∫ (−800x5+2000x6+(800x4−3200x5) log(x)+1200x4 log2(x)) log2(log(16))+(−12800x3+38400x4−25600x3 log(x)) log3(log(16))+(ex(256−256x)+102400x2) log4(log(16))___________________________________________________________________________ 625x12−2500x11 log(x)+3750x10 log2(x)−2500x9 log3(x)+625x8 log4(x)+(40000x10−120000x9 log(x)+120000x8 log2(x)−40000x7 log3(x)) log(log(16))+(−800exx6+960000x8+(1600exx5−1920000x7) log(x)+(−800exx4+960000x6) log2(x)) log2(log(16))+(−25600exx4+10240000x6+(25600exx3−10240000x5) log(x)) log3(log(16))+(256e2x−204800exx2+40960000x4) log4(log(16)) dx

3.55.82 \(\int \frac {(-800 x^5+2000 x^6+(800 x^4-3200 x^5) \log (x)+1200 x^4 \log ^2(x)) \log ^2(\log (16))+(-12800 x^3+38400 x^4-25600 x^3 \log (x)) \log ^3(\log (16))+(e^x (256-256 x)+102400 x^2) \log ^4(\log (16))}{625 x^{12}-2500 x^{11} \log (x)+3750 x^{10} \log ^2(x)-2500 x^9 \log ^3(x)+625 x^8 \log ^4(x)+(40000 x^{10}-120000 x^9 \log (x)+120000 x^8 \log ^2(x)-40000 x^7 \log ^3(x)) \log (\log (16))+(-800 e^x x^6+960000 x^8+(1600 e^x x^5-1920000 x^7) \log (x)+(-800 e^x x^4+960000 x^6) \log ^2(x)) \log ^2(\log (16))+(-25600 e^x x^4+10240000 x^6+(25600 e^x x^3-10240000 x^5) \log (x)) \log ^3(\log (16))+(256 e^{2 x}-204800 e^x x^2+40960000 x^4) \log ^4(\log (16))} \, dx\)

Optimal. Leaf size=33 \[ \frac {x}{e^x-25 x^2 \left (-4+\frac {x (-x+\log (x))}{4 \log (\log (16))}\right )^2} \]

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Rubi [F] time = 19.43, 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 {\left (-800 x^5+2000 x^6+\left (800 x^4-3200 x^5\right ) \log (x)+1200 x^4 \log ^2(x)\right ) \log ^2(\log (16))+\left (-12800 x^3+38400 x^4-25600 x^3 \log (x)\right ) \log ^3(\log (16))+\left (e^x (256-256 x)+102400 x^2\right ) \log ^4(\log (16))}{625 x^{12}-2500 x^{11} \log (x)+3750 x^{10} \log ^2(x)-2500 x^9 \log ^3(x)+625 x^8 \log ^4(x)+\left (40000 x^{10}-120000 x^9 \log (x)+120000 x^8 \log ^2(x)-40000 x^7 \log ^3(x)\right ) \log (\log (16))+\left (-800 e^x x^6+960000 x^8+\left (1600 e^x x^5-1920000 x^7\right ) \log (x)+\left (-800 e^x x^4+960000 x^6\right ) \log ^2(x)\right ) \log ^2(\log (16))+\left (-25600 e^x x^4+10240000 x^6+\left (25600 e^x x^3-10240000 x^5\right ) \log (x)\right ) \log ^3(\log (16))+\left (256 e^{2 x}-204800 e^x x^2+40960000 x^4\right ) \log ^4(\log (16))} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((-800*x^5 + 2000*x^6 + (800*x^4 - 3200*x^5)*Log[x] + 1200*x^4*Log[x]^2)*Log[Log[16]]^2 + (-12800*x^3 + 38

400*x^4 - 25600*x^3*Log[x])*Log[Log[16]]^3 + (E^x*(256 - 256*x) + 102400*x^2)*Log[Log[16]]^4)/(625*x^12 - 2500

*x^11*Log[x] + 3750*x^10*Log[x]^2 - 2500*x^9*Log[x]^3 + 625*x^8*Log[x]^4 + (40000*x^10 - 120000*x^9*Log[x] + 1

20000*x^8*Log[x]^2 - 40000*x^7*Log[x]^3)*Log[Log[16]] + (-800*E^x*x^6 + 960000*x^8 + (1600*E^x*x^5 - 1920000*x

^7)*Log[x] + (-800*E^x*x^4 + 960000*x^6)*Log[x]^2)*Log[Log[16]]^2 + (-25600*E^x*x^4 + 10240000*x^6 + (25600*E^

x*x^3 - 10240000*x^5)*Log[x])*Log[Log[16]]^3 + (256*E^(2*x) - 204800*E^x*x^2 + 40960000*x^4)*Log[Log[16]]^4),x

]

[Out]

