3.6.95 \(\int \frac {e^{\frac {41958+104976 x+122472 x^2+81648 x^3+34020 x^4+9072 x^5+1512 x^6+144 x^7+6 x^8}{19683 x+52488 x^2+61236 x^3+40824 x^4+17010 x^5+4536 x^6+756 x^7+72 x^8+3 x^9+e^{2 x} (6561 x+17496 x^2+20412 x^3+13608 x^4+5670 x^5+1512 x^6+252 x^7+24 x^8+x^9)}} (-377622-1132866 x-1417176 x^2-1102248 x^3-551124 x^4-183708 x^5-40824 x^6-5832 x^7-486 x^8-18 x^9+e^{2 x} (-125874-629370 x-1186164 x^2-1312200 x^3-918540 x^4-428652 x^5-136080 x^6-29160 x^7-4050 x^8-330 x^9-12 x^{10}))}{177147 x^2+531441 x^3+708588 x^4+551124 x^5+275562 x^6+91854 x^7+20412 x^8+2916 x^9+243 x^{10}+9 x^{11}+e^{4 x} (19683 x^2+59049 x^3+78732 x^4+61236 x^5+30618 x^6+10206 x^7+2268 x^8+324 x^9+27 x^{10}+x^{11})+e^{2 x} (118098 x^2+354294 x^3+472392 x^4+367416 x^5+183708 x^6+61236 x^7+13608 x^8+1944 x^9+162 x^{10}+6 x^{11})} \, dx\)

Optimal. Leaf size=25 \[ e^{\frac {2 \left (3+\frac {1296}{(3+x)^8}\right )}{\left (3+e^{2 x}\right ) x}} \]

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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^((41958 + 104976*x + 122472*x^2 + 81648*x^3 + 34020*x^4 + 9072*x^5 + 1512*x^6 + 144*x^7 + 6*x^8)/(19683
*x + 52488*x^2 + 61236*x^3 + 40824*x^4 + 17010*x^5 + 4536*x^6 + 756*x^7 + 72*x^8 + 3*x^9 + E^(2*x)*(6561*x + 1
7496*x^2 + 20412*x^3 + 13608*x^4 + 5670*x^5 + 1512*x^6 + 252*x^7 + 24*x^8 + x^9)))*(-377622 - 1132866*x - 1417
176*x^2 - 1102248*x^3 - 551124*x^4 - 183708*x^5 - 40824*x^6 - 5832*x^7 - 486*x^8 - 18*x^9 + E^(2*x)*(-125874 -
629370*x - 1186164*x^2 - 1312200*x^3 - 918540*x^4 - 428652*x^5 - 136080*x^6 - 29160*x^7 - 4050*x^8 - 330*x^9
- 12*x^10)))/(177147*x^2 + 531441*x^3 + 708588*x^4 + 551124*x^5 + 275562*x^6 + 91854*x^7 + 20412*x^8 + 2916*x^
9 + 243*x^10 + 9*x^11 + E^(4*x)*(19683*x^2 + 59049*x^3 + 78732*x^4 + 61236*x^5 + 30618*x^6 + 10206*x^7 + 2268*
x^8 + 324*x^9 + 27*x^10 + x^11) + E^(2*x)*(118098*x^2 + 354294*x^3 + 472392*x^4 + 367416*x^5 + 183708*x^6 + 61
236*x^7 + 13608*x^8 + 1944*x^9 + 162*x^10 + 6*x^11)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.48, size = 59, normalized size = 2.36 \begin {gather*} e^{\frac {6 \left (6993+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8\right )}{\left (3+e^{2 x}\right ) x (3+x)^8}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((41958 + 104976*x + 122472*x^2 + 81648*x^3 + 34020*x^4 + 9072*x^5 + 1512*x^6 + 144*x^7 + 6*x^8)/
(19683*x + 52488*x^2 + 61236*x^3 + 40824*x^4 + 17010*x^5 + 4536*x^6 + 756*x^7 + 72*x^8 + 3*x^9 + E^(2*x)*(6561
*x + 17496*x^2 + 20412*x^3 + 13608*x^4 + 5670*x^5 + 1512*x^6 + 252*x^7 + 24*x^8 + x^9)))*(-377622 - 1132866*x
- 1417176*x^2 - 1102248*x^3 - 551124*x^4 - 183708*x^5 - 40824*x^6 - 5832*x^7 - 486*x^8 - 18*x^9 + E^(2*x)*(-12
5874 - 629370*x - 1186164*x^2 - 1312200*x^3 - 918540*x^4 - 428652*x^5 - 136080*x^6 - 29160*x^7 - 4050*x^8 - 33
0*x^9 - 12*x^10)))/(177147*x^2 + 531441*x^3 + 708588*x^4 + 551124*x^5 + 275562*x^6 + 91854*x^7 + 20412*x^8 + 2
916*x^9 + 243*x^10 + 9*x^11 + E^(4*x)*(19683*x^2 + 59049*x^3 + 78732*x^4 + 61236*x^5 + 30618*x^6 + 10206*x^7 +
2268*x^8 + 324*x^9 + 27*x^10 + x^11) + E^(2*x)*(118098*x^2 + 354294*x^3 + 472392*x^4 + 367416*x^5 + 183708*x^
6 + 61236*x^7 + 13608*x^8 + 1944*x^9 + 162*x^10 + 6*x^11)),x]

