3.97.48 \(\int \frac {e^{\frac {2 x}{\log (\log (4))}} (-2000-1200 x^2-240 x^4-16 x^6+(600+240 x^2+24 x^4) \log (x)+(-60-12 x^2) \log ^2(x)+2 \log ^3(x))+(-840 x-210 x^3+(164 x+20 x^3) \log (x)-8 x \log ^2(x)) \log (\log (4))+e^{\frac {x}{\log (\log (4))}} (-4000-2600 x^2-560 x^4-40 x^6+(1200+520 x^2+56 x^4) \log (x)+(-120-26 x^2) \log ^2(x)+4 \log ^3(x)+(-420 x-84 x^3+(82 x+8 x^3) \log (x)-4 x \log ^2(x)) \log (\log (4)))}{(-1000-600 x^2-120 x^4-8 x^6+(300+120 x^2+12 x^4) \log (x)+(-30-6 x^2) \log ^2(x)+\log ^3(x)) \log (\log (4))} \, dx\)

Optimal. Leaf size=31 \[ \left (2+e^{\frac {x}{\log (\log (4))}}+\frac {x^2}{2 \left (5+x^2\right )-\log (x)}\right )^2 \]

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Rubi [F]  time = 4.34, 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 {e^{\frac {2 x}{\log (\log (4))}} \left (-2000-1200 x^2-240 x^4-16 x^6+\left (600+240 x^2+24 x^4\right ) \log (x)+\left (-60-12 x^2\right ) \log ^2(x)+2 \log ^3(x)\right )+\left (-840 x-210 x^3+\left (164 x+20 x^3\right ) \log (x)-8 x \log ^2(x)\right ) \log (\log (4))+e^{\frac {x}{\log (\log (4))}} \left (-4000-2600 x^2-560 x^4-40 x^6+\left (1200+520 x^2+56 x^4\right ) \log (x)+\left (-120-26 x^2\right ) \log ^2(x)+4 \log ^3(x)+\left (-420 x-84 x^3+\left (82 x+8 x^3\right ) \log (x)-4 x \log ^2(x)\right ) \log (\log (4))\right )}{\left (-1000-600 x^2-120 x^4-8 x^6+\left (300+120 x^2+12 x^4\right ) \log (x)+\left (-30-6 x^2\right ) \log ^2(x)+\log ^3(x)\right ) \log (\log (4))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((2*x)/Log[Log[4]])*(-2000 - 1200*x^2 - 240*x^4 - 16*x^6 + (600 + 240*x^2 + 24*x^4)*Log[x] + (-60 - 12*
x^2)*Log[x]^2 + 2*Log[x]^3) + (-840*x - 210*x^3 + (164*x + 20*x^3)*Log[x] - 8*x*Log[x]^2)*Log[Log[4]] + E^(x/L
og[Log[4]])*(-4000 - 2600*x^2 - 560*x^4 - 40*x^6 + (1200 + 520*x^2 + 56*x^4)*Log[x] + (-120 - 26*x^2)*Log[x]^2
+ 4*Log[x]^3 + (-420*x - 84*x^3 + (82*x + 8*x^3)*Log[x] - 4*x*Log[x]^2)*Log[Log[4]]))/((-1000 - 600*x^2 - 120
*x^4 - 8*x^6 + (300 + 120*x^2 + 12*x^4)*Log[x] + (-30 - 6*x^2)*Log[x]^2 + Log[x]^3)*Log[Log[4]]),x]

[Out]

