3.4.79 \(\int \frac {-4 x^6+2 x^6 \log (2)+e^{4 x^2} (-4 x^2+2 x^2 \log (2))+e^{3 x^2} (-16 x^3+8 x^3 \log (2))+(-4 x^3-3 x^2 \log (2)) \log (4)+e^{2 x^2} (-24 x^4+12 x^4 \log (2)+(-2 x-4 x^3+(-1-4 x^2) \log (2)) \log (4))+e^{x^2} (-16 x^5+8 x^5 \log (2)+(-6 x^2-4 x^4+(-4 x-4 x^3) \log (2)) \log (4))}{16 x^6+16 x^7+4 x^8+e^{4 x^2} (16 x^2+16 x^3+4 x^4)+e^{3 x^2} (64 x^3+64 x^4+16 x^5)+(8 x^3+4 x^4) \log (4)+\log ^2(4)+e^{2 x^2} (96 x^4+96 x^5+24 x^6+(8 x+4 x^2) \log (4))+e^{x^2} (64 x^5+64 x^6+16 x^7+(16 x^2+8 x^3) \log (4))} \, dx\)
Optimal. Leaf size=31 \[ \frac {-x-\log (2)}{4+2 x+\frac {\log (4)}{x \left (e^{x^2}+x\right )^2}} \]
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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[(-4*x^6 + 2*x^6*Log[2] + E^(4*x^2)*(-4*x^2 + 2*x^2*Log[2]) + E^(3*x^2)*(-16*x^3 + 8*x^3*Log[2]) + (-4*x^3
- 3*x^2*Log[2])*Log[4] + E^(2*x^2)*(-24*x^4 + 12*x^4*Log[2] + (-2*x - 4*x^3 + (-1 - 4*x^2)*Log[2])*Log[4]) + E
^x^2*(-16*x^5 + 8*x^5*Log[2] + (-6*x^2 - 4*x^4 + (-4*x - 4*x^3)*Log[2])*Log[4]))/(16*x^6 + 16*x^7 + 4*x^8 + E^
(4*x^2)*(16*x^2 + 16*x^3 + 4*x^4) + E^(3*x^2)*(64*x^3 + 64*x^4 + 16*x^5) + (8*x^3 + 4*x^4)*Log[4] + Log[4]^2 +
E^(2*x^2)*(96*x^4 + 96*x^5 + 24*x^6 + (8*x + 4*x^2)*Log[4]) + E^x^2*(64*x^5 + 64*x^6 + 16*x^7 + (16*x^2 + 8*x
^3)*Log[4])),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [B] time = 1.00, size = 693, normalized size = 22.35 \begin {gather*} \frac {2 \log ^3(4)+4 x \log ^3(4)+18 x^2 \log ^3(4)-2 e^{2 x^2} x \log (4) \left (16 x^7 (-4+\log (4))+88 x^8 (-4+\log (4))+48 x^9 (-4+\log (4))+8 x^{10} (-4+\log (4))+(-4+\log (4)) \log (4)+2 x (-4+\log (4)) \log (4)+9 x^2 (-4+\log (4)) \log (4)+2 x^6 \left (188-55 \log (4)+2 \log ^2(4)\right )+4 x^3 \left (-16-8 \log (4)+3 \log ^2(4)\right )+4 x^5 \left (52-29 \log (4)+4 \log ^2(4)\right )+4 x^4 \left (-24-14 \log (4)+5 \log ^2(4)\right )\right )-4 e^{x^2} x^2 \log (4) \left (16 x^7 (-4+\log (4))+88 x^8 (-4+\log (4))+48 x^9 (-4+\log (4))+8 x^{10} (-4+\log (4))+(-4+\log (4)) \log (4)+2 x (-4+\log (4)) \log (4)+9 x^2 (-4+\log (4)) \log (4)+2 x^6 \left (188-55 \log (4)+2 \log ^2(4)\right )+4 x^3 \left (-16-8 \log (4)+3 \log ^2(4)\right )+4 x^5 \left (52-29 \log (4)+4 \log ^2(4)\right )+4 x^4 \left (-24-14 \log (4)+5 \log ^2(4)\right )\right )+4 x^4 \log ^2(4) \left (16-2 \log ^2(4)+\log (4) (9+\log (16))\right )-4 x^8 \log (4) \left (104-(105+16 \log (2)) \log (4)+16 \log ^2(4)+\log (64)\right )-4 x^{11} (-4+\log (4)) (35 \log (4)+3 \log (64))-8 x^{12} \left (-63 \log (4)+12 \log ^2(4)+5 \log (64)\right )-4 x^{13} \left (-85 \log (4)+4 \log ^2(4)+23 \log (64)\right )-2 x^9 \log (4) \left (376+8 \log ^2(4)+25 \log (64)-\log (4) (233+\log (256))\right )+x^7 \left (192 \log (4)-54 \log ^3(4)-\log ^2(16) \log (64)+4 \log ^2(4) (36+\log (8192))\right )+16 x^{10} \left (8 \log ^2(4)-\log ^2(64)+\log (65536)\right )+x^3 \log ^2(4) \left (40-3 \log ^2(4)+\log (4) (14+\log (64))+\log (65536)\right )+4 x^6 \log (4) \left (32+9 \log ^2(4)-\log (4) (31+\log (67108864))\right )+x^5 \log ^2(4) \left (-32-4 \log ^2(4)+\log (4) \log (256)+\log (268435456)\right )}{4 \log (4) \left (4 x^3+2 x^4+2 e^{2 x^2} x (2+x)+4 e^{x^2} x^2 (2+x)+\log (4)\right ) \left (16 x^7+88 x^8+48 x^9+8 x^{10}+\log (4)+9 x^2 \log (4)+4 x^4 (6+5 \log (4))+x \log (16)+4 x^3 (4+\log (64))+x^6 (-94+\log (256))+4 x^5 (-13+\log (256))\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-4*x^6 + 2*x^6*Log[2] + E^(4*x^2)*(-4*x^2 + 2*x^2*Log[2]) + E^(3*x^2)*(-16*x^3 + 8*x^3*Log[2]) + (-
4*x^3 - 3*x^2*Log[2])*Log[4] + E^(2*x^2)*(-24*x^4 + 12*x^4*Log[2] + (-2*x - 4*x^3 + (-1 - 4*x^2)*Log[2])*Log[4
]) + E^x^2*(-16*x^5 + 8*x^5*Log[2] + (-6*x^2 - 4*x^4 + (-4*x - 4*x^3)*Log[2])*Log[4]))/(16*x^6 + 16*x^7 + 4*x^
8 + E^(4*x^2)*(16*x^2 + 16*x^3 + 4*x^4) + E^(3*x^2)*(64*x^3 + 64*x^4 + 16*x^5) + (8*x^3 + 4*x^4)*Log[4] + Log[
4]^2 + E^(2*x^2)*(96*x^4 + 96*x^5 + 24*x^6 + (8*x + 4*x^2)*Log[4]) + E^x^2*(64*x^5 + 64*x^6 + 16*x^7 + (16*x^2
+ 8*x^3)*Log[4])),x]
[Out]
(2*Log[4]^3 + 4*x*Log[4]^3 + 18*x^2*Log[4]^3 - 2*E^(2*x^2)*x*Log[4]*(16*x^7*(-4 + Log[4]) + 88*x^8*(-4 + Log[4
]) + 48*x^9*(-4 + Log[4]) + 8*x^10*(-4 + Log[4]) + (-4 + Log[4])*Log[4] + 2*x*(-4 + Log[4])*Log[4] + 9*x^2*(-4
+ Log[4])*Log[4] + 2*x^6*(188 - 55*Log[4] + 2*Log[4]^2) + 4*x^3*(-16 - 8*Log[4] + 3*Log[4]^2) + 4*x^5*(52 - 2
9*Log[4] + 4*Log[4]^2) + 4*x^4*(-24 - 14*Log[4] + 5*Log[4]^2)) - 4*E^x^2*x^2*Log[4]*(16*x^7*(-4 + Log[4]) + 88
*x^8*(-4 + Log[4]) + 48*x^9*(-4 + Log[4]) + 8*x^10*(-4 + Log[4]) + (-4 + Log[4])*Log[4] + 2*x*(-4 + Log[4])*Lo