[Out]

E^((6*(6993 + 17496*x + 20412*x^2 + 13608*x^3 + 5670*x^4 + 1512*x^5 + 252*x^6 + 24*x^7 + x^8))/((3 + E^(2*x))*
x*(3 + x)^8))

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fricas [B]  time = 0.74, size = 134, normalized size = 5.36 \begin {gather*} e^{\left (\frac {6 \, {\left (x^{8} + 24 \, x^{7} + 252 \, x^{6} + 1512 \, x^{5} + 5670 \, x^{4} + 13608 \, x^{3} + 20412 \, x^{2} + 17496 \, x + 6993\right )}}{3 \, x^{9} + 72 \, x^{8} + 756 \, x^{7} + 4536 \, x^{6} + 17010 \, x^{5} + 40824 \, x^{4} + 61236 \, x^{3} + 52488 \, x^{2} + {\left (x^{9} + 24 \, x^{8} + 252 \, x^{7} + 1512 \, x^{6} + 5670 \, x^{5} + 13608 \, x^{4} + 20412 \, x^{3} + 17496 \, x^{2} + 6561 \, x\right )} e^{\left (2 \, x\right )} + 19683 \, x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x^10-330*x^9-4050*x^8-29160*x^7-136080*x^6-428652*x^5-918540*x^4-1312200*x^3-1186164*x^2-62937
0*x-125874)*exp(x)^2-18*x^9-486*x^8-5832*x^7-40824*x^6-183708*x^5-551124*x^4-1102248*x^3-1417176*x^2-1132866*x
-377622)*exp((6*x^8+144*x^7+1512*x^6+9072*x^5+34020*x^4+81648*x^3+122472*x^2+104976*x+41958)/((x^9+24*x^8+252*
x^7+1512*x^6+5670*x^5+13608*x^4+20412*x^3+17496*x^2+6561*x)*exp(x)^2+3*x^9+72*x^8+756*x^7+4536*x^6+17010*x^5+4
0824*x^4+61236*x^3+52488*x^2+19683*x))/((x^11+27*x^10+324*x^9+2268*x^8+10206*x^7+30618*x^6+61236*x^5+78732*x^4
+59049*x^3+19683*x^2)*exp(x)^4+(6*x^11+162*x^10+1944*x^9+13608*x^8+61236*x^7+183708*x^6+367416*x^5+472392*x^4+
354294*x^3+118098*x^2)*exp(x)^2+9*x^11+243*x^10+2916*x^9+20412*x^8+91854*x^7+275562*x^6+551124*x^5+708588*x^4+
531441*x^3+177147*x^2),x, algorithm="fricas")

