3.83.77 \(\int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+(128-32 x-32 x^2) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+(128-32 x-32 x^2) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+(96 x-48 x^2-506 x^3+96 x^4+64 x^5) \log (4)+(24 x-6 x^2-64 x^3) \log ^2(4)+2 x \log ^3(4))}{64-48 x+12 x^2-x^3+(48-24 x+3 x^2) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx\) [8277]

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

[Out]

exp(exp((4*x^2/(4+2*ln(2)-x)-4)^2)*x^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[(E^(E^((256 - 128*x - 112*x^2 + 32*x^3 + 16*x^4 + (128 - 32*x - 32*x^2)*Log[4] + 16*Log[4]^2)/(16 - 8*x +
x^2 + (8 - 2*x)*Log[4] + Log[4]^2))*x^2 + (256 - 128*x - 112*x^2 + 32*x^3 + 16*x^4 + (128 - 32*x - 32*x^2)*Log
[4] + 16*Log[4]^2)/(16 - 8*x + x^2 + (8 - 2*x)*Log[4] + Log[4]^2))*(128*x - 96*x^2 - 1000*x^3 + 382*x^4 + 224*
x^5 - 32*x^6 + (96*x - 48*x^2 - 506*x^3 + 96*x^4 + 64*x^5)*Log[4] + (24*x - 6*x^2 - 64*x^3)*Log[4]^2 + 2*x*Log
[4]^3))/(64 - 48*x + 12*x^2 - x^3 + (48 - 24*x + 3*x^2)*Log[4] + (12 - 3*x)*Log[4]^2 + Log[4]^3),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]
time = 180.00, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^(E^((256 - 128*x - 112*x^2 + 32*x^3 + 16*x^4 + (128 - 32*x - 32*x^2)*Log[4] + 16*Log[4]^2)/(16 -
8*x + x^2 + (8 - 2*x)*Log[4] + Log[4]^2))*x^2 + (256 - 128*x - 112*x^2 + 32*x^3 + 16*x^4 + (128 - 32*x - 32*x^
2)*Log[4] + 16*Log[4]^2)/(16 - 8*x + x^2 + (8 - 2*x)*Log[4] + Log[4]^2))*(128*x - 96*x^2 - 1000*x^3 + 382*x^4
+ 224*x^5 - 32*x^6 + (96*x - 48*x^2 - 506*x^3 + 96*x^4 + 64*x^5)*Log[4] + (24*x - 6*x^2 - 64*x^3)*Log[4]^2 + 2
*x*Log[4]^3))/(64 - 48*x + 12*x^2 - x^3 + (48 - 24*x + 3*x^2)*Log[4] + (12 - 3*x)*Log[4]^2 + Log[4]^3),x]

[Out]

$Aborted

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Maple [A]
time = 2.16, size = 36, normalized size = 1.38

method	result	size
risch	\({\mathrm e}^{x^{2} {\mathrm e}^{\frac {16 \left (-x^{2}+2 \ln \left (2\right )-x +4\right )^{2}}{\left (4+2 \ln \left (2\right )-x \right )^{2}}}}\)	\(36\)
norman	\(\frac {x^{2} {\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}+2 \left (-2 x +8\right ) \ln \left (2\right )+x^{2}-8 x +16}}}+\left (4 \ln \left (2\right )^{2}+16 \ln \left (2\right )+16\right ) {\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}+2 \left (-2 x +8\right ) \ln \left (2\right )+x^{2}-8 x +16}}}+\left (-4 \ln \left (2\right )-8\right ) x \,{\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}+2 \left (-2 x +8\right ) \ln \left (2\right )+x^{2}-8 x +16}}}}{\left (4+2 \ln \left (2\right )-x \right )^{2}}\)	\(255\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*x*ln(2)^3+4*(-64*x^3-6*x^2+24*x)*ln(2)^2+2*(64*x^5+96*x^4-506*x^3-48*x^2+96*x)*ln(2)-32*x^6+224*x^5+38
2*x^4-1000*x^3-96*x^2+128*x)*exp((64*ln(2)^2+2*(-32*x^2-32*x+128)*ln(2)+16*x^4+32*x^3-112*x^2-128*x+256)/(4*ln
(2)^2+2*(-2*x+8)*ln(2)+x^2-8*x+16))*exp(x^2*exp((64*ln(2)^2+2*(-32*x^2-32*x+128)*ln(2)+16*x^4+32*x^3-112*x^2-1
28*x+256)/(4*ln(2)^2+2*(-2*x+8)*ln(2)+x^2-8*x+16)))/(8*ln(2)^3+4*(-3*x+12)*ln(2)^2+2*(3*x^2-24*x+48)*ln(2)-x^3
+12*x^2-48*x+64),x,method=_RETURNVERBOSE)