E^((2*x)/Log[Log[4]]) + (2*E^(x/Log[Log[4]])*(200 + 90*x^2 + 10*x^4 - 40*Log[x] - 9*x^2*Log[x] + 2*Log[x]^2))/
(10 + 2*x^2 - Log[x])^2 + 2*Defer[Int][x^3/(10 + 2*x^2 - Log[x])^3, x] - 8*Defer[Int][x^5/(10 + 2*x^2 - Log[x]
)^3, x] + 4*Defer[Int][x/(10 + 2*x^2 - Log[x])^2, x] - 12*Defer[Int][x^3/(10 + 2*x^2 - Log[x])^2, x] + 8*Defer
[Int][x/(10 + 2*x^2 - Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{\frac {2 x}{\log (\log (4))}} \left (-2000-1200 x^2-240 x^4-16 x^6+\left (600+240 x^2+24 x^4\right ) \log (x)+\left (-60-12 x^2\right ) \log ^2(x)+2 \log ^3(x)\right )+\left (-840 x-210 x^3+\left (164 x+20 x^3\right ) \log (x)-8 x \log ^2(x)\right ) \log (\log (4))+e^{\frac {x}{\log (\log (4))}} \left (-4000-2600 x^2-560 x^4-40 x^6+\left (1200+520 x^2+56 x^4\right ) \log (x)+\left (-120-26 x^2\right ) \log ^2(x)+4 \log ^3(x)+\left (-420 x-84 x^3+\left (82 x+8 x^3\right ) \log (x)-4 x \log ^2(x)\right ) \log (\log (4))\right )}{-1000-600 x^2-120 x^4-8 x^6+\left (300+120 x^2+12 x^4\right ) \log (x)+\left (-30-6 x^2\right ) \log ^2(x)+\log ^3(x)} \, dx}{\log (\log (4))}\\ &=\frac {\int \frac {2 \left (5 \left (4+x^2\right )+2 e^{\frac {x}{\log (\log (4))}} \left (5+x^2\right )-\left (2+e^{\frac {x}{\log (\log (4))}}\right ) \log (x)\right ) \left (4 e^{\frac {x}{\log (\log (4))}} \left (5+x^2\right )^2+e^{\frac {x}{\log (\log (4))}} \log ^2(x)+21 x \log (\log (4))-2 \log (x) \left (2 e^{\frac {x}{\log (\log (4))}} \left (5+x^2\right )+x \log (\log (4))\right )\right )}{\left (2 \left (5+x^2\right )-\log (x)\right )^3} \, dx}{\log (\log (4))}\\ &=\frac {2 \int \frac {\left (5 \left (4+x^2\right )+2 e^{\frac {x}{\log (\log (4))}} \left (5+x^2\right )-\left (2+e^{\frac {x}{\log (\log (4))}}\right ) \log (x)\right ) \left (4 e^{\frac {x}{\log (\log (4))}} \left (5+x^2\right )^2+e^{\frac {x}{\log (\log (4))}} \log ^2(x)+21 x \log (\log (4))-2 \log (x) \left (2 e^{\frac {x}{\log (\log (4))}} \left (5+x^2\right )+x \log (\log (4))\right )\right )}{\left (2 \left (5+x^2\right )-\log (x)\right )^3} \, dx}{\log (\log (4))}\\ &=\frac {2 \int \left (e^{\frac {2 x}{\log (\log (4))}}+\frac {105 x \left (4+x^2\right ) \log (\log (4))}{\left (10+2 x^2-\log (x)\right )^3}-\frac {42 x \log (x) \log (\log (4))}{\left (10+2 x^2-\log (x)\right )^3}-\frac {10 x \left (4+x^2\right ) \log (x) \log (\log (4))}{\left (10+2 x^2-\log (x)\right )^3}+\frac {4 x \log ^2(x) \log (\log (4))}{\left (10+2 x^2-\log (x)\right )^3}+\frac {e^{\frac {x}{\log (\log (4))}} \left (200+90 x^2+10 x^4-40 \log (x)-9 x^2 \log (x)+2 \log ^2(x)+21 x \log (\log (4))-2 x \log (x) \log (\log (4))\right )}{\left (10+2 x^2-\log (x)\right )^2}\right ) \, dx}{\log (\log (4))}\\ &=8 \int \frac {x \log ^2(x)}{\left (10+2 x^2-\log (x)\right )^3} \, dx-20 \int \frac {x \left (4+x^2\right ) \log (x)}{\left (10+2 x^2-\log (x)\right )^3} \, dx-84 \int \frac {x \log (x)}{\left (10+2 x^2-\log (x)\right )^3} \, dx+210 \int \frac {x \left (4+x^2\right )}{\left (10+2 x^2-\log (x)\right )^3} \, dx+\frac {2 \int e^{\frac {2 x}{\log (\log (4))}} \, dx}{\log (\log (4))}+\frac {2 \int \frac {e^{\frac {x}{\log (\log (4))}} \left (200+90 x^2+10 x^4-40 \log (x)-9 x^2 \log (x)+2 \log ^2(x)+21 x \log (\log (4))-2 x \log (x) \log (\log (4))\right )}{\left (10+2 x^2-\log (x)\right )^2} \, dx}{\log (\log (4))}\\ &=e^{\frac {2 x}{\log (\log (4))}}+\frac {2 e^{\frac {x}{\log (\log (4))}} \left (200+90 x^2+10 x^4-40 \log (x)-9 x^2 \log (x)+2 \log ^2(x)\right )}{\left (10+2 x^2-\log (x)\right )^2}+8 \int \left (\frac {4 x \left (5+x^2\right )^2}{\left (10+2 x^2-\log (x)\right )^3}-\frac {4 x \left (5+x^2\right )}{\left (10+2 x^2-\log (x)\right )^2}+\frac {x}{10+2 x^2-\log (x)}\right ) \, dx-20 \int \left (\frac {2 x \left (20+9 x^2+x^4\right )}{\left (10+2 x^2-\log (x)\right )^3}-\frac {x \left (4+x^2\right )}{\left (10+2 x^2-\log (x)\right )^2}\right ) \, dx-84 \int \left (\frac {2 x \left (5+x^2\right )}{\left (10+2 x^2-\log (x)\right )^3}-\frac {x}{\left (10+2 x^2-\log (x)\right )^2}\right ) \, dx+210 \int \left (\frac {4 x}{\left (10+2 x^2-\log (x)\right )^3}+\frac {x^3}{\left (10+2 x^2-\log (x)\right )^3}\right ) \, dx\\ &=e^{\frac {2 x}{\log (\log (4))}}+\frac {2 e^{\frac {x}{\log (\log (4))}} \left (200+90 x^2+10 x^4-40 \log (x)-9 x^2 \log (x)+2 \log ^2(x)\right )}{\left (10+2 x^2-\log (x)\right )^2}+8 \int \frac {x}{10+2 x^2-\log (x)} \, dx+20 \int \frac {x \left (4+x^2\right )}{\left (10+2 x^2-\log (x)\right )^2} \, dx+32 \int \frac {x \left (5+x^2\right )^2}{\left (10+2 x^2-\log (x)\right )^3} \, dx-32 \int \frac {x \left (5+x^2\right )}{\left (10+2 x^2-\log (x)\right )^2} \, dx-40 \int \frac {x \left (20+9 x^2+x^4\right )}{\left (10+2 x^2-\log (x)\right )^3} \, dx+84 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^2} \, dx-168 \int \frac {x \left (5+x^2\right )}{\left (10+2 x^2-\log (x)\right )^3} \, dx+210 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^3} \, dx+840 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^3} \, dx\\ &=e^{\frac {2 x}{\log (\log (4))}}+\frac {2 e^{\frac {x}{\log (\log (4))}} \left (200+90 x^2+10 x^4-40 \log (x)-9 x^2 \log (x)+2 \log ^2(x)\right )}{\left (10+2 x^2-\log (x)\right )^2}+8 \int \frac {x}{10+2 x^2-\log (x)} \, dx+20 \int \left (\frac {4 x}{\left (10+2 x^2-\log (x)\right )^2}+\frac {x^3}{\left (10+2 x^2-\log (x)\right )^2}\right ) \, dx+32 \int \left (\frac {25 x}{\left (10+2 x^2-\log (x)\right )^3}+\frac {10 x^3}{\left (10+2 x^2-\log (x)\right )^3}+\frac {x^5}{\left (10+2 x^2-\log (x)\right )^3}\right ) \, dx-32 \int \left (\frac {5 x}{\left (10+2 x^2-\log (x)\right )^2}+\frac {x^3}{\left (10+2 x^2-\log (x)\right )^2}\right ) \, dx-40 \int \left (\frac {20 x}{\left (10+2 x^2-\log (x)\right )^3}+\frac {9 x^3}{\left (10+2 x^2-\log (x)\right )^3}+\frac {x^5}{\left (10+2 x^2-\log (x)\right )^3}\right ) \, dx+84 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^2} \, dx-168 \int \left (\frac {5 x}{\left (10+2 x^2-\log (x)\right )^3}+\frac {x^3}{\left (10+2 x^2-\log (x)\right )^3}\right ) \, dx+210 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^3} \, dx+840 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^3} \, dx\\ &=e^{\frac {2 x}{\log (\log (4))}}+\frac {2 e^{\frac {x}{\log (\log (4))}} \left (200+90 x^2+10 x^4-40 \log (x)-9 x^2 \log (x)+2 \log ^2(x)\right )}{\left (10+2 x^2-\log (x)\right )^2}+8 \int \frac {x}{10+2 x^2-\log (x)} \, dx+20 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^2} \, dx+32 \int \frac {x^5}{\left (10+2 x^2-\log (x)\right )^3} \, dx-32 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^2} \, dx-40 \int \frac {x^5}{\left (10+2 x^2-\log (x)\right )^3} \, dx+80 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^2} \, dx+84 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^2} \, dx-160 \int \frac {x}{\left (10+2 x^2-\log (x)\right )^2} \, dx-168 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^3} \, dx+210 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^3} \, dx+320 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^3} \, dx-360 \int \frac {x^3}{\left (10+2 x^2-\log (x)\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.17, size = 68, normalized size = 2.19 \begin {gather*} 4 e^{\frac {x}{\log (\log (4))}}+e^{\frac {2 x}{\log (\log (4))}}+\frac {2 \left (2+e^{\frac {x}{\log (\log (4))}}\right ) x^2}{2 \left (5+x^2\right )-\log (x)}+\frac {x^4}{\left (-2 \left (5+x^2\right )+\log (x)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((2*x)/Log[Log[4]])*(-2000 - 1200*x^2 - 240*x^4 - 16*x^6 + (600 + 240*x^2 + 24*x^4)*Log[x] + (-60
- 12*x^2)*Log[x]^2 + 2*Log[x]^3) + (-840*x - 210*x^3 + (164*x + 20*x^3)*Log[x] - 8*x*Log[x]^2)*Log[Log[4]] +
E^(x/Log[Log[4]])*(-4000 - 2600*x^2 - 560*x^4 - 40*x^6 + (1200 + 520*x^2 + 56*x^4)*Log[x] + (-120 - 26*x^2)*Lo
g[x]^2 + 4*Log[x]^3 + (-420*x - 84*x^3 + (82*x + 8*x^3)*Log[x] - 4*x*Log[x]^2)*Log[Log[4]]))/((-1000 - 600*x^2
- 120*x^4 - 8*x^6 + (300 + 120*x^2 + 12*x^4)*Log[x] + (-30 - 6*x^2)*Log[x]^2 + Log[x]^3)*Log[Log[4]]),x]

