + 81920*x + 693248*x^2 + 3407872*x^3 + 11917824*x^4 + 34328064*x^5 + 78478560*x^6 + 1183198
72*x^7 + 97752008*x^8 + 40329056*x^9 + 7831044*x^10 + 802040*x^11 + 45152*x^12 + 1328*x^13 + 16*x^14))/(1024 +
20480*x + 165120*x^2 + 675840*x^3 + 1434240*x^4 + 1383936*x^5 + 358560*x^6 + 42240*x^7 + 2580*x^8 + 80*x^9 +
x^10),x]

[Out]

4*E^((x^2*(32 + 272*x + 631*x^2 + 328*x^3 + 34*x^4 + x^5)^2)/(4 + 16*x + x^2)^4)*x

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fricas [B]  time = 0.65, size = 99, normalized size = 3.81 \begin {gather*} 4 \, x e^{\left (\frac {x^{12} + 68 \, x^{11} + 1812 \, x^{10} + 23566 \, x^{9} + 151036 \, x^{8} + 432496 \, x^{7} + 578769 \, x^{6} + 364256 \, x^{5} + 114368 \, x^{4} + 17408 \, x^{3} + 1024 \, x^{2}}{x^{8} + 64 \, x^{7} + 1552 \, x^{6} + 17152 \, x^{5} + 77920 \, x^{4} + 68608 \, x^{3} + 24832 \, x^{2} + 4096 \, x + 256}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^14+1328*x^13+45152*x^12+802040*x^11+7831044*x^10+40329056*x^9+97752008*x^8+118319872*x^7+78478
560*x^6+34328064*x^5+11917824*x^4+3407872*x^3+693248*x^2+81920*x+4096)*exp((x^12+68*x^11+1812*x^10+23566*x^9+1
51036*x^8+432496*x^7+578769*x^6+364256*x^5+114368*x^4+17408*x^3+1024*x^2)/(x^8+64*x^7+1552*x^6+17152*x^5+77920
*x^4+68608*x^3+24832*x^2+4096*x+256))/(x^10+80*x^9+2580*x^8+42240*x^7+358560*x^6+1383936*x^5+1434240*x^4+67584
0*x^3+165120*x^2+20480*x+1024),x, algorithm="fricas")

[Out]

4*x*e^((x^12 + 68*x^11 + 1812*x^10 + 23566*x^9 + 151036*x^8 + 432496*x^7 + 578769*x^6 + 364256*x^5 + 114368*x^
4 + 17408*x^3 + 1024*x^2)/(x^8 + 64*x^7 + 1552*x^6 + 17152*x^5 + 77920*x^4 + 68608*x^3 + 24832*x^2 + 4096*x +
256))

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giac [B]  time = 5.67, size = 99, normalized size = 3.81 \begin {gather*} 4 \, x e^{\left (\frac {x^{12} + 68 \, x^{11} + 1812 \, x^{10} + 23566 \, x^{9} + 151036 \, x^{8} + 432496 \, x^{7} + 578769 \, x^{6} + 364256 \, x^{5} + 114368 \, x^{4} + 17408 \, x^{3} + 1024 \, x^{2}}{x^{8} + 64 \, x^{7} + 1552 \, x^{6} + 17152 \, x^{5} + 77920 \, x^{4} + 68608 \, x^{3} + 24832 \, x^{2} + 4096 \, x + 256}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^14+1328*x^13+45152*x^12+802040*x^11+7831044*x^10+40329056*x^9+97752008*x^8+118319872*x^7+78478
560*x^6+34328064*x^5+11917824*x^4+3407872*x^3+693248*x^2+81920*x+4096)*exp((x^12+68*x^11+1812*x^10+23566*x^9+1
51036*x^8+432496*x^7+578769*x^6+364256*x^5+114368*x^4+17408*x^3+1024*x^2)/(x^8+64*x^7+1552*x^6+17152*x^5+77920
*x^4+68608*x^3+24832*x^2+4096*x+256))/(x^10+80*x^9+2580*x^8+42240*x^7+358560*x^6+1383936*x^5+1434240*x^4+67584
0*x^3+165120*x^2+20480*x+1024),x, algorithm="giac")