[Out]

e^(6*(x^8 + 24*x^7 + 252*x^6 + 1512*x^5 + 5670*x^4 + 13608*x^3 + 20412*x^2 + 17496*x + 6993)/(3*x^9 + 72*x^8 +
756*x^7 + 4536*x^6 + 17010*x^5 + 40824*x^4 + 61236*x^3 + 52488*x^2 + (x^9 + 24*x^8 + 252*x^7 + 1512*x^6 + 567
0*x^5 + 13608*x^4 + 20412*x^3 + 17496*x^2 + 6561*x)*e^(2*x) + 19683*x))

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x^10-330*x^9-4050*x^8-29160*x^7-136080*x^6-428652*x^5-918540*x^4-1312200*x^3-1186164*x^2-62937
0*x-125874)*exp(x)^2-18*x^9-486*x^8-5832*x^7-40824*x^6-183708*x^5-551124*x^4-1102248*x^3-1417176*x^2-1132866*x
-377622)*exp((6*x^8+144*x^7+1512*x^6+9072*x^5+34020*x^4+81648*x^3+122472*x^2+104976*x+41958)/((x^9+24*x^8+252*
x^7+1512*x^6+5670*x^5+13608*x^4+20412*x^3+17496*x^2+6561*x)*exp(x)^2+3*x^9+72*x^8+756*x^7+4536*x^6+17010*x^5+4
0824*x^4+61236*x^3+52488*x^2+19683*x))/((x^11+27*x^10+324*x^9+2268*x^8+10206*x^7+30618*x^6+61236*x^5+78732*x^4
+59049*x^3+19683*x^2)*exp(x)^4+(6*x^11+162*x^10+1944*x^9+13608*x^8+61236*x^7+183708*x^6+367416*x^5+472392*x^4+
354294*x^3+118098*x^2)*exp(x)^2+9*x^11+243*x^10+2916*x^9+20412*x^8+91854*x^7+275562*x^6+551124*x^5+708588*x^4+
531441*x^3+177147*x^2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 38.9Unable to divide, perhaps due to rounding error%%%{-864,[1,61]%%%}+%%%{-140832,[1,60]%
%%}+%%%{-11

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maple [B]  time = 0.86, size = 58, normalized size = 2.32

method	result	size
risch	\({\mathrm e}^{\frac {6 x^{8}+144 x^{7}+1512 x^{6}+9072 x^{5}+34020 x^{4}+81648 x^{3}+122472 x^{2}+104976 x +41958}{x \left (3+x \right )^{8} \left ({\mathrm e}^{2 x}+3\right )}}\)	\(58\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-12*x^10-330*x^9-4050*x^8-29160*x^7-136080*x^6-428652*x^5-918540*x^4-1312200*x^3-1186164*x^2-629370*x-12
5874)*exp(x)^2-18*x^9-486*x^8-5832*x^7-40824*x^6-183708*x^5-551124*x^4-1102248*x^3-1417176*x^2-1132866*x-37762
2)*exp((6*x^8+144*x^7+1512*x^6+9072*x^5+34020*x^4+81648*x^3+122472*x^2+104976*x+41958)/((x^9+24*x^8+252*x^7+15
12*x^6+5670*x^5+13608*x^4+20412*x^3+17496*x^2+6561*x)*exp(x)^2+3*x^9+72*x^8+756*x^7+4536*x^6+17010*x^5+40824*x
^4+61236*x^3+52488*x^2+19683*x))/((x^11+27*x^10+324*x^9+2268*x^8+10206*x^7+30618*x^6+61236*x^5+78732*x^4+59049
*x^3+19683*x^2)*exp(x)^4+(6*x^11+162*x^10+1944*x^9+13608*x^8+61236*x^7+183708*x^6+367416*x^5+472392*x^4+354294
*x^3+118098*x^2)*exp(x)^2+9*x^11+243*x^10+2916*x^9+20412*x^8+91854*x^7+275562*x^6+551124*x^5+708588*x^4+531441
*x^3+177147*x^2),x,method=_RETURNVERBOSE)

[Out]

exp(6*(x^8+24*x^7+252*x^6+1512*x^5+5670*x^4+13608*x^3+20412*x^2+17496*x+6993)/x/(3+x)^8/(exp(2*x)+3))

