\(\int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+(4-405 x+5 x^2) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} (256 x^{10}-2560 x^{11}+1280 x^{12}+(-320 x^4+128 x^5+160 x^6-160 x^7) \log ^2(2)+(-4+5 x^2) \log ^4(2))}{1280 x^{10}-2560 x^{11}+1280 x^{12}+(160 x^6-160 x^7) \log ^2(2)+5 x^2 \log ^4(2)} \, dx\) [6660]

Optimal result

Integrand size = 152, antiderivative size = 32 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx=e^{-81+x-\frac {4}{5 \left (-x+\frac {x}{x-\frac {\log ^2(2)}{16 x^4}}\right )}} \]

[Out]

exp(x-81-4/(5*x/(x-1/16*ln(2)^2/x^4)-5*x))

Rubi [F]

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

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.15 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx=e^{-81+\frac {4}{5 x}+x-\frac {64 x^3}{80 x^4-80 x^5+5 \log ^2(2)}} \]

[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))

Maple [A] (verified)

Time = 4.14 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.72

method	result	size
parallelrisch	\({\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \left (2\right )^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \left (-16 x^{5}+16 x^{4}+\ln \left (2\right )^{2}\right )}}\)	\(55\)
gosper	\({\mathrm e}^{\frac {-80 x^{7}+6560 x^{6}-6544 x^{5}+5 x^{2} \ln \left (2\right )^{2}-405 x \ln \left (2\right )^{2}+4 \ln \left (2\right )^{2}}{5 x \left (-16 x^{5}+16 x^{4}+\ln \left (2\right )^{2}\right )}}\)	\(62\)
risch	\({\mathrm e}^{\frac {-80 x^{7}+6560 x^{6}-6544 x^{5}+5 x^{2} \ln \left (2\right )^{2}-405 x \ln \left (2\right )^{2}+4 \ln \left (2\right )^{2}}{5 x \left (-16 x^{5}+16 x^{4}+\ln \left (2\right )^{2}\right )}}\)	\(62\)
norman	\(\frac {x \ln \left (2\right )^{2} {\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \left (2\right )^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \ln \left (2\right )^{2}-80 x^{6}+80 x^{5}}}+16 x^{5} {\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \left (2\right )^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \ln \left (2\right )^{2}-80 x^{6}+80 x^{5}}}-16 x^{6} {\mathrm e}^{\frac {\left (5 x^{2}-405 x +4\right ) \ln \left (2\right )^{2}-80 x^{7}+6560 x^{6}-6544 x^{5}}{5 x \ln \left (2\right )^{2}-80 x^{6}+80 x^{5}}}}{x \left (-16 x^{5}+16 x^{4}+\ln \left (2\right )^{2}\right )}\)	\(198\)

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

Fricas [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.72 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx=e^{\left (\frac {80 \, x^{7} - 6560 \, x^{6} + 6544 \, x^{5} - {\left (5 \, x^{2} - 405 \, x + 4\right )} \log \left (2\right )^{2}}{5 \, {\left (16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}\right )}}\right )} \]

[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))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (24) = 48\).

Time = 1.53 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.53 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx=e^{\frac {- 80 x^{7} + 6560 x^{6} - 6544 x^{5} + \left (5 x^{2} - 405 x + 4\right ) \log {\left (2 \right )}^{2}}{- 80 x^{6} + 80 x^{5} + 5 x \log {\left (2 \right )}^{2}}} \]

[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))

Maxima [A] (verification not implemented)

none

Time = 97.03 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.03 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx=e^{\left (\frac {64 \, x^{3}}{5 \, {\left (16 \, x^{5} - 16 \, x^{4} - \log \left (2\right )^{2}\right )}} + x + \frac {4}{5 \, x} - 81\right )} \]

[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)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 159 vs. \(2 (28) = 56\).

Time = 0.33 (sec) , antiderivative size = 159, normalized size of antiderivative = 4.97 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx=e^{\left (\frac {16 \, x^{7}}{16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}} - \frac {1312 \, x^{6}}{16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}} + \frac {6544 \, x^{5}}{5 \, {\left (16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}\right )}} - \frac {x^{2} \log \left (2\right )^{2}}{16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}} + \frac {81 \, x \log \left (2\right )^{2}}{16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}} - \frac {4 \, \log \left (2\right )^{2}}{5 \, {\left (16 \, x^{6} - 16 \, x^{5} - x \log \left (2\right )^{2}\right )}}\right )} \]

[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))

Mupad [B] (verification not implemented)

Time = 13.04 (sec) , antiderivative size = 147, normalized size of antiderivative = 4.59 \[ \int \frac {e^{\frac {-6544 x^5+6560 x^6-80 x^7+\left (4-405 x+5 x^2\right ) \log ^2(2)}{80 x^5-80 x^6+5 x \log ^2(2)}} \left (256 x^{10}-2560 x^{11}+1280 x^{12}+\left (-320 x^4+128 x^5+160 x^6-160 x^7\right ) \log ^2(2)+\left (-4+5 x^2\right ) \log ^4(2)\right )}{1280 x^{10}-2560 x^{11}+1280 x^{12}+\left (160 x^6-160 x^7\right ) \log ^2(2)+5 x^2 \log ^4(2)} \, dx={\mathrm {e}}^{\frac {x\,{\ln \left (2\right )}^2}{-16\,x^5+16\,x^4+{\ln \left (2\right )}^2}}\,{\mathrm {e}}^{\frac {4\,{\ln \left (2\right )}^2}{-80\,x^6+80\,x^5+5\,{\ln \left (2\right )}^2\,x}}\,{\mathrm {e}}^{-\frac {81\,{\ln \left (2\right )}^2}{-16\,x^5+16\,x^4+{\ln \left (2\right )}^2}}\,{\mathrm {e}}^{-\frac {16\,x^6}{-16\,x^5+16\,x^4+{\ln \left (2\right )}^2}}\,{\mathrm {e}}^{\frac {1312\,x^5}{-16\,x^5+16\,x^4+{\ln \left (2\right )}^2}}\,{\mathrm {e}}^{-\frac {6544\,x^4}{-80\,x^5+80\,x^4+5\,{\ln \left (2\right )}^2}} \]

[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))