g[4] + 9*x^2*(-4 + Log[4])*Log[4] + 2*x^6*(188 - 55*Log[4] + 2*Log[4]^2) + 4*x^3*(-16 - 8*Log[4] + 3*Log[4]^2)
+ 4*x^5*(52 - 29*Log[4] + 4*Log[4]^2) + 4*x^4*(-24 - 14*Log[4] + 5*Log[4]^2)) + 4*x^4*Log[4]^2*(16 - 2*Log[4]
^2 + Log[4]*(9 + Log[16])) - 4*x^8*Log[4]*(104 - (105 + 16*Log[2])*Log[4] + 16*Log[4]^2 + Log[64]) - 4*x^11*(-
4 + Log[4])*(35*Log[4] + 3*Log[64]) - 8*x^12*(-63*Log[4] + 12*Log[4]^2 + 5*Log[64]) - 4*x^13*(-85*Log[4] + 4*L
og[4]^2 + 23*Log[64]) - 2*x^9*Log[4]*(376 + 8*Log[4]^2 + 25*Log[64] - Log[4]*(233 + Log[256])) + x^7*(192*Log[
4] - 54*Log[4]^3 - Log[16]^2*Log[64] + 4*Log[4]^2*(36 + Log[8192])) + 16*x^10*(8*Log[4]^2 - Log[64]^2 + Log[65
536]) + x^3*Log[4]^2*(40 - 3*Log[4]^2 + Log[4]*(14 + Log[64]) + Log[65536]) + 4*x^6*Log[4]*(32 + 9*Log[4]^2 -
Log[4]*(31 + Log[67108864])) + x^5*Log[4]^2*(-32 - 4*Log[4]^2 + Log[4]*Log[256] + Log[268435456]))/(4*Log[4]*(
4*x^3 + 2*x^4 + 2*E^(2*x^2)*x*(2 + x) + 4*E^x^2*x^2*(2 + x) + Log[4])*(16*x^7 + 88*x^8 + 48*x^9 + 8*x^10 + Log
[4] + 9*x^2*Log[4] + 4*x^4*(6 + 5*Log[4]) + x*Log[16] + 4*x^3*(4 + Log[64]) + x^6*(-94 + Log[256]) + 4*x^5*(-1
3 + Log[256])))
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fricas [B] time = 0.87, size = 93, normalized size = 3.00 \begin {gather*} \frac {2 \, x^{3} - {\left (x \log \relax (2) - 2 \, x\right )} e^{\left (2 \, x^{2}\right )} - 2 \, {\left (x^{2} \log \relax (2) - 2 \, x^{2}\right )} e^{\left (x^{2}\right )} - {\left (x^{3} - 1\right )} \log \relax (2)}{2 \, {\left (x^{4} + 2 \, x^{3} + {\left (x^{2} + 2 \, x\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (x^{2}\right )} + \log \relax (2)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x^2*log(2)-4*x^2)*exp(x^2)^4+(8*x^3*log(2)-16*x^3)*exp(x^2)^3+(2*((-4*x^2-1)*log(2)-4*x^3-2*x)*l
og(2)+12*x^4*log(2)-24*x^4)*exp(x^2)^2+(2*((-4*x^3-4*x)*log(2)-4*x^4-6*x^2)*log(2)+8*x^5*log(2)-16*x^5)*exp(x^
2)+2*(-3*x^2*log(2)-4*x^3)*log(2)+2*x^6*log(2)-4*x^6)/((4*x^4+16*x^3+16*x^2)*exp(x^2)^4+(16*x^5+64*x^4+64*x^3)
*exp(x^2)^3+(2*(4*x^2+8*x)*log(2)+24*x^6+96*x^5+96*x^4)*exp(x^2)^2+(2*(8*x^3+16*x^2)*log(2)+16*x^7+64*x^6+64*x
^5)*exp(x^2)+4*log(2)^2+2*(4*x^4+8*x^3)*log(2)+4*x^8+16*x^7+16*x^6),x, algorithm="fricas")
[Out]
1/2*(2*x^3 - (x*log(2) - 2*x)*e^(2*x^2) - 2*(x^2*log(2) - 2*x^2)*e^(x^2) - (x^3 - 1)*log(2))/(x^4 + 2*x^3 + (x