[Out]

4*E^(x/Log[Log[4]]) + E^((2*x)/Log[Log[4]]) + (2*(2 + E^(x/Log[Log[4]]))*x^2)/(2*(5 + x^2) - Log[x]) + x^4/(-2
*(5 + x^2) + Log[x])^2

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fricas [B]  time = 0.50, size = 124, normalized size = 4.00 \begin {gather*} \frac {9 \, x^{4} - 4 \, x^{2} \log \relax (x) + 40 \, x^{2} + {\left (4 \, x^{4} + 40 \, x^{2} - 4 \, {\left (x^{2} + 5\right )} \log \relax (x) + \log \relax (x)^{2} + 100\right )} e^{\left (\frac {2 \, x}{\log \left (2 \, \log \relax (2)\right )}\right )} + 2 \, {\left (10 \, x^{4} + 90 \, x^{2} - {\left (9 \, x^{2} + 40\right )} \log \relax (x) + 2 \, \log \relax (x)^{2} + 200\right )} e^{\left (\frac {x}{\log \left (2 \, \log \relax (2)\right )}\right )}}{4 \, x^{4} + 40 \, x^{2} - 4 \, {\left (x^{2} + 5\right )} \log \relax (x) + \log \relax (x)^{2} + 100} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*log(x)^3+(-12*x^2-60)*log(x)^2+(24*x^4+240*x^2+600)*log(x)-16*x^6-240*x^4-1200*x^2-2000)*exp(x/l
og(2*log(2)))^2+((-4*x*log(x)^2+(8*x^3+82*x)*log(x)-84*x^3-420*x)*log(2*log(2))+4*log(x)^3+(-26*x^2-120)*log(x
)^2+(56*x^4+520*x^2+1200)*log(x)-40*x^6-560*x^4-2600*x^2-4000)*exp(x/log(2*log(2)))+(-8*x*log(x)^2+(20*x^3+164
*x)*log(x)-210*x^3-840*x)*log(2*log(2)))/(log(x)^3+(-6*x^2-30)*log(x)^2+(12*x^4+120*x^2+300)*log(x)-8*x^6-120*
x^4-600*x^2-1000)/log(2*log(2)),x, algorithm="fricas")

[Out]

(9*x^4 - 4*x^2*log(x) + 40*x^2 + (4*x^4 + 40*x^2 - 4*(x^2 + 5)*log(x) + log(x)^2 + 100)*e^(2*x/log(2*log(2)))
+ 2*(10*x^4 + 90*x^2 - (9*x^2 + 40)*log(x) + 2*log(x)^2 + 200)*e^(x/log(2*log(2))))/(4*x^4 + 40*x^2 - 4*(x^2 +
5)*log(x) + log(x)^2 + 100)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*log(x)^3+(-12*x^2-60)*log(x)^2+(24*x^4+240*x^2+600)*log(x)-16*x^6-240*x^4-1200*x^2-2000)*exp(x/l
og(2*log(2)))^2+((-4*x*log(x)^2+(8*x^3+82*x)*log(x)-84*x^3-420*x)*log(2*log(2))+4*log(x)^3+(-26*x^2-120)*log(x
)^2+(56*x^4+520*x^2+1200)*log(x)-40*x^6-560*x^4-2600*x^2-4000)*exp(x/log(2*log(2)))+(-8*x*log(x)^2+(20*x^3+164
*x)*log(x)-210*x^3-840*x)*log(2*log(2)))/(log(x)^3+(-6*x^2-30)*log(x)^2+(12*x^4+120*x^2+300)*log(x)-8*x^6-120*
x^4-600*x^2-1000)/log(2*log(2)),x, algorithm="giac")

[Out]

undef

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maple [B]  time = 0.10, size = 262, normalized size = 8.45