[Out]

4*x*e^((x^12 + 68*x^11 + 1812*x^10 + 23566*x^9 + 151036*x^8 + 432496*x^7 + 578769*x^6 + 364256*x^5 + 114368*x^
4 + 17408*x^3 + 1024*x^2)/(x^8 + 64*x^7 + 1552*x^6 + 17152*x^5 + 77920*x^4 + 68608*x^3 + 24832*x^2 + 4096*x +
256))

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maple [A]  time = 0.48, size = 44, normalized size = 1.69

method	result	size
risch	\(4 x \,{\mathrm e}^{\frac {x^{2} \left (x^{5}+34 x^{4}+328 x^{3}+631 x^{2}+272 x +32\right )^{2}}{\left (x^{2}+16 x +4\right )^{4}}}\)	\(44\)
gosper	\(4 x \,{\mathrm e}^{\frac {x^{2} \left (x^{10}+68 x^{9}+1812 x^{8}+23566 x^{7}+151036 x^{6}+432496 x^{5}+578769 x^{4}+364256 x^{3}+114368 x^{2}+17408 x +1024\right )}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}\)	\(97\)
norman	\(\frac {1024 x \,{\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+16384 x^{2} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+99328 x^{3} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+274432 x^{4} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+311680 x^{5} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+68608 x^{6} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+6208 x^{7} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+256 x^{8} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}+4 x^{9} {\mathrm e}^{\frac {x^{12}+68 x^{11}+1812 x^{10}+23566 x^{9}+151036 x^{8}+432496 x^{7}+578769 x^{6}+364256 x^{5}+114368 x^{4}+17408 x^{3}+1024 x^{2}}{x^{8}+64 x^{7}+1552 x^{6}+17152 x^{5}+77920 x^{4}+68608 x^{3}+24832 x^{2}+4096 x +256}}}{\left (x^{2}+16 x +4\right )^{4}}\)	\(920\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*x^14+1328*x^13+45152*x^12+802040*x^11+7831044*x^10+40329056*x^9+97752008*x^8+118319872*x^7+78478560*x^
6+34328064*x^5+11917824*x^4+3407872*x^3+693248*x^2+81920*x+4096)*exp((x^12+68*x^11+1812*x^10+23566*x^9+151036*
x^8+432496*x^7+578769*x^6+364256*x^5+114368*x^4+17408*x^3+1024*x^2)/(x^8+64*x^7+1552*x^6+17152*x^5+77920*x^4+6
8608*x^3+24832*x^2+4096*x+256))/(x^10+80*x^9+2580*x^8+42240*x^7+358560*x^6+1383936*x^5+1434240*x^4+675840*x^3+
165120*x^2+20480*x+1024),x,method=_RETURNVERBOSE)

[Out]

4*x*exp(x^2*(x^5+34*x^4+328*x^3+631*x^2+272*x+32)^2/(x^2+16*x+4)^4)

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maxima [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((16*x^14+1328*x^13+45152*x^12+802040*x^11+7831044*x^10+40329056*x^9+97752008*x^8+118319872*x^7+78478
560*x^6+34328064*x^5+11917824*x^4+3407872*x^3+693248*x^2+81920*x+4096)*exp((x^12+68*x^11+1812*x^10+23566*x^9+1
51036*x^8+432496*x^7+578769*x^6+364256*x^5+114368*x^4+17408*x^3+1024*x^2)/(x^8+64*x^7+1552*x^6+17152*x^5+77920
*x^4+68608*x^3+24832*x^2+4096*x+256))/(x^10+80*x^9+2580*x^8+42240*x^7+358560*x^6+1383936*x^5+1434240*x^4+67584
0*x^3+165120*x^2+20480*x+1024),x, algorithm="maxima")

[Out]