^2 + 2*x)*e^(2*x^2) + 2*(x^3 + 2*x^2)*e^(x^2) + log(2))
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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(((2*x^2*log(2)-4*x^2)*exp(x^2)^4+(8*x^3*log(2)-16*x^3)*exp(x^2)^3+(2*((-4*x^2-1)*log(2)-4*x^3-2*x)*l
og(2)+12*x^4*log(2)-24*x^4)*exp(x^2)^2+(2*((-4*x^3-4*x)*log(2)-4*x^4-6*x^2)*log(2)+8*x^5*log(2)-16*x^5)*exp(x^
2)+2*(-3*x^2*log(2)-4*x^3)*log(2)+2*x^6*log(2)-4*x^6)/((4*x^4+16*x^3+16*x^2)*exp(x^2)^4+(16*x^5+64*x^4+64*x^3)
*exp(x^2)^3+(2*(4*x^2+8*x)*log(2)+24*x^6+96*x^5+96*x^4)*exp(x^2)^2+(2*(8*x^3+16*x^2)*log(2)+16*x^7+64*x^6+64*x
^5)*exp(x^2)+4*log(2)^2+2*(4*x^4+8*x^3)*log(2)+4*x^8+16*x^7+16*x^6),x, algorithm="giac")
[Out]
Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 3.14Unable to divide, perhaps due to rounding error%%%{67108864,[0,2,112,6]%%%}+%%%{456340
2752,[0,2,1
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maple [B] time = 0.11, size = 79, normalized size = 2.55
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result |
size |
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| risch |
\(\frac {1}{2+x}-\frac {\ln \relax (2)}{2 \left (2+x \right )}+\frac {\ln \relax (2) \left (\ln \relax (2)+x \right )}{2 \left (2+x \right ) \left (x^{2} {\mathrm e}^{2 x^{2}}+2 x^{3} {\mathrm e}^{x^{2}}+x^{4}+2 x \,{\mathrm e}^{2 x^{2}}+4 x^{2} {\mathrm e}^{x^{2}}+2 x^{3}+\ln \relax (2)\right )}\) |
\(79\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((2*x^2*ln(2)-4*x^2)*exp(x^2)^4+(8*x^3*ln(2)-16*x^3)*exp(x^2)^3+(2*((-4*x^2-1)*ln(2)-4*x^3-2*x)*ln(2)+12*x
^4*ln(2)-24*x^4)*exp(x^2)^2+(2*((-4*x^3-4*x)*ln(2)-4*x^4-6*x^2)*ln(2)+8*x^5*ln(2)-16*x^5)*exp(x^2)+2*(-3*x^2*l
n(2)-4*x^3)*ln(2)+2*x^6*ln(2)-4*x^6)/((4*x^4+16*x^3+16*x^2)*exp(x^2)^4+(16*x^5+64*x^4+64*x^3)*exp(x^2)^3+(2*(4
*x^2+8*x)*ln(2)+24*x^6+96*x^5+96*x^4)*exp(x^2)^2+(2*(8*x^3+16*x^2)*ln(2)+16*x^7+64*x^6+64*x^5)*exp(x^2)+4*ln(2
)^2+2*(4*x^4+8*x^3)*ln(2)+4*x^8+16*x^7+16*x^6),x,method=_RETURNVERBOSE)
[Out]
1/(2+x)-1/2*ln(2)/(2+x)+1/2*ln(2)*(ln(2)+x)/(2+x)/(x^2*exp(2*x^2)+2*x^3*exp(x^2)+x^4+2*x*exp(2*x^2)+4*x^2*exp(
x^2)+2*x^3+ln(2))
