3.36.33 \(\int \frac {e^{\frac {92416-184832 x^2-92416 x^3+138624 x^4+138624 x^5-11552 x^6-69312 x^7-28880 x^8+5776 x^9+8664 x^{10}+2888 x^{11}+361 x^{12}+e (-9728+19456 x^2+9728 x^3-14592 x^4-14592 x^5+1216 x^6+7296 x^7+3040 x^8-608 x^9-912 x^{10}-304 x^{11}-38 x^{12})+e^2 (256-512 x^2-256 x^3+384 x^4+384 x^5-32 x^6-192 x^7-80 x^8+16 x^9+24 x^{10}+8 x^{11}+x^{12})}{x^4}} (-369664+369664 x^2+92416 x^3+138624 x^5-23104 x^6-207936 x^7-115520 x^8+28880 x^9+51984 x^{10}+20216 x^{11}+2888 x^{12}+e (38912-38912 x^2-9728 x^3-14592 x^5+2432 x^6+21888 x^7+12160 x^8-3040 x^9-5472 x^{10}-2128 x^{11}-304 x^{12})+e^2 (-1024+1024 x^2+256 x^3+384 x^5-64 x^6-576 x^7-320 x^8+80 x^9+144 x^{10}+56 x^{11}+8 x^{12}))}{x^5} \, dx\)
Optimal. Leaf size=21 \[ e^{(-19+e)^2 x^4 \left (2-\frac {4}{x^2}+x\right )^4} \]
________________________________________________________________________________________
Rubi [A] time = 145.55, antiderivative size = 27, normalized size of antiderivative = 1.29,
number of steps used = 3, number of rules used = 3, integrand size = 347, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used
= {6688, 12, 6706} \begin {gather*} e^{\frac {(19-e)^2 \left (-x^3-2 x^2+4\right )^4}{x^4}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(E^((92416 - 184832*x^2 - 92416*x^3 + 138624*x^4 + 138624*x^5 - 11552*x^6 - 69312*x^7 - 28880*x^8 + 5776*x
^9 + 8664*x^10 + 2888*x^11 + 361*x^12 + E*(-9728 + 19456*x^2 + 9728*x^3 - 14592*x^4 - 14592*x^5 + 1216*x^6 + 7
296*x^7 + 3040*x^8 - 608*x^9 - 912*x^10 - 304*x^11 - 38*x^12) + E^2*(256 - 512*x^2 - 256*x^3 + 384*x^4 + 384*x
^5 - 32*x^6 - 192*x^7 - 80*x^8 + 16*x^9 + 24*x^10 + 8*x^11 + x^12))/x^4)*(-369664 + 369664*x^2 + 92416*x^3 + 1
38624*x^5 - 23104*x^6 - 207936*x^7 - 115520*x^8 + 28880*x^9 + 51984*x^10 + 20216*x^11 + 2888*x^12 + E*(38912 -
38912*x^2 - 9728*x^3 - 14592*x^5 + 2432*x^6 + 21888*x^7 + 12160*x^8 - 3040*x^9 - 5472*x^10 - 2128*x^11 - 304*
x^12) + E^2*(-1024 + 1024*x^2 + 256*x^3 + 384*x^5 - 64*x^6 - 576*x^7 - 320*x^8 + 80*x^9 + 144*x^10 + 56*x^11 +
8*x^12)))/x^5,x]
[Out]
E^(((19 - E)^2*(4 - 2*x^2 - x^3)^4)/x^4)
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 6688
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rule 6706
Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /; !FalseQ[q]