204800*Log[Log[16]]^4*Defer[Int][x^2/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^

3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] - 12800*Log[Log[16]]^3*(1 + 8*L

og[Log[16]])*Defer[Int][x^3/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*

Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] + 51200*Log[Log[16]]^3*Defer[Int][x^4/(2

5*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[

16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] - 800*Log[Log[16]]^2*(1 + 16*Log[Log[16]])*Defer[Int][x^5/(25*x^6 - 50

*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6

400*x^2*Log[Log[16]]^2)^2, x] + 2400*Log[Log[16]]^2*Defer[Int][x^6/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 +

800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] -

400*Log[Log[16]]^2*Defer[Int][x^7/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*

Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] - 38400*Log[Log[16]]^3*Defer[Int]

[(x^3*Log[x])/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] -

16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] + 800*Log[Log[16]]^2*(1 + 16*Log[Log[16]])*Defer[Int][

(x^4*Log[x])/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] -

16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] - 4000*Log[Log[16]]^2*Defer[Int][(x^5*Log[x])/(25*x^6 -

50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2

+ 6400*x^2*Log[Log[16]]^2)^2, x] + 800*Log[Log[16]]^2*Defer[Int][(x^6*Log[x])/(25*x^6 - 50*x^5*Log[x] + 25*x^4

*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]

^2)^2, x] + 1600*Log[Log[16]]^2*Defer[Int][(x^4*Log[x]^2)/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*

Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] - 400*Log[

Log[16]]^2*Defer[Int][(x^5*Log[x]^2)/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^

3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)^2, x] - 16*Log[Log[16]]^2*Defer[Int][

(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Lo

g[16]]^2 + 6400*x^2*Log[Log[16]]^2)^(-1), x] + 16*Log[Log[16]]^2*Defer[Int][x/(25*x^6 - 50*x^5*Log[x] + 25*x^4

*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[Log[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]

^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 \log ^2(\log (16)) \left (-50 x^5+125 x^6+75 x^4 \log ^2(x)-800 x^3 \log (\log (16))+2400 x^4 \log (\log (16))+16 e^x \log ^2(\log (16))-16 e^x x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))-50 x^3 \log (x) \left (-x+4 x^2+32 \log (\log (16))\right )\right )}{\left (25 x^6+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))-50 \log (x) \left (x^5+16 x^3 \log (\log (16))\right )\right )^2} \, dx\\ &=\left (16 \log ^2(\log (16))\right ) \int \frac {-50 x^5+125 x^6+75 x^4 \log ^2(x)-800 x^3 \log (\log (16))+2400 x^4 \log (\log (16))+16 e^x \log ^2(\log (16))-16 e^x x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))-50 x^3 \log (x) \left (-x+4 x^2+32 \log (\log (16))\right )}{\left (25 x^6+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))-50 \log (x) \left (x^5+16 x^3 \log (\log (16))\right )\right )^2} \, dx\\ &=\left (16 \log ^2(\log (16))\right ) \int \left (\frac {-1+x}{25 x^6-50 x^5 \log (x)+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-800 x^3 \log (x) \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))}+\frac {25 x^2 \left (6 x^4-x^5-10 x^3 \log (x)+2 x^4 \log (x)+4 x^2 \log ^2(x)-x^3 \log ^2(x)+128 x^2 \log (\log (16))-96 x \log (x) \log (\log (16))+512 \log ^2(\log (16))-32 x \log (\log (16)) (1+8 \log (\log (16)))-2 x^3 (1+16 \log (\log (16)))+2 x^2 \log (x) (1+16 \log (\log (16)))\right )}{\left (25 x^6-50 x^5 \log (x)+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-800 x^3 \log (x) \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))\right )^2}\right ) \, dx\\ &=\left (16 \log ^2(\log (16))\right ) \int \frac {-1+x}{25 x^6-50 x^5 \log (x)+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-800 x^3 \log (x) \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))} \, dx+\left (400 \log ^2(\log (16))\right ) \int \frac {x^2 \left (6 x^4-x^5-10 x^3 \log (x)+2 x^4 \log (x)+4 x^2 \log ^2(x)-x^3 \log ^2(x)+128 x^2 \log (\log (16))-96 x \log (x) \log (\log (16))+512 \log ^2(\log (16))-32 x \log (\log (16)) (1+8 \log (\log (16)))-2 x^3 (1+16 \log (\log (16)))+2 x^2 \log (x) (1+16 \log (\log (16)))\right )}{\left (25 x^6-50 x^5 \log (x)+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-800 x^3 \log (x) \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] time = 0.20, size = 70, normalized size = 2.12 \begin {gather*} -\frac {16 x \log ^2(\log (16))}{25 x^6-50 x^5 \log (x)+25 x^4 \log ^2(x)+800 x^4 \log (\log (16))-800 x^3 \log (x) \log (\log (16))-16 e^x \log ^2(\log (16))+6400 x^2 \log ^2(\log (16))} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((-800*x^5 + 2000*x^6 + (800*x^4 - 3200*x^5)*Log[x] + 1200*x^4*Log[x]^2)*Log[Log[16]]^2 + (-12800*x^