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maxima [B] time = 0.85, size = 82, normalized size = 2.65 \begin {gather*} -\frac {x^{3} {\left (\log \relax (2) - 2\right )} + 2 \, x^{2} {\left (\log \relax (2) - 2\right )} e^{\left (x^{2}\right )} + x {\left (\log \relax (2) - 2\right )} e^{\left (2 \, x^{2}\right )} - \log \relax (2)}{2 \, {\left (x^{4} + 2 \, x^{3} + {\left (x^{2} + 2 \, x\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (x^{2}\right )} + \log \relax (2)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x^2*log(2)-4*x^2)*exp(x^2)^4+(8*x^3*log(2)-16*x^3)*exp(x^2)^3+(2*((-4*x^2-1)*log(2)-4*x^3-2*x)*l
og(2)+12*x^4*log(2)-24*x^4)*exp(x^2)^2+(2*((-4*x^3-4*x)*log(2)-4*x^4-6*x^2)*log(2)+8*x^5*log(2)-16*x^5)*exp(x^
2)+2*(-3*x^2*log(2)-4*x^3)*log(2)+2*x^6*log(2)-4*x^6)/((4*x^4+16*x^3+16*x^2)*exp(x^2)^4+(16*x^5+64*x^4+64*x^3)
*exp(x^2)^3+(2*(4*x^2+8*x)*log(2)+24*x^6+96*x^5+96*x^4)*exp(x^2)^2+(2*(8*x^3+16*x^2)*log(2)+16*x^7+64*x^6+64*x
^5)*exp(x^2)+4*log(2)^2+2*(4*x^4+8*x^3)*log(2)+4*x^8+16*x^7+16*x^6),x, algorithm="maxima")
[Out]
-1/2*(x^3*(log(2) - 2) + 2*x^2*(log(2) - 2)*e^(x^2) + x*(log(2) - 2)*e^(2*x^2) - log(2))/(x^4 + 2*x^3 + (x^2 +
2*x)*e^(2*x^2) + 2*(x^3 + 2*x^2)*e^(x^2) + log(2))
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {2\,\ln \relax (2)\,\left (4\,x^3+3\,\ln \relax (2)\,x^2\right )-{\mathrm {e}}^{4\,x^2}\,\left (2\,x^2\,\ln \relax (2)-4\,x^2\right )-{\mathrm {e}}^{3\,x^2}\,\left (8\,x^3\,\ln \relax (2)-16\,x^3\right )-2\,x^6\,\ln \relax (2)+{\mathrm {e}}^{x^2}\,\left (2\,\ln \relax (2)\,\left (\ln \relax (2)\,\left (4\,x^3+4\,x\right )+6\,x^2+4\,x^4\right )-8\,x^5\,\ln \relax (2)+16\,x^5\right )+{\mathrm {e}}^{2\,x^2}\,\left (2\,\ln \relax (2)\,\left (2\,x+\ln \relax (2)\,\left (4\,x^2+1\right )+4\,x^3\right )-12\,x^4\,\ln \relax (2)+24\,x^4\right )+4\,x^6}{{\mathrm {e}}^{2\,x^2}\,\left (2\,\ln \relax (2)\,\left (4\,x^2+8\,x\right )+96\,x^4+96\,x^5+24\,x^6\right )+{\mathrm {e}}^{x^2}\,\left (2\,\ln \relax (2)\,\left (8\,x^3+16\,x^2\right )+64\,x^5+64\,x^6+16\,x^7\right )+2\,\ln \relax (2)\,\left (4\,x^4+8\,x^3\right )+4\,{\ln \relax (2)}^2+16\,x^6+16\,x^7+4\,x^8+{\mathrm {e}}^{4\,x^2}\,\left (4\,x^4+16\,x^3+16\,x^2\right )+{\mathrm {e}}^{3\,x^2}\,\left (16\,x^5+64\,x^4+64\,x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(2*log(2)*(3*x^2*log(2) + 4*x^3) - exp(4*x^2)*(2*x^2*log(2) - 4*x^2) - exp(3*x^2)*(8*x^3*log(2) - 16*x^3)