] /; FreeQ[F, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 (19-e)^2 e^{\frac {(-19+e)^2 \left (-4+2 x^2+x^3\right )^4}{x^4}} \left (4-2 x^2-x^3\right )^3 \left (-2-x^2-x^3\right )}{x^5} \, dx\\ &=\left (8 (19-e)^2\right ) \int \frac {e^{\frac {(-19+e)^2 \left (-4+2 x^2+x^3\right )^4}{x^4}} \left (4-2 x^2-x^3\right )^3 \left (-2-x^2-x^3\right )}{x^5} \, dx\\ &=e^{\frac {(19-e)^2 \left (4-2 x^2-x^3\right )^4}{x^4}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 6.26, size = 23, normalized size = 1.10 \begin {gather*} e^{\frac {(-19+e)^2 \left (-4+2 x^2+x^3\right )^4}{x^4}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^((92416 - 184832*x^2 - 92416*x^3 + 138624*x^4 + 138624*x^5 - 11552*x^6 - 69312*x^7 - 28880*x^8 +
5776*x^9 + 8664*x^10 + 2888*x^11 + 361*x^12 + E*(-9728 + 19456*x^2 + 9728*x^3 - 14592*x^4 - 14592*x^5 + 1216*x
^6 + 7296*x^7 + 3040*x^8 - 608*x^9 - 912*x^10 - 304*x^11 - 38*x^12) + E^2*(256 - 512*x^2 - 256*x^3 + 384*x^4 +
384*x^5 - 32*x^6 - 192*x^7 - 80*x^8 + 16*x^9 + 24*x^10 + 8*x^11 + x^12))/x^4)*(-369664 + 369664*x^2 + 92416*x
^3 + 138624*x^5 - 23104*x^6 - 207936*x^7 - 115520*x^8 + 28880*x^9 + 51984*x^10 + 20216*x^11 + 2888*x^12 + E*(3
8912 - 38912*x^2 - 9728*x^3 - 14592*x^5 + 2432*x^6 + 21888*x^7 + 12160*x^8 - 3040*x^9 - 5472*x^10 - 2128*x^11
- 304*x^12) + E^2*(-1024 + 1024*x^2 + 256*x^3 + 384*x^5 - 64*x^6 - 576*x^7 - 320*x^8 + 80*x^9 + 144*x^10 + 56*
x^11 + 8*x^12)))/x^5,x]
[Out]
E^(((-19 + E)^2*(-4 + 2*x^2 + x^3)^4)/x^4)
________________________________________________________________________________________
fricas [B] time = 0.90, size = 179, normalized size = 8.52 \begin {gather*} e^{\left (\frac {361 \, x^{12} + 2888 \, x^{11} + 8664 \, x^{10} + 5776 \, x^{9} - 28880 \, x^{8} - 69312 \, x^{7} - 11552 \, x^{6} + 138624 \, x^{5} + 138624 \, x^{4} - 92416 \, x^{3} - 184832 \, x^{2} + {\left (x^{12} + 8 \, x^{11} + 24 \, x^{10} + 16 \, x^{9} - 80 \, x^{8} - 192 \, x^{7} - 32 \, x^{6} + 384 \, x^{5} + 384 \, x^{4} - 256 \, x^{3} - 512 \, x^{2} + 256\right )} e^{2} - 38 \, {\left (x^{12} + 8 \, x^{11} + 24 \, x^{10} + 16 \, x^{9} - 80 \, x^{8} - 192 \, x^{7} - 32 \, x^{6} + 384 \, x^{5} + 384 \, x^{4} - 256 \, x^{3} - 512 \, x^{2} + 256\right )} e + 92416}{x^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x^12+56*x^11+144*x^10+80*x^9-320*x^8-576*x^7-64*x^6+384*x^5+256*x^3+1024*x^2-1024)*exp(1)^2+(-30
4*x^12-2128*x^11-5472*x^10-3040*x^9+12160*x^8+21888*x^7+2432*x^6-14592*x^5-9728*x^3-38912*x^2+38912)*exp(1)+28
88*x^12+20216*x^11+51984*x^10+28880*x^9-115520*x^8-207936*x^7-23104*x^6+138624*x^5+92416*x^3+369664*x^2-369664