3 + 38400*x^4 - 25600*x^3*Log[x])*Log[Log[16]]^3 + (E^x*(256 - 256*x) + 102400*x^2)*Log[Log[16]]^4)/(625*x^12

- 2500*x^11*Log[x] + 3750*x^10*Log[x]^2 - 2500*x^9*Log[x]^3 + 625*x^8*Log[x]^4 + (40000*x^10 - 120000*x^9*Log[

x] + 120000*x^8*Log[x]^2 - 40000*x^7*Log[x]^3)*Log[Log[16]] + (-800*E^x*x^6 + 960000*x^8 + (1600*E^x*x^5 - 192

0000*x^7)*Log[x] + (-800*E^x*x^4 + 960000*x^6)*Log[x]^2)*Log[Log[16]]^2 + (-25600*E^x*x^4 + 10240000*x^6 + (25

600*E^x*x^3 - 10240000*x^5)*Log[x])*Log[Log[16]]^3 + (256*E^(2*x) - 204800*E^x*x^2 + 40960000*x^4)*Log[Log[16]

]^4),x]

[Out]

(-16*x*Log[Log[16]]^2)/(25*x^6 - 50*x^5*Log[x] + 25*x^4*Log[x]^2 + 800*x^4*Log[Log[16]] - 800*x^3*Log[x]*Log[L

og[16]] - 16*E^x*Log[Log[16]]^2 + 6400*x^2*Log[Log[16]]^2)

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fricas [B] time = 1.34, size = 71, normalized size = 2.15 \begin {gather*} -\frac {16 \, x \log \left (4 \, \log \relax (2)\right )^{2}}{25 \, x^{6} - 50 \, x^{5} \log \relax (x) + 25 \, x^{4} \log \relax (x)^{2} + 16 \, {\left (400 \, x^{2} - e^{x}\right )} \log \left (4 \, \log \relax (2)\right )^{2} + 800 \, {\left (x^{4} - x^{3} \log \relax (x)\right )} \log \left (4 \, \log \relax (2)\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-256*x+256)*exp(x)+102400*x^2)*log(4*log(2))^4+(-25600*x^3*log(x)+38400*x^4-12800*x^3)*log(4*log(

2))^3+(1200*x^4*log(x)^2+(-3200*x^5+800*x^4)*log(x)+2000*x^6-800*x^5)*log(4*log(2))^2)/((256*exp(x)^2-204800*e

xp(x)*x^2+40960000*x^4)*log(4*log(2))^4+((25600*exp(x)*x^3-10240000*x^5)*log(x)-25600*exp(x)*x^4+10240000*x^6)

*log(4*log(2))^3+((-800*exp(x)*x^4+960000*x^6)*log(x)^2+(1600*x^5*exp(x)-1920000*x^7)*log(x)-800*x^6*exp(x)+96

0000*x^8)*log(4*log(2))^2+(-40000*x^7*log(x)^3+120000*x^8*log(x)^2-120000*x^9*log(x)+40000*x^10)*log(4*log(2))

+625*x^8*log(x)^4-2500*x^9*log(x)^3+3750*x^10*log(x)^2-2500*x^11*log(x)+625*x^12),x, algorithm="fricas")

[Out]

-16*x*log(4*log(2))^2/(25*x^6 - 50*x^5*log(x) + 25*x^4*log(x)^2 + 16*(400*x^2 - e^x)*log(4*log(2))^2 + 800*(x^

4 - x^3*log(x))*log(4*log(2)))

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-256*x+256)*exp(x)+102400*x^2)*log(4*log(2))^4+(-25600*x^3*log(x)+38400*x^4-12800*x^3)*log(4*log(

2))^3+(1200*x^4*log(x)^2+(-3200*x^5+800*x^4)*log(x)+2000*x^6-800*x^5)*log(4*log(2))^2)/((256*exp(x)^2-204800*e

xp(x)*x^2+40960000*x^4)*log(4*log(2))^4+((25600*exp(x)*x^3-10240000*x^5)*log(x)-25600*exp(x)*x^4+10240000*x^6)

*log(4*log(2))^3+((-800*exp(x)*x^4+960000*x^6)*log(x)^2+(1600*x^5*exp(x)-1920000*x^7)*log(x)-800*x^6*exp(x)+96

0000*x^8)*log(4*log(2))^2+(-40000*x^7*log(x)^3+120000*x^8*log(x)^2-120000*x^9*log(x)+40000*x^10)*log(4*log(2))