Timed out

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mupad [B]  time = 2.37, size = 508, normalized size = 19.54 \begin {gather*} 4\,x\,{\mathrm {e}}^{\frac {x^{12}}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {68\,x^{11}}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {1024\,x^2}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {1812\,x^{10}}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {17408\,x^3}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {23566\,x^9}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {114368\,x^4}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {151036\,x^8}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {364256\,x^5}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {432496\,x^7}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}}\,{\mathrm {e}}^{\frac {578769\,x^6}{x^8+64\,x^7+1552\,x^6+17152\,x^5+77920\,x^4+68608\,x^3+24832\,x^2+4096\,x+256}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((1024*x^2 + 17408*x^3 + 114368*x^4 + 364256*x^5 + 578769*x^6 + 432496*x^7 + 151036*x^8 + 23566*x^9 +
1812*x^10 + 68*x^11 + x^12)/(4096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8
+ 256))*(81920*x + 693248*x^2 + 3407872*x^3 + 11917824*x^4 + 34328064*x^5 + 78478560*x^6 + 118319872*x^7 + 977
52008*x^8 + 40329056*x^9 + 7831044*x^10 + 802040*x^11 + 45152*x^12 + 1328*x^13 + 16*x^14 + 4096))/(20480*x + 1
65120*x^2 + 675840*x^3 + 1434240*x^4 + 1383936*x^5 + 358560*x^6 + 42240*x^7 + 2580*x^8 + 80*x^9 + x^10 + 1024)
,x)

[Out]

4*x*exp(x^12/(4096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((68
*x^11)/(4096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((1024*x^2
)/(4096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((1812*x^10)/(4
096*x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((17408*x^3)/(4096*
x + 24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((23566*x^9)/(4096*x +
24832*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((114368*x^4)/(4096*x + 248
32*x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((151036*x^8)/(4096*x + 24832*
x^2 + 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((364256*x^5)/(4096*x + 24832*x^2
+ 68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((432496*x^7)/(4096*x + 24832*x^2 +
68608*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))*exp((578769*x^6)/(4096*x + 24832*x^2 + 686
08*x^3 + 77920*x^4 + 17152*x^5 + 1552*x^6 + 64*x^7 + x^8 + 256))

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sympy [B]  time = 0.67, size = 97, normalized size = 3.73 \begin {gather*} 4 x e^{\frac {x^{12} + 68 x^{11} + 1812 x^{10} + 23566 x^{9} + 151036 x^{8} + 432496 x^{7} + 578769 x^{6} + 364256 x^{5} + 114368 x^{4} + 17408 x^{3} + 1024 x^{2}}{x^{8} + 64 x^{7} + 1552 x^{6} + 17152 x^{5} + 77920 x^{4} + 68608 x^{3} + 24832 x^{2} + 4096 x + 256}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x**14+1328*x**13+45152*x**12+802040*x**11+7831044*x**10+40329056*x**9+97752008*x**8+118319872*x*
*7+78478560*x**6+34328064*x**5+11917824*x**4+3407872*x**3+693248*x**2+81920*x+4096)*exp((x**12+68*x**11+1812*x
**10+23566*x**9+151036*x**8+432496*x**7+578769*x**6+364256*x**5+114368*x**4+17408*x**3+1024*x**2)/(x**8+64*x**
7+1552*x**6+17152*x**5+77920*x**4+68608*x**3+24832*x**2+4096*x+256))/(x**10+80*x**9+2580*x**8+42240*x**7+35856
0*x**6+1383936*x**5+1434240*x**4+675840*x**3+165120*x**2+20480*x+1024),x)

[Out]

4*x*exp((x**12 + 68*x**11 + 1812*x**10 + 23566*x**9 + 151036*x**8 + 432496*x**7 + 578769*x**6 + 364256*x**5 +
114368*x**4 + 17408*x**3 + 1024*x**2)/(x**8 + 64*x**7 + 1552*x**6 + 17152*x**5 + 77920*x**4 + 68608*x**3 + 248
32*x**2 + 4096*x + 256))

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