)*exp(((x^12+8*x^11+24*x^10+16*x^9-80*x^8-192*x^7-32*x^6+384*x^5+384*x^4-256*x^3-512*x^2+256)*exp(1)^2+(-38*x^
12-304*x^11-912*x^10-608*x^9+3040*x^8+7296*x^7+1216*x^6-14592*x^5-14592*x^4+9728*x^3+19456*x^2-9728)*exp(1)+36
1*x^12+2888*x^11+8664*x^10+5776*x^9-28880*x^8-69312*x^7-11552*x^6+138624*x^5+138624*x^4-92416*x^3-184832*x^2+9
2416)/x^4)/x^5,x, algorithm="fricas")
[Out]
e^((361*x^12 + 2888*x^11 + 8664*x^10 + 5776*x^9 - 28880*x^8 - 69312*x^7 - 11552*x^6 + 138624*x^5 + 138624*x^4
- 92416*x^3 - 184832*x^2 + (x^12 + 8*x^11 + 24*x^10 + 16*x^9 - 80*x^8 - 192*x^7 - 32*x^6 + 384*x^5 + 384*x^4 -
256*x^3 - 512*x^2 + 256)*e^2 - 38*(x^12 + 8*x^11 + 24*x^10 + 16*x^9 - 80*x^8 - 192*x^7 - 32*x^6 + 384*x^5 + 3
84*x^4 - 256*x^3 - 512*x^2 + 256)*e + 92416)/x^4)
________________________________________________________________________________________
giac [B] time = 0.22, size = 213, normalized size = 10.14 \begin {gather*} e^{\left (x^{8} e^{2} - 38 \, x^{8} e + 361 \, x^{8} + 8 \, x^{7} e^{2} - 304 \, x^{7} e + 2888 \, x^{7} + 24 \, x^{6} e^{2} - 912 \, x^{6} e + 8664 \, x^{6} + 16 \, x^{5} e^{2} - 608 \, x^{5} e + 5776 \, x^{5} - 80 \, x^{4} e^{2} + 3040 \, x^{4} e - 28880 \, x^{4} - 192 \, x^{3} e^{2} + 7296 \, x^{3} e - 69312 \, x^{3} - 32 \, x^{2} e^{2} + 1216 \, x^{2} e - 11552 \, x^{2} + 384 \, x e^{2} - 14592 \, x e + 138624 \, x - \frac {256 \, e^{2}}{x} + \frac {9728 \, e}{x} - \frac {92416}{x} - \frac {512 \, e^{2}}{x^{2}} + \frac {19456 \, e}{x^{2}} - \frac {184832}{x^{2}} + \frac {256 \, e^{2}}{x^{4}} - \frac {9728 \, e}{x^{4}} + \frac {92416}{x^{4}} + 384 \, e^{2} - 14592 \, e + 138624\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x^12+56*x^11+144*x^10+80*x^9-320*x^8-576*x^7-64*x^6+384*x^5+256*x^3+1024*x^2-1024)*exp(1)^2+(-30
4*x^12-2128*x^11-5472*x^10-3040*x^9+12160*x^8+21888*x^7+2432*x^6-14592*x^5-9728*x^3-38912*x^2+38912)*exp(1)+28
88*x^12+20216*x^11+51984*x^10+28880*x^9-115520*x^8-207936*x^7-23104*x^6+138624*x^5+92416*x^3+369664*x^2-369664
)*exp(((x^12+8*x^11+24*x^10+16*x^9-80*x^8-192*x^7-32*x^6+384*x^5+384*x^4-256*x^3-512*x^2+256)*exp(1)^2+(-38*x^
12-304*x^11-912*x^10-608*x^9+3040*x^8+7296*x^7+1216*x^6-14592*x^5-14592*x^4+9728*x^3+19456*x^2-9728)*exp(1)+36
1*x^12+2888*x^11+8664*x^10+5776*x^9-28880*x^8-69312*x^7-11552*x^6+138624*x^5+138624*x^4-92416*x^3-184832*x^2+9
2416)/x^4)/x^5,x, algorithm="giac")
[Out]
