3.67.60 \(\int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+(4-405 x+5 x^2) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} (256 x^{10}-2560 x^{11}+1280 x^{12}+(-320 x^4+128 x^5+160 x^6-160 x^7) \log ^2(2)+(-4+5 x^2) \log ^4(2))}{1280 x^{10}-2560 x^{11}+1280 x^{12}+(160 x^6-160 x^7) \log ^2(2)+5 x^2 \log ^4(2)} \, dx\)

Optimal. Leaf size=32 \[ e^{-81+x-\frac {4}{5 \left (-x+\frac {x}{x-\frac {\log ^2(2)}{16 x^4}}\right )}} \]

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Rubi [F]  time = 12.63, 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*} \int \frac {\exp \left (\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}\right ) \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(80*x^5 - 80*x^6 + 5*x*Log[2]^2))*(256*
x^10 - 2560*x^11 + 1280*x^12 + (-320*x^4 + 128*x^5 + 160*x^6 - 160*x^7)*Log[2]^2 + (-4 + 5*x^2)*Log[2]^4))/(12
80*x^10 - 2560*x^11 + 1280*x^12 + (160*x^6 - 160*x^7)*Log[2]^2 + 5*x^2*Log[2]^4),x]

[Out]

Defer[Int][E^(-1/5*(-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(x*(-16*x^4 + 16*x^5 - Log[2
]^2))), x] - (4*Defer[Int][1/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4
+ 16*x^5 - Log[2]^2)))*x^2), x])/5 - (64*Log[2]^2*Defer[Int][x/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x
+ 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Log[2]^2)))*(-16*x^4 + 16*x^5 - Log[2]^2)^2), x])/5 - 64*Log[2]^2
*Defer[Int][x^2/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Lo
g[2]^2)))*(-16*x^4 + 16*x^5 - Log[2]^2)^2), x] - (1024*Defer[Int][x^4/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4
- 405*x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Log[2]^2)))*(-16*x^4 + 16*x^5 - Log[2]^2)^2), x])/5 - (64*
Defer[Int][1/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Log[2
]^2)))*(-16*x^4 + 16*x^5 - Log[2]^2)), x])/5 - (64*Defer[Int][x/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*
x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Log[2]^2)))*(-16*x^4 + 16*x^5 - Log[2]^2)), x])/5 - (128*Defer[I
nt][x^2/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Log[2]^2))
)*(-16*x^4 + 16*x^5 - Log[2]^2)), x])/5 - (64*Log[2]^2*Defer[Int][1/(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 -
405*x + 5*x^2)*Log[2]^2)/(5*x*(-16*x^4 + 16*x^5 - Log[2]^2)))*(16*x^4 - 16*x^5 + Log[2]^2)^2), x])/5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{5 x^2 \left (16 x^4-16 x^5+\log ^2(2)\right )^2} \, dx\\ &=\frac {1}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{x^2 \left (16 x^4-16 x^5+\log ^2(2)\right )^2} \, dx\\ &=\frac {1}{5} \int \left (5 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )-\frac {4 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{x^2}-\frac {64 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \left (1+x+2 x^2\right )}{-16 x^4+16 x^5-\log ^2(2)}-\frac {64 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \left (16 x^4+\log ^2(2)+x \log ^2(2)+5 x^2 \log ^2(2)\right )}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2}\right ) \, dx\\ &=-\left (\frac {4}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{x^2} \, dx\right )-\frac {64}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \left (1+x+2 x^2\right )}{-16 x^4+16 x^5-\log ^2(2)} \, dx-\frac {64}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \left (16 x^4+\log ^2(2)+x \log ^2(2)+5 x^2 \log ^2(2)\right )}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2} \, dx+\int \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \, dx\\ &=-\left (\frac {4}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{x^2} \, dx\right )-\frac {64}{5} \int \left (\frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{-16 x^4+16 x^5-\log ^2(2)}+\frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x}{-16 x^4+16 x^5-\log ^2(2)}+\frac {2 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x^2}{-16 x^4+16 x^5-\log ^2(2)}\right ) \, dx-\frac {64}{5} \int \left (\frac {16 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x^4}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2}+\frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x \log ^2(2)}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2}+\frac {5 \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x^2 \log ^2(2)}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2}+\frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \log ^2(2)}{\left (16 x^4-16 x^5+\log ^2(2)\right )^2}\right ) \, dx+\int \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \, dx\\ &=-\left (\frac {4}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{x^2} \, dx\right )-\frac {64}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{-16 x^4+16 x^5-\log ^2(2)} \, dx-\frac {64}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x}{-16 x^4+16 x^5-\log ^2(2)} \, dx-\frac {128}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x^2}{-16 x^4+16 x^5-\log ^2(2)} \, dx-\frac {1024}{5} \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x^4}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2} \, dx-\frac {1}{5} \left (64 \log ^2(2)\right ) \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2} \, dx-\frac {1}{5} \left (64 \log ^2(2)\right ) \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right )}{\left (16 x^4-16 x^5+\log ^2(2)\right )^2} \, dx-\left (64 \log ^2(2)\right ) \int \frac {\exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) x^2}{\left (-16 x^4+16 x^5-\log ^2(2)\right )^2} \, dx+\int \exp \left (-\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{5 x \left (-16 x^4+16 x^5-\log ^2(2)\right )}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.15, size = 36, normalized size = 1.12 \begin {gather*} e^{-81+\frac {4}{5 x}+x-\frac {64 x^3}{80 x^4-80 x^5+5 \log ^2(2)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-6544*x^5 + 6560*x^6 - 80*x^7 + (4 - 405*x + 5*x^2)*Log[2]^2)/(80*x^5 - 80*x^6 + 5*x*Log[2]^2))
*(256*x^10 - 2560*x^11 + 1280*x^12 + (-320*x^4 + 128*x^5 + 160*x^6 - 160*x^7)*Log[2]^2 + (-4 + 5*x^2)*Log[2]^4
))/(1280*x^10 - 2560*x^11 + 1280*x^12 + (160*x^6 - 160*x^7)*Log[2]^2 + 5*x^2*Log[2]^4),x]