[Out]

exp(x^2*exp(16*(-x^2+2*ln(2)-x+4)^2/(4+2*ln(2)-x)^2))

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 226 vs. \(2 (25) = 50\).
time = 3.92, size = 226, normalized size = 8.69 \begin {gather*} e^{\left (28638903918474961204418783933674838490721739172170652529441449702311064005352904159345284265824628375429359509218999720074396860757073376700445026041564579620512874307979212102266801261478978776245040008231745247475930553606737583615358787106474295296 \, x^{2} e^{\left (\frac {256 \, \log \left (2\right )^{4}}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + 16 \, x^{2} + 64 \, x \log \left (2\right ) + 192 \, \log \left (2\right )^{2} + \frac {2048 \, \log \left (2\right )^{3}}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {512 \, \log \left (2\right )^{3}}{x - 2 \, \log \left (2\right ) - 4} + 160 \, x + \frac {6144 \, \log \left (2\right )^{2}}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {3200 \, \log \left (2\right )^{2}}{x - 2 \, \log \left (2\right ) - 4} + \frac {8192 \, \log \left (2\right )}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {6656 \, \log \left (2\right )}{x - 2 \, \log \left (2\right ) - 4} + \frac {4096}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {4608}{x - 2 \, \log \left (2\right ) - 4} + 912\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x*log(2)^3+4*(-64*x^3-6*x^2+24*x)*log(2)^2+2*(64*x^5+96*x^4-506*x^3-48*x^2+96*x)*log(2)-32*x^6+2
24*x^5+382*x^4-1000*x^3-96*x^2+128*x)*exp((64*log(2)^2+2*(-32*x^2-32*x+128)*log(2)+16*x^4+32*x^3-112*x^2-128*x
+256)/(4*log(2)^2+2*(-2*x+8)*log(2)+x^2-8*x+16))*exp(x^2*exp((64*log(2)^2+2*(-32*x^2-32*x+128)*log(2)+16*x^4+3
2*x^3-112*x^2-128*x+256)/(4*log(2)^2+2*(-2*x+8)*log(2)+x^2-8*x+16)))/(8*log(2)^3+4*(-3*x+12)*log(2)^2+2*(3*x^2
-24*x+48)*log(2)-x^3+12*x^2-48*x+64),x, algorithm="maxima")

[Out]

e^(28638903918474961204418783933674838490721739172170652529441449702311064005352904159345284265824628375429359
50921899972007439686075707337670044502604156457962051287430797921210226680126147897877624504000823174524747593
0553606737583615358787106474295296*x^2*e^(256*log(2)^4/(x^2 - 4*x*(log(2) + 2) + 4*log(2)^2 + 16*log(2) + 16)
+ 16*x^2 + 64*x*log(2) + 192*log(2)^2 + 2048*log(2)^3/(x^2 - 4*x*(log(2) + 2) + 4*log(2)^2 + 16*log(2) + 16) +
512*log(2)^3/(x - 2*log(2) - 4) + 160*x + 6144*log(2)^2/(x^2 - 4*x*(log(2) + 2) + 4*log(2)^2 + 16*log(2) + 16
) + 3200*log(2)^2/(x - 2*log(2) - 4) + 8192*log(2)/(x^2 - 4*x*(log(2) + 2) + 4*log(2)^2 + 16*log(2) + 16) + 66
56*log(2)/(x - 2*log(2) - 4) + 4096/(x^2 - 4*x*(log(2) + 2) + 4*log(2)^2 + 16*log(2) + 16) + 4608/(x - 2*log(2
) - 4) + 912))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 218 vs. \(2 (25) = 50\).
time = 0.38, size = 218, normalized size = 8.38 \begin {gather*} e^{\left (\frac {16 \, x^{4} + 32 \, x^{3} - 112 \, x^{2} + {\left (x^{4} + 4 \, x^{2} \log \left (2\right )^{2} - 8 \, x^{3} + 16 \, x^{2} - 4 \, {\left (x^{3} - 4 \, x^{2}\right )} \log \left (2\right )\right )} e^{\left (\frac {16 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 4 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16\right )}}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16}\right )} - 64 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 64 \, \log \left (2\right )^{2} - 128 \, x + 256}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16} - \frac {16 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 4 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16\right )}}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x*log(2)^3+4*(-64*x^3-6*x^2+24*x)*log(2)^2+2*(64*x^5+96*x^4-506*x^3-48*x^2+96*x)*log(2)-32*x^6+2
24*x^5+382*x^4-1000*x^3-96*x^2+128*x)*exp((64*log(2)^2+2*(-32*x^2-32*x+128)*log(2)+16*x^4+32*x^3-112*x^2-128*x
+256)/(4*log(2)^2+2*(-2*x+8)*log(2)+x^2-8*x+16))*exp(x^2*exp((64*log(2)^2+2*(-32*x^2-32*x+128)*log(2)+16*x^4+3
2*x^3-112*x^2-128*x+256)/(4*log(2)^2+2*(-2*x+8)*log(2)+x^2-8*x+16)))/(8*log(2)^3+4*(-3*x+12)*log(2)^2+2*(3*x^2
-24*x+48)*log(2)-x^3+12*x^2-48*x+64),x, algorithm="fricas")