method	result	size
risch	\(\frac {{\mathrm e}^{\frac {2 x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}} \ln \relax (2)}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}+\frac {{\mathrm e}^{\frac {2 x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}} \ln \left (\ln \relax (2)\right )}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}+\frac {4 \ln \relax (2) {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}}}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}+\frac {4 \ln \left (\ln \relax (2)\right ) {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}}}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}+\frac {\left (4 \ln \relax (2) x^{2} {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}}+4 \ln \left (\ln \relax (2)\right ) x^{2} {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}}+9 x^{2} \ln \relax (2)-2 \ln \relax (2) {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}} \ln \relax (x )+9 x^{2} \ln \left (\ln \relax (2)\right )-2 \ln \left (\ln \relax (2)\right ) {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}} \ln \relax (x )+20 \ln \relax (2) {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}}-4 \ln \relax (2) \ln \relax (x )+20 \ln \left (\ln \relax (2)\right ) {\mathrm e}^{\frac {x}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}}-4 \ln \relax (x ) \ln \left (\ln \relax (2)\right )+40 \ln \relax (2)+40 \ln \left (\ln \relax (2)\right )\right ) x^{2}}{\left (\ln \relax (2)+\ln \left (\ln \relax (2)\right )\right ) \left (2 x^{2}+10-\ln \relax (x )\right )^{2}}\)	\(262\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*ln(x)^3+(-12*x^2-60)*ln(x)^2+(24*x^4+240*x^2+600)*ln(x)-16*x^6-240*x^4-1200*x^2-2000)*exp(x/ln(2*ln(2)
))^2+((-4*x*ln(x)^2+(8*x^3+82*x)*ln(x)-84*x^3-420*x)*ln(2*ln(2))+4*ln(x)^3+(-26*x^2-120)*ln(x)^2+(56*x^4+520*x
^2+1200)*ln(x)-40*x^6-560*x^4-2600*x^2-4000)*exp(x/ln(2*ln(2)))+(-8*x*ln(x)^2+(20*x^3+164*x)*ln(x)-210*x^3-840
*x)*ln(2*ln(2)))/(ln(x)^3+(-6*x^2-30)*ln(x)^2+(12*x^4+120*x^2+300)*ln(x)-8*x^6-120*x^4-600*x^2-1000)/ln(2*ln(2
)),x,method=_RETURNVERBOSE)

[Out]

1/(ln(2)+ln(ln(2)))*exp(2*x/(ln(2)+ln(ln(2))))*ln(2)+1/(ln(2)+ln(ln(2)))*exp(2*x/(ln(2)+ln(ln(2))))*ln(ln(2))+
4/(ln(2)+ln(ln(2)))*ln(2)*exp(x/(ln(2)+ln(ln(2))))+4/(ln(2)+ln(ln(2)))*ln(ln(2))*exp(x/(ln(2)+ln(ln(2))))+1/(l
n(2)+ln(ln(2)))*(4*ln(2)*x^2*exp(x/(ln(2)+ln(ln(2))))+4*ln(ln(2))*x^2*exp(x/(ln(2)+ln(ln(2))))+9*x^2*ln(2)-2*l
n(2)*exp(x/(ln(2)+ln(ln(2))))*ln(x)+9*x^2*ln(ln(2))-2*ln(ln(2))*exp(x/(ln(2)+ln(ln(2))))*ln(x)+20*ln(2)*exp(x/
(ln(2)+ln(ln(2))))-4*ln(2)*ln(x)+20*ln(ln(2))*exp(x/(ln(2)+ln(ln(2))))-4*ln(x)*ln(ln(2))+40*ln(2)+40*ln(ln(2))
)*x^2/(2*x^2+10-ln(x))^2

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maxima [B]  time = 0.51, size = 233, normalized size = 7.52 \begin {gather*} \frac {9 \, x^{4} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} - 4 \, x^{2} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} \log \relax (x) + 40 \, x^{2} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + {\left (4 \, x^{4} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + 40 \, x^{2} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} \log \relax (x)^{2} - 4 \, {\left (x^{2} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + 5 \, \log \relax (2) + 5 \, \log \left (\log \relax (2)\right )\right )} \log \relax (x) + 100 \, \log \relax (2) + 100 \, \log \left (\log \relax (2)\right )\right )} e^{\left (\frac {2 \, x}{\log \relax (2) + \log \left (\log \relax (2)\right )}\right )} + 2 \, {\left (10 \, x^{4} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + 90 \, x^{2} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + 2 \, {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} \log \relax (x)^{2} - {\left (9 \, x^{2} {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} + 40 \, \log \relax (2) + 40 \, \log \left (\log \relax (2)\right )\right )} \log \relax (x) + 200 \, \log \relax (2) + 200 \, \log \left (\log \relax (2)\right )\right )} e^{\left (\frac {x}{\log \relax (2) + \log \left (\log \relax (2)\right )}\right )}}{{\left (4 \, x^{4} + 40 \, x^{2} - 4 \, {\left (x^{2} + 5\right )} \log \relax (x) + \log \relax (x)^{2} + 100\right )} \log \left (2 \, \log \relax (2)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*log(x)^3+(-12*x^2-60)*log(x)^2+(24*x^4+240*x^2+600)*log(x)-16*x^6-240*x^4-1200*x^2-2000)*exp(x/l
og(2*log(2)))^2+((-4*x*log(x)^2+(8*x^3+82*x)*log(x)-84*x^3-420*x)*log(2*log(2))+4*log(x)^3+(-26*x^2-120)*log(x
)^2+(56*x^4+520*x^2+1200)*log(x)-40*x^6-560*x^4-2600*x^2-4000)*exp(x/log(2*log(2)))+(-8*x*log(x)^2+(20*x^3+164
*x)*log(x)-210*x^3-840*x)*log(2*log(2)))/(log(x)^3+(-6*x^2-30)*log(x)^2+(12*x^4+120*x^2+300)*log(x)-8*x^6-120*
x^4-600*x^2-1000)/log(2*log(2)),x, algorithm="maxima")