e^(x^8*e^2 - 38*x^8*e + 361*x^8 + 8*x^7*e^2 - 304*x^7*e + 2888*x^7 + 24*x^6*e^2 - 912*x^6*e + 8664*x^6 + 16*x^
5*e^2 - 608*x^5*e + 5776*x^5 - 80*x^4*e^2 + 3040*x^4*e - 28880*x^4 - 192*x^3*e^2 + 7296*x^3*e - 69312*x^3 - 32
*x^2*e^2 + 1216*x^2*e - 11552*x^2 + 384*x*e^2 - 14592*x*e + 138624*x - 256*e^2/x + 9728*e/x - 92416/x - 512*e^
2/x^2 + 19456*e/x^2 - 184832/x^2 + 256*e^2/x^4 - 9728*e/x^4 + 92416/x^4 + 384*e^2 - 14592*e + 138624)
________________________________________________________________________________________
maple [B] time = 0.02, size = 248, normalized size = 11.81 \[{\mathrm e}^{\frac {92416+384 \,{\mathrm e}^{2} x^{5}+3040 x^{8} {\mathrm e}+7296 x^{7} {\mathrm e}-9728 \,{\mathrm e}+2888 x^{11}+361 x^{12}-69312 x^{7}-28880 x^{8}+8664 x^{10}+5776 x^{9}+256 \,{\mathrm e}^{2}-11552 x^{6}+138624 x^{5}+138624 x^{4}-92416 x^{3}-184832 x^{2}-32 x^{6} {\mathrm e}^{2}-80 x^{8} {\mathrm e}^{2}-14592 x^{5} {\mathrm e}-256 x^{3} {\mathrm e}^{2}-512 x^{2} {\mathrm e}^{2}+384 x^{4} {\mathrm e}^{2}+19456 x^{2} {\mathrm e}+9728 x^{3} {\mathrm e}-14592 x^{4} {\mathrm e}-38 \,{\mathrm e} x^{12}-304 \,{\mathrm e} x^{11}-912 \,{\mathrm e} x^{10}-608 \,{\mathrm e} x^{9}-192 \,{\mathrm e}^{2} x^{7}+1216 x^{6} {\mathrm e}+{\mathrm e}^{2} x^{12}+8 \,{\mathrm e}^{2} x^{11}+24 \,{\mathrm e}^{2} x^{10}+16 \,{\mathrm e}^{2} x^{9}}{x^{4}}}\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((8*x^12+56*x^11+144*x^10+80*x^9-320*x^8-576*x^7-64*x^6+384*x^5+256*x^3+1024*x^2-1024)*exp(1)^2+(-304*x^12
-2128*x^11-5472*x^10-3040*x^9+12160*x^8+21888*x^7+2432*x^6-14592*x^5-9728*x^3-38912*x^2+38912)*exp(1)+2888*x^1
2+20216*x^11+51984*x^10+28880*x^9-115520*x^8-207936*x^7-23104*x^6+138624*x^5+92416*x^3+369664*x^2-369664)*exp(
((x^12+8*x^11+24*x^10+16*x^9-80*x^8-192*x^7-32*x^6+384*x^5+384*x^4-256*x^3-512*x^2+256)*exp(1)^2+(-38*x^12-304
*x^11-912*x^10-608*x^9+3040*x^8+7296*x^7+1216*x^6-14592*x^5-14592*x^4+9728*x^3+19456*x^2-9728)*exp(1)+361*x^12
+2888*x^11+8664*x^10+5776*x^9-28880*x^8-69312*x^7-11552*x^6+138624*x^5+138624*x^4-92416*x^3-184832*x^2+92416)/
x^4)/x^5,x)
[Out]
exp((92416+3040*x^8*exp(1)+7296*x^7*exp(1)-9728*exp(1)+2888*x^11+361*x^12+256*exp(1)^2-69312*x^7-28880*x^8+866
4*x^10+5776*x^9-11552*x^6+138624*x^5+138624*x^4-92416*x^3-184832*x^2-14592*x^5*exp(1)-256*x^3*exp(1)^2+384*x^4
*exp(1)^2-512*x^2*exp(1)^2+19456*x^2*exp(1)+9728*x^3*exp(1)-32*x^6*exp(1)^2-14592*x^4*exp(1)-80*x^8*exp(1)^2-1
92*exp(1)^2*x^7+exp(1)^2*x^12+8*exp(1)^2*x^11-38*exp(1)*x^12+24*exp(1)^2*x^10-304*exp(1)*x^11+16*exp(1)^2*x^9-