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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(((-12*x^10-330*x^9-4050*x^8-29160*x^7-136080*x^6-428652*x^5-918540*x^4-1312200*x^3-1186164*x^2-62937
0*x-125874)*exp(x)^2-18*x^9-486*x^8-5832*x^7-40824*x^6-183708*x^5-551124*x^4-1102248*x^3-1417176*x^2-1132866*x
-377622)*exp((6*x^8+144*x^7+1512*x^6+9072*x^5+34020*x^4+81648*x^3+122472*x^2+104976*x+41958)/((x^9+24*x^8+252*
x^7+1512*x^6+5670*x^5+13608*x^4+20412*x^3+17496*x^2+6561*x)*exp(x)^2+3*x^9+72*x^8+756*x^7+4536*x^6+17010*x^5+4
0824*x^4+61236*x^3+52488*x^2+19683*x))/((x^11+27*x^10+324*x^9+2268*x^8+10206*x^7+30618*x^6+61236*x^5+78732*x^4
+59049*x^3+19683*x^2)*exp(x)^4+(6*x^11+162*x^10+1944*x^9+13608*x^8+61236*x^7+183708*x^6+367416*x^5+472392*x^4+
354294*x^3+118098*x^2)*exp(x)^2+9*x^11+243*x^10+2916*x^9+20412*x^8+91854*x^7+275562*x^6+551124*x^5+708588*x^4+
531441*x^3+177147*x^2),x, algorithm="maxima")

[Out]

Timed out

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mupad [B]  time = 1.51, size = 1107, normalized size = 44.28 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((104976*x + 122472*x^2 + 81648*x^3 + 34020*x^4 + 9072*x^5 + 1512*x^6 + 144*x^7 + 6*x^8 + 41958)/(196
83*x + exp(2*x)*(6561*x + 17496*x^2 + 20412*x^3 + 13608*x^4 + 5670*x^5 + 1512*x^6 + 252*x^7 + 24*x^8 + x^9) +
52488*x^2 + 61236*x^3 + 40824*x^4 + 17010*x^5 + 4536*x^6 + 756*x^7 + 72*x^8 + 3*x^9))*(1132866*x + exp(2*x)*(6
29370*x + 1186164*x^2 + 1312200*x^3 + 918540*x^4 + 428652*x^5 + 136080*x^6 + 29160*x^7 + 4050*x^8 + 330*x^9 +
12*x^10 + 125874) + 1417176*x^2 + 1102248*x^3 + 551124*x^4 + 183708*x^5 + 40824*x^6 + 5832*x^7 + 486*x^8 + 18*
x^9 + 377622))/(exp(2*x)*(118098*x^2 + 354294*x^3 + 472392*x^4 + 367416*x^5 + 183708*x^6 + 61236*x^7 + 13608*x
^8 + 1944*x^9 + 162*x^10 + 6*x^11) + exp(4*x)*(19683*x^2 + 59049*x^3 + 78732*x^4 + 61236*x^5 + 30618*x^6 + 102
06*x^7 + 2268*x^8 + 324*x^9 + 27*x^10 + x^11) + 177147*x^2 + 531441*x^3 + 708588*x^4 + 551124*x^5 + 275562*x^6
+ 91854*x^7 + 20412*x^8 + 2916*x^9 + 243*x^10 + 9*x^11),x)

[Out]