[Out]

E^(-81 + 4/(5*x) + x - (64*x^3)/(80*x^4 - 80*x^5 + 5*Log[2]^2))

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fricas [A]  time = 0.55, size = 55, normalized size = 1.72 \begin {gather*} e^{\left (\frac {80 \, x^{7} - 6560 \, x^{6} + 6544 \, x^{5} - {\left (5 \, x^{2} - 405 \, x + 4\right )} \log \relax (2)^{2}}{5 \, {\left (16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2-4)*log(2)^4+(-160*x^7+160*x^6+128*x^5-320*x^4)*log(2)^2+1280*x^12-2560*x^11+256*x^10)*exp(((
5*x^2-405*x+4)*log(2)^2-80*x^7+6560*x^6-6544*x^5)/(5*x*log(2)^2-80*x^6+80*x^5))/(5*x^2*log(2)^4+(-160*x^7+160*
x^6)*log(2)^2+1280*x^12-2560*x^11+1280*x^10),x, algorithm="fricas")

[Out]

e^(1/5*(80*x^7 - 6560*x^6 + 6544*x^5 - (5*x^2 - 405*x + 4)*log(2)^2)/(16*x^6 - 16*x^5 - x*log(2)^2))

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giac [B]  time = 0.67, size = 159, normalized size = 4.97 \begin {gather*} e^{\left (\frac {16 \, x^{7}}{16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}} - \frac {1312 \, x^{6}}{16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}} + \frac {6544 \, x^{5}}{5 \, {\left (16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}\right )}} - \frac {x^{2} \log \relax (2)^{2}}{16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}} + \frac {81 \, x \log \relax (2)^{2}}{16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}} - \frac {4 \, \log \relax (2)^{2}}{5 \, {\left (16 \, x^{6} - 16 \, x^{5} - x \log \relax (2)^{2}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2-4)*log(2)^4+(-160*x^7+160*x^6+128*x^5-320*x^4)*log(2)^2+1280*x^12-2560*x^11+256*x^10)*exp(((
5*x^2-405*x+4)*log(2)^2-80*x^7+6560*x^6-6544*x^5)/(5*x*log(2)^2-80*x^6+80*x^5))/(5*x^2*log(2)^4+(-160*x^7+160*
x^6)*log(2)^2+1280*x^12-2560*x^11+1280*x^10),x, algorithm="giac")

[Out]

e^(16*x^7/(16*x^6 - 16*x^5 - x*log(2)^2) - 1312*x^6/(16*x^6 - 16*x^5 - x*log(2)^2) + 6544/5*x^5/(16*x^6 - 16*x
^5 - x*log(2)^2) - x^2*log(2)^2/(16*x^6 - 16*x^5 - x*log(2)^2) + 81*x*log(2)^2/(16*x^6 - 16*x^5 - x*log(2)^2)
- 4/5*log(2)^2/(16*x^6 - 16*x^5 - x*log(2)^2))

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maple [B]  time = 0.50, size = 62, normalized size = 1.94

method	result	size
gosper	\({\mathrm e}^{\frac {-80 x^{7}+6560 x^{6}-6544 x^{5}+5 x^{2} \ln \relax (2)^{2}-405 x \ln \relax (2)^{2}+4 \ln \relax (2)^{2}}{5 x \left (-16 x^{5}+16 x^{4}+\ln \relax (2)^{2}\right )}}\)	\(62\)
risch	\({\mathrm e}^{\frac {-80 x^{7}+6560 x^{6}-6544 x^{5}+5 x^{2} \ln \relax (2)^{2}-405 x \ln \relax (2)^{2}+4 \ln \relax (2)^{2}}{5 x \left (-16 x^{5}+16 x^{4}+\ln \relax (2)^{2}\right )}}\)	\(62\)
norman	\(\frac {x \ln \relax (2)^{2} {\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \relax (2)^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \ln \relax (2)^{2}-80 x^{6}+80 x^{5}}}+16 x^{5} {\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \relax (2)^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \ln \relax (2)^{2}-80 x^{6}+80 x^{5}}}-16 x^{6} {\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \relax (2)^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \ln \relax (2)^{2}-80 x^{6}+80 x^{5}}}}{x \left (-16 x^{5}+16 x^{4}+\ln \relax (2)^{2}\right )}\)	\(198\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*x^2-4)*ln(2)^4+(-160*x^7+160*x^6+128*x^5-320*x^4)*ln(2)^2+1280*x^12-2560*x^11+256*x^10)*exp(((5*x^2-40
5*x+4)*ln(2)^2-80*x^7+6560*x^6-6544*x^5)/(5*x*ln(2)^2-80*x^6+80*x^5))/(5*x^2*ln(2)^4+(-160*x^7+160*x^6)*ln(2)^
2+1280*x^12-2560*x^11+1280*x^10),x,method=_RETURNVERBOSE)

[Out]

exp(1/5*(-80*x^7+6560*x^6-6544*x^5+5*x^2*ln(2)^2-405*x*ln(2)^2+4*ln(2)^2)/x/(-16*x^5+16*x^4+ln(2)^2))

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maxima [A]  time = 116.48, size = 33, normalized size = 1.03 \begin {gather*} e^{\left (\frac {64 \, x^{3}}{5 \, {\left (16 \, x^{5} - 16 \, x^{4} - \log \relax (2)^{2}\right )}} + x + \frac {4}{5 \, x} - 81\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2-4)*log(2)^4+(-160*x^7+160*x^6+128*x^5-320*x^4)*log(2)^2+1280*x^12-2560*x^11+256*x^10)*exp(((
5*x^2-405*x+4)*log(2)^2-80*x^7+6560*x^6-6544*x^5)/(5*x*log(2)^2-80*x^6+80*x^5))/(5*x^2*log(2)^4+(-160*x^7+160*
x^6)*log(2)^2+1280*x^12-2560*x^11+1280*x^10),x, algorithm="maxima")