- 2*x^6*log(2) + exp(x^2)*(2*log(2)*(log(2)*(4*x + 4*x^3) + 6*x^2 + 4*x^4) - 8*x^5*log(2) + 16*x^5) + exp(2*x
^2)*(2*log(2)*(2*x + log(2)*(4*x^2 + 1) + 4*x^3) - 12*x^4*log(2) + 24*x^4) + 4*x^6)/(exp(2*x^2)*(2*log(2)*(8*x
+ 4*x^2) + 96*x^4 + 96*x^5 + 24*x^6) + exp(x^2)*(2*log(2)*(16*x^2 + 8*x^3) + 64*x^5 + 64*x^6 + 16*x^7) + 2*lo
g(2)*(8*x^3 + 4*x^4) + 4*log(2)^2 + 16*x^6 + 16*x^7 + 4*x^8 + exp(4*x^2)*(16*x^2 + 16*x^3 + 4*x^4) + exp(3*x^2
)*(64*x^3 + 64*x^4 + 16*x^5)),x)
[Out]
int(-(2*log(2)*(3*x^2*log(2) + 4*x^3) - exp(4*x^2)*(2*x^2*log(2) - 4*x^2) - exp(3*x^2)*(8*x^3*log(2) - 16*x^3)
- 2*x^6*log(2) + exp(x^2)*(2*log(2)*(log(2)*(4*x + 4*x^3) + 6*x^2 + 4*x^4) - 8*x^5*log(2) + 16*x^5) + exp(2*x
^2)*(2*log(2)*(2*x + log(2)*(4*x^2 + 1) + 4*x^3) - 12*x^4*log(2) + 24*x^4) + 4*x^6)/(exp(2*x^2)*(2*log(2)*(8*x
+ 4*x^2) + 96*x^4 + 96*x^5 + 24*x^6) + exp(x^2)*(2*log(2)*(16*x^2 + 8*x^3) + 64*x^5 + 64*x^6 + 16*x^7) + 2*lo
g(2)*(8*x^3 + 4*x^4) + 4*log(2)^2 + 16*x^6 + 16*x^7 + 4*x^8 + exp(4*x^2)*(16*x^2 + 16*x^3 + 4*x^4) + exp(3*x^2
)*(64*x^3 + 64*x^4 + 16*x^5)), x)
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sympy [B] time = 0.68, size = 87, normalized size = 2.81 \begin {gather*} \frac {x \log {\relax (2 )} + \log {\relax (2 )}^{2}}{2 x^{5} + 8 x^{4} + 8 x^{3} + 2 x \log {\relax (2 )} + \left (2 x^{3} + 8 x^{2} + 8 x\right ) e^{2 x^{2}} + \left (4 x^{4} + 16 x^{3} + 16 x^{2}\right ) e^{x^{2}} + 4 \log {\relax (2 )}} - \frac {-2 + \log {\relax (2 )}}{2 x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x**2*ln(2)-4*x**2)*exp(x**2)**4+(8*x**3*ln(2)-16*x**3)*exp(x**2)**3+(2*((-4*x**2-1)*ln(2)-4*x**3
-2*x)*ln(2)+12*x**4*ln(2)-24*x**4)*exp(x**2)**2+(2*((-4*x**3-4*x)*ln(2)-4*x**4-6*x**2)*ln(2)+8*x**5*ln(2)-16*x
**5)*exp(x**2)+2*(-3*x**2*ln(2)-4*x**3)*ln(2)+2*x**6*ln(2)-4*x**6)/((4*x**4+16*x**3+16*x**2)*exp(x**2)**4+(16*
x**5+64*x**4+64*x**3)*exp(x**2)**3+(2*(4*x**2+8*x)*ln(2)+24*x**6+96*x**5+96*x**4)*exp(x**2)**2+(2*(8*x**3+16*x
**2)*ln(2)+16*x**7+64*x**6+64*x**5)*exp(x**2)+4*ln(2)**2+2*(4*x**4+8*x**3)*ln(2)+4*x**8+16*x**7+16*x**6),x)
[Out]
(x*log(2) + log(2)**2)/(2*x**5 + 8*x**4 + 8*x**3 + 2*x*log(2) + (2*x**3 + 8*x**2 + 8*x)*exp(2*x**2) + (4*x**4
+ 16*x**3 + 16*x**2)*exp(x**2) + 4*log(2)) - (-2 + log(2))/(2*x + 4)
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