exp((122472*x)/(52488*x + 6561*exp(2*x) + 17496*x*exp(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 5670*x^
4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x) + 24*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3 + 1
7010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 + 19683))*exp((6*x^7)/(52488*x + 6561*exp(2*x) + 17496*x*exp(2*
x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 5670*x^4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x) + 24*x
^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3 + 17010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 + 19683))
*exp((144*x^6)/(52488*x + 6561*exp(2*x) + 17496*x*exp(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 5670*x^
4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x) + 24*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3 + 1
7010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 + 19683))*exp((1512*x^5)/(52488*x + 6561*exp(2*x) + 17496*x*exp
(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 5670*x^4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x) + 2
4*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3 + 17010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 + 1968
3))*exp((9072*x^4)/(52488*x + 6561*exp(2*x) + 17496*x*exp(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 567
0*x^4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x) + 24*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3
+ 17010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 + 19683))*exp((34020*x^3)/(52488*x + 6561*exp(2*x) + 17496*
x*exp(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 5670*x^4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x
) + 24*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3 + 17010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 +
19683))*exp((81648*x^2)/(52488*x + 6561*exp(2*x) + 17496*x*exp(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x)
+ 5670*x^4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*x) + 24*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 408
24*x^3 + 17010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8 + 19683))*exp(104976/(52488*x + 6561*exp(2*x) + 17496
*x*exp(2*x) + 20412*x^2*exp(2*x) + 13608*x^3*exp(2*x) + 5670*x^4*exp(2*x) + 1512*x^5*exp(2*x) + 252*x^6*exp(2*
x) + 24*x^7*exp(2*x) + x^8*exp(2*x) + 61236*x^2 + 40824*x^3 + 17010*x^4 + 4536*x^5 + 756*x^6 + 72*x^7 + 3*x^8
+ 19683))*exp(41958/(19683*x + 6561*x*exp(2*x) + 17496*x^2*exp(2*x) + 20412*x^3*exp(2*x) + 13608*x^4*exp(2*x)
+ 5670*x^5*exp(2*x) + 1512*x^6*exp(2*x) + 252*x^7*exp(2*x) + 24*x^8*exp(2*x) + x^9*exp(2*x) + 52488*x^2 + 6123
6*x^3 + 40824*x^4 + 17010*x^5 + 4536*x^6 + 756*x^7 + 72*x^8 + 3*x^9))

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sympy [B]  time = 4.02, size = 133, normalized size = 5.32 \begin {gather*} e^{\frac {6 x^{8} + 144 x^{7} + 1512 x^{6} + 9072 x^{5} + 34020 x^{4} + 81648 x^{3} + 122472 x^{2} + 104976 x + 41958}{3 x^{9} + 72 x^{8} + 756 x^{7} + 4536 x^{6} + 17010 x^{5} + 40824 x^{4} + 61236 x^{3} + 52488 x^{2} + 19683 x + \left (x^{9} + 24 x^{8} + 252 x^{7} + 1512 x^{6} + 5670 x^{5} + 13608 x^{4} + 20412 x^{3} + 17496 x^{2} + 6561 x\right ) e^{2 x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x**10-330*x**9-4050*x**8-29160*x**7-136080*x**6-428652*x**5-918540*x**4-1312200*x**3-1186164*x
**2-629370*x-125874)*exp(x)**2-18*x**9-486*x**8-5832*x**7-40824*x**6-183708*x**5-551124*x**4-1102248*x**3-1417
176*x**2-1132866*x-377622)*exp((6*x**8+144*x**7+1512*x**6+9072*x**5+34020*x**4+81648*x**3+122472*x**2+104976*x
+41958)/((x**9+24*x**8+252*x**7+1512*x**6+5670*x**5+13608*x**4+20412*x**3+17496*x**2+6561*x)*exp(x)**2+3*x**9+
72*x**8+756*x**7+4536*x**6+17010*x**5+40824*x**4+61236*x**3+52488*x**2+19683*x))/((x**11+27*x**10+324*x**9+226
8*x**8+10206*x**7+30618*x**6+61236*x**5+78732*x**4+59049*x**3+19683*x**2)*exp(x)**4+(6*x**11+162*x**10+1944*x*
*9+13608*x**8+61236*x**7+183708*x**6+367416*x**5+472392*x**4+354294*x**3+118098*x**2)*exp(x)**2+9*x**11+243*x*
*10+2916*x**9+20412*x**8+91854*x**7+275562*x**6+551124*x**5+708588*x**4+531441*x**3+177147*x**2),x)

[Out]

exp((6*x**8 + 144*x**7 + 1512*x**6 + 9072*x**5 + 34020*x**4 + 81648*x**3 + 122472*x**2 + 104976*x + 41958)/(3*
x**9 + 72*x**8 + 756*x**7 + 4536*x**6 + 17010*x**5 + 40824*x**4 + 61236*x**3 + 52488*x**2 + 19683*x + (x**9 +
24*x**8 + 252*x**7 + 1512*x**6 + 5670*x**5 + 13608*x**4 + 20412*x**3 + 17496*x**2 + 6561*x)*exp(2*x)))

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