912*exp(1)*x^10-608*exp(1)*x^9+384*x^5*exp(1)^2+1216*x^6*exp(1))/x^4)
________________________________________________________________________________________
maxima [B] time = 94.18, size = 213, normalized size = 10.14 \begin {gather*} e^{\left (x^{8} e^{2} - 38 \, x^{8} e + 361 \, x^{8} + 8 \, x^{7} e^{2} - 304 \, x^{7} e + 2888 \, x^{7} + 24 \, x^{6} e^{2} - 912 \, x^{6} e + 8664 \, x^{6} + 16 \, x^{5} e^{2} - 608 \, x^{5} e + 5776 \, x^{5} - 80 \, x^{4} e^{2} + 3040 \, x^{4} e - 28880 \, x^{4} - 192 \, x^{3} e^{2} + 7296 \, x^{3} e - 69312 \, x^{3} - 32 \, x^{2} e^{2} + 1216 \, x^{2} e - 11552 \, x^{2} + 384 \, x e^{2} - 14592 \, x e + 138624 \, x - \frac {256 \, e^{2}}{x} + \frac {9728 \, e}{x} - \frac {92416}{x} - \frac {512 \, e^{2}}{x^{2}} + \frac {19456 \, e}{x^{2}} - \frac {184832}{x^{2}} + \frac {256 \, e^{2}}{x^{4}} - \frac {9728 \, e}{x^{4}} + \frac {92416}{x^{4}} + 384 \, e^{2} - 14592 \, e + 138624\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x^12+56*x^11+144*x^10+80*x^9-320*x^8-576*x^7-64*x^6+384*x^5+256*x^3+1024*x^2-1024)*exp(1)^2+(-30
4*x^12-2128*x^11-5472*x^10-3040*x^9+12160*x^8+21888*x^7+2432*x^6-14592*x^5-9728*x^3-38912*x^2+38912)*exp(1)+28
88*x^12+20216*x^11+51984*x^10+28880*x^9-115520*x^8-207936*x^7-23104*x^6+138624*x^5+92416*x^3+369664*x^2-369664
)*exp(((x^12+8*x^11+24*x^10+16*x^9-80*x^8-192*x^7-32*x^6+384*x^5+384*x^4-256*x^3-512*x^2+256)*exp(1)^2+(-38*x^
12-304*x^11-912*x^10-608*x^9+3040*x^8+7296*x^7+1216*x^6-14592*x^5-14592*x^4+9728*x^3+19456*x^2-9728)*exp(1)+36
1*x^12+2888*x^11+8664*x^10+5776*x^9-28880*x^8-69312*x^7-11552*x^6+138624*x^5+138624*x^4-92416*x^3-184832*x^2+9
2416)/x^4)/x^5,x, algorithm="maxima")
[Out]
e^(x^8*e^2 - 38*x^8*e + 361*x^8 + 8*x^7*e^2 - 304*x^7*e + 2888*x^7 + 24*x^6*e^2 - 912*x^6*e + 8664*x^6 + 16*x^
5*e^2 - 608*x^5*e + 5776*x^5 - 80*x^4*e^2 + 3040*x^4*e - 28880*x^4 - 192*x^3*e^2 + 7296*x^3*e - 69312*x^3 - 32
*x^2*e^2 + 1216*x^2*e - 11552*x^2 + 384*x*e^2 - 14592*x*e + 138624*x - 256*e^2/x + 9728*e/x - 92416/x - 512*e^
2/x^2 + 19456*e/x^2 - 184832/x^2 + 256*e^2/x^4 - 9728*e/x^4 + 92416/x^4 + 384*e^2 - 14592*e + 138624)