[Out]

(9*x^4*(log(2) + log(log(2))) - 4*x^2*(log(2) + log(log(2)))*log(x) + 40*x^2*(log(2) + log(log(2))) + (4*x^4*(
log(2) + log(log(2))) + 40*x^2*(log(2) + log(log(2))) + (log(2) + log(log(2)))*log(x)^2 - 4*(x^2*(log(2) + log
(log(2))) + 5*log(2) + 5*log(log(2)))*log(x) + 100*log(2) + 100*log(log(2)))*e^(2*x/(log(2) + log(log(2)))) +
2*(10*x^4*(log(2) + log(log(2))) + 90*x^2*(log(2) + log(log(2))) + 2*(log(2) + log(log(2)))*log(x)^2 - (9*x^2*
(log(2) + log(log(2))) + 40*log(2) + 40*log(log(2)))*log(x) + 200*log(2) + 200*log(log(2)))*e^(x/(log(2) + log
(log(2)))))/((4*x^4 + 40*x^2 - 4*(x^2 + 5)*log(x) + log(x)^2 + 100)*log(2*log(2)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{\frac {2\,x}{\ln \left (2\,\ln \relax (2)\right )}}\,\left ({\ln \relax (x)}^2\,\left (12\,x^2+60\right )-\ln \relax (x)\,\left (24\,x^4+240\,x^2+600\right )-2\,{\ln \relax (x)}^3+1200\,x^2+240\,x^4+16\,x^6+2000\right )+\ln \left (2\,\ln \relax (2)\right )\,\left (840\,x+8\,x\,{\ln \relax (x)}^2-\ln \relax (x)\,\left (20\,x^3+164\,x\right )+210\,x^3\right )+{\mathrm {e}}^{\frac {x}{\ln \left (2\,\ln \relax (2)\right )}}\,\left ({\ln \relax (x)}^2\,\left (26\,x^2+120\right )-\ln \relax (x)\,\left (56\,x^4+520\,x^2+1200\right )-4\,{\ln \relax (x)}^3+\ln \left (2\,\ln \relax (2)\right )\,\left (420\,x+4\,x\,{\ln \relax (x)}^2-\ln \relax (x)\,\left (8\,x^3+82\,x\right )+84\,x^3\right )+2600\,x^2+560\,x^4+40\,x^6+4000\right )}{\ln \left (2\,\ln \relax (2)\right )\,\left ({\ln \relax (x)}^2\,\left (6\,x^2+30\right )-\ln \relax (x)\,\left (12\,x^4+120\,x^2+300\right )-{\ln \relax (x)}^3+600\,x^2+120\,x^4+8\,x^6+1000\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*x)/log(2*log(2)))*(log(x)^2*(12*x^2 + 60) - log(x)*(240*x^2 + 24*x^4 + 600) - 2*log(x)^3 + 1200*x^
2 + 240*x^4 + 16*x^6 + 2000) + log(2*log(2))*(840*x + 8*x*log(x)^2 - log(x)*(164*x + 20*x^3) + 210*x^3) + exp(
x/log(2*log(2)))*(log(x)^2*(26*x^2 + 120) - log(x)*(520*x^2 + 56*x^4 + 1200) - 4*log(x)^3 + log(2*log(2))*(420
*x + 4*x*log(x)^2 - log(x)*(82*x + 8*x^3) + 84*x^3) + 2600*x^2 + 560*x^4 + 40*x^6 + 4000))/(log(2*log(2))*(log
(x)^2*(6*x^2 + 30) - log(x)*(120*x^2 + 12*x^4 + 300) - log(x)^3 + 600*x^2 + 120*x^4 + 8*x^6 + 1000)),x)