[Out]

e^((16*x^4 + 32*x^3 - 112*x^2 + (x^4 + 4*x^2*log(2)^2 - 8*x^3 + 16*x^2 - 4*(x^3 - 4*x^2)*log(2))*e^(16*(x^4 +
2*x^3 - 7*x^2 - 4*(x^2 + x - 4)*log(2) + 4*log(2)^2 - 8*x + 16)/(x^2 - 4*(x - 4)*log(2) + 4*log(2)^2 - 8*x + 1
6)) - 64*(x^2 + x - 4)*log(2) + 64*log(2)^2 - 128*x + 256)/(x^2 - 4*(x - 4)*log(2) + 4*log(2)^2 - 8*x + 16) -
16*(x^4 + 2*x^3 - 7*x^2 - 4*(x^2 + x - 4)*log(2) + 4*log(2)^2 - 8*x + 16)/(x^2 - 4*(x - 4)*log(2) + 4*log(2)^2
- 8*x + 16))

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (22) = 44\).
time = 2.35, size = 70, normalized size = 2.69 \begin {gather*} e^{x^{2} e^{\frac {16 x^{4} + 32 x^{3} - 112 x^{2} - 128 x + \left (- 64 x^{2} - 64 x + 256\right ) \log {\left (2 \right )} + 64 \log {\left (2 \right )}^{2} + 256}{x^{2} - 8 x + \left (16 - 4 x\right ) \log {\left (2 \right )} + 4 \log {\left (2 \right )}^{2} + 16}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x*ln(2)**3+4*(-64*x**3-6*x**2+24*x)*ln(2)**2+2*(64*x**5+96*x**4-506*x**3-48*x**2+96*x)*ln(2)-32*
x**6+224*x**5+382*x**4-1000*x**3-96*x**2+128*x)*exp((64*ln(2)**2+2*(-32*x**2-32*x+128)*ln(2)+16*x**4+32*x**3-1
12*x**2-128*x+256)/(4*ln(2)**2+2*(-2*x+8)*ln(2)+x**2-8*x+16))*exp(x**2*exp((64*ln(2)**2+2*(-32*x**2-32*x+128)*
ln(2)+16*x**4+32*x**3-112*x**2-128*x+256)/(4*ln(2)**2+2*(-2*x+8)*ln(2)+x**2-8*x+16)))/(8*ln(2)**3+4*(-3*x+12)*
ln(2)**2+2*(3*x**2-24*x+48)*ln(2)-x**3+12*x**2-48*x+64),x)

[Out]

exp(x**2*exp((16*x**4 + 32*x**3 - 112*x**2 - 128*x + (-64*x**2 - 64*x + 256)*log(2) + 64*log(2)**2 + 256)/(x**
2 - 8*x + (16 - 4*x)*log(2) + 4*log(2)**2 + 16)))