________________________________________________________________________________________
mupad [B] time = 3.00, size = 248, normalized size = 11.81 \begin {gather*} {\mathrm {e}}^{x^8\,{\mathrm {e}}^2}\,{\mathrm {e}}^{8\,x^7\,{\mathrm {e}}^2}\,{\mathrm {e}}^{16\,x^5\,{\mathrm {e}}^2}\,{\mathrm {e}}^{24\,x^6\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-32\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-38\,x^8\,\mathrm {e}}\,{\mathrm {e}}^{-80\,x^4\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-192\,x^3\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-\frac {256\,{\mathrm {e}}^2}{x}}\,{\mathrm {e}}^{\frac {256\,{\mathrm {e}}^2}{x^4}}\,{\mathrm {e}}^{-304\,x^7\,\mathrm {e}}\,{\mathrm {e}}^{-\frac {512\,{\mathrm {e}}^2}{x^2}}\,{\mathrm {e}}^{-608\,x^5\,\mathrm {e}}\,{\mathrm {e}}^{-912\,x^6\,\mathrm {e}}\,{\mathrm {e}}^{1216\,x^2\,\mathrm {e}}\,{\mathrm {e}}^{3040\,x^4\,\mathrm {e}}\,{\mathrm {e}}^{7296\,x^3\,\mathrm {e}}\,{\mathrm {e}}^{\frac {9728\,\mathrm {e}}{x}}\,{\mathrm {e}}^{-\frac {9728\,\mathrm {e}}{x^4}}\,{\mathrm {e}}^{\frac {19456\,\mathrm {e}}{x^2}}\,{\mathrm {e}}^{384\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-14592\,\mathrm {e}}\,{\mathrm {e}}^{138624\,x}\,{\mathrm {e}}^{138624}\,{\mathrm {e}}^{361\,x^8}\,{\mathrm {e}}^{2888\,x^7}\,{\mathrm {e}}^{5776\,x^5}\,{\mathrm {e}}^{8664\,x^6}\,{\mathrm {e}}^{-11552\,x^2}\,{\mathrm {e}}^{-28880\,x^4}\,{\mathrm {e}}^{-69312\,x^3}\,{\mathrm {e}}^{-\frac {92416}{x}}\,{\mathrm {e}}^{\frac {92416}{x^4}}\,{\mathrm {e}}^{-\frac {184832}{x^2}}\,{\mathrm {e}}^{384\,x\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-14592\,x\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp((exp(2)*(384*x^4 - 256*x^3 - 512*x^2 + 384*x^5 - 32*x^6 - 192*x^7 - 80*x^8 + 16*x^9 + 24*x^10 + 8*x^1
1 + x^12 + 256) - exp(1)*(14592*x^4 - 9728*x^3 - 19456*x^2 + 14592*x^5 - 1216*x^6 - 7296*x^7 - 3040*x^8 + 608*
x^9 + 912*x^10 + 304*x^11 + 38*x^12 + 9728) - 184832*x^2 - 92416*x^3 + 138624*x^4 + 138624*x^5 - 11552*x^6 - 6
9312*x^7 - 28880*x^8 + 5776*x^9 + 8664*x^10 + 2888*x^11 + 361*x^12 + 92416)/x^4)*(exp(2)*(1024*x^2 + 256*x^3 +
384*x^5 - 64*x^6 - 576*x^7 - 320*x^8 + 80*x^9 + 144*x^10 + 56*x^11 + 8*x^12 - 1024) - exp(1)*(38912*x^2 + 972
8*x^3 + 14592*x^5 - 2432*x^6 - 21888*x^7 - 12160*x^8 + 3040*x^9 + 5472*x^10 + 2128*x^11 + 304*x^12 - 38912) +
369664*x^2 + 92416*x^3 + 138624*x^5 - 23104*x^6 - 207936*x^7 - 115520*x^8 + 28880*x^9 + 51984*x^10 + 20216*x^1
1 + 2888*x^12 - 369664))/x^5,x)
[Out]
exp(x^8*exp(2))*exp(8*x^7*exp(2))*exp(16*x^5*exp(2))*exp(24*x^6*exp(2))*exp(-32*x^2*exp(2))*exp(-38*x^8*exp(1)
)*exp(-80*x^4*exp(2))*exp(-192*x^3*exp(2))*exp(-(256*exp(2))/x)*exp((256*exp(2))/x^4)*exp(-304*x^7*exp(1))*exp