[Out]

int((exp((2*x)/log(2*log(2)))*(log(x)^2*(12*x^2 + 60) - log(x)*(240*x^2 + 24*x^4 + 600) - 2*log(x)^3 + 1200*x^
2 + 240*x^4 + 16*x^6 + 2000) + log(2*log(2))*(840*x + 8*x*log(x)^2 - log(x)*(164*x + 20*x^3) + 210*x^3) + exp(
x/log(2*log(2)))*(log(x)^2*(26*x^2 + 120) - log(x)*(520*x^2 + 56*x^4 + 1200) - 4*log(x)^3 + log(2*log(2))*(420
*x + 4*x*log(x)^2 - log(x)*(82*x + 8*x^3) + 84*x^3) + 2600*x^2 + 560*x^4 + 40*x^6 + 4000))/(log(2*log(2))*(log
(x)^2*(6*x^2 + 30) - log(x)*(120*x^2 + 12*x^4 + 300) - log(x)^3 + 600*x^2 + 120*x^4 + 8*x^6 + 1000)), x)

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sympy [B]  time = 0.80, size = 100, normalized size = 3.23 \begin {gather*} \frac {\left (2 x^{2} - \log {\relax (x )} + 10\right ) e^{\frac {2 x}{\log {\left (2 \log {\relax (2 )} \right )}}} + \left (10 x^{2} - 4 \log {\relax (x )} + 40\right ) e^{\frac {x}{\log {\left (2 \log {\relax (2 )} \right )}}}}{2 x^{2} - \log {\relax (x )} + 10} + \frac {9 x^{4} - 4 x^{2} \log {\relax (x )} + 40 x^{2}}{4 x^{4} + 40 x^{2} + \left (- 4 x^{2} - 20\right ) \log {\relax (x )} + \log {\relax (x )}^{2} + 100} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*ln(x)**3+(-12*x**2-60)*ln(x)**2+(24*x**4+240*x**2+600)*ln(x)-16*x**6-240*x**4-1200*x**2-2000)*ex
p(x/ln(2*ln(2)))**2+((-4*x*ln(x)**2+(8*x**3+82*x)*ln(x)-84*x**3-420*x)*ln(2*ln(2))+4*ln(x)**3+(-26*x**2-120)*l
n(x)**2+(56*x**4+520*x**2+1200)*ln(x)-40*x**6-560*x**4-2600*x**2-4000)*exp(x/ln(2*ln(2)))+(-8*x*ln(x)**2+(20*x
**3+164*x)*ln(x)-210*x**3-840*x)*ln(2*ln(2)))/(ln(x)**3+(-6*x**2-30)*ln(x)**2+(12*x**4+120*x**2+300)*ln(x)-8*x
**6-120*x**4-600*x**2-1000)/ln(2*ln(2)),x)

[Out]

((2*x**2 - log(x) + 10)*exp(2*x/log(2*log(2))) + (10*x**2 - 4*log(x) + 40)*exp(x/log(2*log(2))))/(2*x**2 - log
(x) + 10) + (9*x**4 - 4*x**2*log(x) + 40*x**2)/(4*x**4 + 40*x**2 + (-4*x**2 - 20)*log(x) + log(x)**2 + 100)

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