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x*log(2)^3+4*(-64*x^3-6*x^2+24*x)*log(2)^2+2*(64*x^5+96*x^4-506*x^3-48*x^2+96*x)*log(2)-32*x^6+2
24*x^5+382*x^4-1000*x^3-96*x^2+128*x)*exp((64*log(2)^2+2*(-32*x^2-32*x+128)*log(2)+16*x^4+32*x^3-112*x^2-128*x
+256)/(4*log(2)^2+2*(-2*x+8)*log(2)+x^2-8*x+16))*exp(x^2*exp((64*log(2)^2+2*(-32*x^2-32*x+128)*log(2)+16*x^4+3
2*x^3-112*x^2-128*x+256)/(4*log(2)^2+2*(-2*x+8)*log(2)+x^2-8*x+16)))/(8*log(2)^3+4*(-3*x+12)*log(2)^2+2*(3*x^2
-24*x+48)*log(2)-x^3+12*x^2-48*x+64),x, algorithm="giac")

[Out]

integrate(2*(16*x^6 - 112*x^5 - 191*x^4 - 8*x*log(2)^3 + 500*x^3 + 4*(32*x^3 + 3*x^2 - 12*x)*log(2)^2 + 48*x^2
- 2*(32*x^5 + 48*x^4 - 253*x^3 - 24*x^2 + 48*x)*log(2) - 64*x)*e^(x^2*e^(16*(x^4 + 2*x^3 - 7*x^2 - 4*(x^2 + x
- 4)*log(2) + 4*log(2)^2 - 8*x + 16)/(x^2 - 4*(x - 4)*log(2) + 4*log(2)^2 - 8*x + 16)) + 16*(x^4 + 2*x^3 - 7*
x^2 - 4*(x^2 + x - 4)*log(2) + 4*log(2)^2 - 8*x + 16)/(x^2 - 4*(x - 4)*log(2) + 4*log(2)^2 - 8*x + 16))/(x^3 +
12*(x - 4)*log(2)^2 - 8*log(2)^3 - 12*x^2 - 6*(x^2 - 8*x + 16)*log(2) + 48*x - 64), x)

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Mupad [B]
time = 12.86, size = 221, normalized size = 8.50 \begin {gather*} {\mathrm {e}}^{{\left (\frac {1}{18446744073709551616}\right )}^{\frac {x^2+x-4}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,x^2\,{\mathrm {e}}^{\frac {64\,{\ln \left (2\right )}^2}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{\frac {16\,x^4}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{\frac {32\,x^3}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{-\frac {112\,x^2}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{\frac {256}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{-\frac {128\,x}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2*exp((64*log(2)^2 - 2*log(2)*(32*x + 32*x^2 - 128) - 128*x - 112*x^2 + 32*x^3 + 16*x^4 + 256)/(4*l
og(2)^2 - 2*log(2)*(2*x - 8) - 8*x + x^2 + 16)))*exp((64*log(2)^2 - 2*log(2)*(32*x + 32*x^2 - 128) - 128*x - 1
12*x^2 + 32*x^3 + 16*x^4 + 256)/(4*log(2)^2 - 2*log(2)*(2*x - 8) - 8*x + x^2 + 16))*(128*x + 16*x*log(2)^3 - 4
*log(2)^2*(6*x^2 - 24*x + 64*x^3) - 96*x^2 - 1000*x^3 + 382*x^4 + 224*x^5 - 32*x^6 + 2*log(2)*(96*x - 48*x^2 -
506*x^3 + 96*x^4 + 64*x^5)))/(2*log(2)*(3*x^2 - 24*x + 48) - 48*x - 4*log(2)^2*(3*x - 12) + 8*log(2)^3 + 12*x
^2 - x^3 + 64),x)

[Out]

exp((1/18446744073709551616)^((x + x^2 - 4)/(16*log(2) - 8*x - 4*x*log(2) + 4*log(2)^2 + x^2 + 16))*x^2*exp((6
4*log(2)^2)/(16*log(2) - 8*x - 4*x*log(2) + 4*log(2)^2 + x^2 + 16))*exp((16*x^4)/(16*log(2) - 8*x - 4*x*log(2)
+ 4*log(2)^2 + x^2 + 16))*exp((32*x^3)/(16*log(2) - 8*x - 4*x*log(2) + 4*log(2)^2 + x^2 + 16))*exp(-(112*x^2)
/(16*log(2) - 8*x - 4*x*log(2) + 4*log(2)^2 + x^2 + 16))*exp(256/(16*log(2) - 8*x - 4*x*log(2) + 4*log(2)^2 +
x^2 + 16))*exp(-(128*x)/(16*log(2) - 8*x - 4*x*log(2) + 4*log(2)^2 + x^2 + 16)))

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