[Out]

e^(64/5*x^3/(16*x^5 - 16*x^4 - log(2)^2) + x + 4/5/x - 81)

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mupad [B]  time = 5.14, size = 147, normalized size = 4.59 \begin {gather*} {\mathrm {e}}^{\frac {x\,{\ln \relax (2)}^2}{-16\,x^5+16\,x^4+{\ln \relax (2)}^2}}\,{\mathrm {e}}^{\frac {4\,{\ln \relax (2)}^2}{-80\,x^6+80\,x^5+5\,{\ln \relax (2)}^2\,x}}\,{\mathrm {e}}^{-\frac {81\,{\ln \relax (2)}^2}{-16\,x^5+16\,x^4+{\ln \relax (2)}^2}}\,{\mathrm {e}}^{-\frac {16\,x^6}{-16\,x^5+16\,x^4+{\ln \relax (2)}^2}}\,{\mathrm {e}}^{\frac {1312\,x^5}{-16\,x^5+16\,x^4+{\ln \relax (2)}^2}}\,{\mathrm {e}}^{-\frac {6544\,x^4}{-80\,x^5+80\,x^4+5\,{\ln \relax (2)}^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((log(2)^2*(5*x^2 - 405*x + 4) - 6544*x^5 + 6560*x^6 - 80*x^7)/(5*x*log(2)^2 + 80*x^5 - 80*x^6))*(log(
2)^4*(5*x^2 - 4) - log(2)^2*(320*x^4 - 128*x^5 - 160*x^6 + 160*x^7) + 256*x^10 - 2560*x^11 + 1280*x^12))/(5*x^
2*log(2)^4 + 1280*x^10 - 2560*x^11 + 1280*x^12 + log(2)^2*(160*x^6 - 160*x^7)),x)

[Out]

exp((x*log(2)^2)/(log(2)^2 + 16*x^4 - 16*x^5))*exp((4*log(2)^2)/(5*x*log(2)^2 + 80*x^5 - 80*x^6))*exp(-(81*log
(2)^2)/(log(2)^2 + 16*x^4 - 16*x^5))*exp(-(16*x^6)/(log(2)^2 + 16*x^4 - 16*x^5))*exp((1312*x^5)/(log(2)^2 + 16
*x^4 - 16*x^5))*exp(-(6544*x^4)/(5*log(2)^2 + 80*x^4 - 80*x^5))

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sympy [B]  time = 2.11, size = 49, normalized size = 1.53 \begin {gather*} e^{\frac {- 80 x^{7} + 6560 x^{6} - 6544 x^{5} + \left (5 x^{2} - 405 x + 4\right ) \log {\relax (2 )}^{2}}{- 80 x^{6} + 80 x^{5} + 5 x \log {\relax (2 )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x**2-4)*ln(2)**4+(-160*x**7+160*x**6+128*x**5-320*x**4)*ln(2)**2+1280*x**12-2560*x**11+256*x**10
)*exp(((5*x**2-405*x+4)*ln(2)**2-80*x**7+6560*x**6-6544*x**5)/(5*x*ln(2)**2-80*x**6+80*x**5))/(5*x**2*ln(2)**4
+(-160*x**7+160*x**6)*ln(2)**2+1280*x**12-2560*x**11+1280*x**10),x)

[Out]

exp((-80*x**7 + 6560*x**6 - 6544*x**5 + (5*x**2 - 405*x + 4)*log(2)**2)/(-80*x**6 + 80*x**5 + 5*x*log(2)**2))

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