(-(512*exp(2))/x^2)*exp(-608*x^5*exp(1))*exp(-912*x^6*exp(1))*exp(1216*x^2*exp(1))*exp(3040*x^4*exp(1))*exp(72
96*x^3*exp(1))*exp((9728*exp(1))/x)*exp(-(9728*exp(1))/x^4)*exp((19456*exp(1))/x^2)*exp(384*exp(2))*exp(-14592
*exp(1))*exp(138624*x)*exp(138624)*exp(361*x^8)*exp(2888*x^7)*exp(5776*x^5)*exp(8664*x^6)*exp(-11552*x^2)*exp(
-28880*x^4)*exp(-69312*x^3)*exp(-92416/x)*exp(92416/x^4)*exp(-184832/x^2)*exp(384*x*exp(2))*exp(-14592*x*exp(1
))
________________________________________________________________________________________
sympy [B] time = 2.27, size = 182, normalized size = 8.67 \begin {gather*} e^{\frac {361 x^{12} + 2888 x^{11} + 8664 x^{10} + 5776 x^{9} - 28880 x^{8} - 69312 x^{7} - 11552 x^{6} + 138624 x^{5} + 138624 x^{4} - 92416 x^{3} - 184832 x^{2} + e \left (- 38 x^{12} - 304 x^{11} - 912 x^{10} - 608 x^{9} + 3040 x^{8} + 7296 x^{7} + 1216 x^{6} - 14592 x^{5} - 14592 x^{4} + 9728 x^{3} + 19456 x^{2} - 9728\right ) + \left (x^{12} + 8 x^{11} + 24 x^{10} + 16 x^{9} - 80 x^{8} - 192 x^{7} - 32 x^{6} + 384 x^{5} + 384 x^{4} - 256 x^{3} - 512 x^{2} + 256\right ) e^{2} + 92416}{x^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x**12+56*x**11+144*x**10+80*x**9-320*x**8-576*x**7-64*x**6+384*x**5+256*x**3+1024*x**2-1024)*exp
(1)**2+(-304*x**12-2128*x**11-5472*x**10-3040*x**9+12160*x**8+21888*x**7+2432*x**6-14592*x**5-9728*x**3-38912*
x**2+38912)*exp(1)+2888*x**12+20216*x**11+51984*x**10+28880*x**9-115520*x**8-207936*x**7-23104*x**6+138624*x**
5+92416*x**3+369664*x**2-369664)*exp(((x**12+8*x**11+24*x**10+16*x**9-80*x**8-192*x**7-32*x**6+384*x**5+384*x*
*4-256*x**3-512*x**2+256)*exp(1)**2+(-38*x**12-304*x**11-912*x**10-608*x**9+3040*x**8+7296*x**7+1216*x**6-1459
2*x**5-14592*x**4+9728*x**3+19456*x**2-9728)*exp(1)+361*x**12+2888*x**11+8664*x**10+5776*x**9-28880*x**8-69312
*x**7-11552*x**6+138624*x**5+138624*x**4-92416*x**3-184832*x**2+92416)/x**4)/x**5,x)
[Out]
exp((361*x**12 + 2888*x**11 + 8664*x**10 + 5776*x**9 - 28880*x**8 - 69312*x**7 - 11552*x**6 + 138624*x**5 + 13
8624*x**4 - 92416*x**3 - 184832*x**2 + E*(-38*x**12 - 304*x**11 - 912*x**10 - 608*x**9 + 3040*x**8 + 7296*x**7
+ 1216*x**6 - 14592*x**5 - 14592*x**4 + 9728*x**3 + 19456*x**2 - 9728) + (x**12 + 8*x**11 + 24*x**10 + 16*x**
9 - 80*x**8 - 192*x**7 - 32*x**6 + 384*x**5 + 384*x**4 - 256*x**3 - 512*x**2 + 256)*exp(2) + 92416)/x**4)
________________________________________________________________________________________