+625*x^8*log(x)^4-2500*x^9*log(x)^3+3750*x^10*log(x)^2-2500*x^11*log(x)+625*x^12),x, algorithm="giac")

[Out]

Timed out

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maple [B] time = 0.15, size = 136, normalized size = 4.12


method	result	size

risch	\(-\frac {16 x \left (4 \ln \relax (2)^{2}+4 \ln \relax (2) \ln \left (\ln \relax (2)\right )+\ln \left (\ln \relax (2)\right )^{2}\right )}{25 x^{6}-50 x^{5} \ln \relax (x )+25 x^{4} \ln \relax (x )^{2}+1600 x^{4} \ln \relax (2)-1600 \ln \relax (x ) \ln \relax (2) x^{3}+800 \ln \left (\ln \relax (2)\right ) x^{4}-800 \ln \relax (x ) \ln \left (\ln \relax (2)\right ) x^{3}+25600 x^{2} \ln \relax (2)^{2}+25600 \ln \relax (2) \ln \left (\ln \relax (2)\right ) x^{2}+6400 x^{2} \ln \left (\ln \relax (2)\right )^{2}-64 \ln \relax (2)^{2} {\mathrm e}^{x}-64 \ln \relax (2) {\mathrm e}^{x} \ln \left (\ln \relax (2)\right )-16 \,{\mathrm e}^{x} \ln \left (\ln \relax (2)\right )^{2}}\)	\(136\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((-256*x+256)*exp(x)+102400*x^2)*ln(4*ln(2))^4+(-25600*x^3*ln(x)+38400*x^4-12800*x^3)*ln(4*ln(2))^3+(1200

*x^4*ln(x)^2+(-3200*x^5+800*x^4)*ln(x)+2000*x^6-800*x^5)*ln(4*ln(2))^2)/((256*exp(x)^2-204800*exp(x)*x^2+40960

000*x^4)*ln(4*ln(2))^4+((25600*exp(x)*x^3-10240000*x^5)*ln(x)-25600*exp(x)*x^4+10240000*x^6)*ln(4*ln(2))^3+((-

800*exp(x)*x^4+960000*x^6)*ln(x)^2+(1600*x^5*exp(x)-1920000*x^7)*ln(x)-800*x^6*exp(x)+960000*x^8)*ln(4*ln(2))^

2+(-40000*x^7*ln(x)^3+120000*x^8*ln(x)^2-120000*x^9*ln(x)+40000*x^10)*ln(4*ln(2))+625*x^8*ln(x)^4-2500*x^9*ln(

x)^3+3750*x^10*ln(x)^2-2500*x^11*ln(x)+625*x^12),x,method=_RETURNVERBOSE)

[Out]

-16*x*(4*ln(2)^2+4*ln(2)*ln(ln(2))+ln(ln(2))^2)/(25*x^6-50*x^5*ln(x)+25*x^4*ln(x)^2+1600*x^4*ln(2)-1600*ln(x)*

ln(2)*x^3+800*ln(ln(2))*x^4-800*ln(x)*ln(ln(2))*x^3+25600*x^2*ln(2)^2+25600*ln(2)*ln(ln(2))*x^2+6400*x^2*ln(ln

(2))^2-64*ln(2)^2*exp(x)-64*ln(2)*exp(x)*ln(ln(2))-16*exp(x)*ln(ln(2))^2)

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maxima [B] time = 0.64, size = 120, normalized size = 3.64 \begin {gather*} -\frac {16 \, {\left (4 \, \log \relax (2)^{2} + 4 \, \log \relax (2) \log \left (\log \relax (2)\right ) + \log \left (\log \relax (2)\right )^{2}\right )} x}{25 \, x^{6} + 25 \, x^{4} \log \relax (x)^{2} + 800 \, x^{4} {\left (2 \, \log \relax (2) + \log \left (\log \relax (2)\right )\right )} + 6400 \, {\left (4 \, \log \relax (2)^{2} + 4 \, \log \relax (2) \log \left (\log \relax (2)\right ) + \log \left (\log \relax (2)\right )^{2}\right )} x^{2} - 16 \, {\left (4 \, \log \relax (2)^{2} + 4 \, \log \relax (2) \log \left (\log \relax (2)\right ) + \log \left (\log \relax (2)\right )^{2}\right )} e^{x} - 50 \, {\left (x^{5} + 16 \, x^{3} {\left (2 \, \log \relax (2) + \log \left (\log \relax (2)\right )\right )}\right )} \log \relax (x)} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-256*x+256)*exp(x)+102400*x^2)*log(4*log(2))^4+(-25600*x^3*log(x)+38400*x^4-12800*x^3)*log(4*log(

2))^3+(1200*x^4*log(x)^2+(-3200*x^5+800*x^4)*log(x)+2000*x^6-800*x^5)*log(4*log(2))^2)/((256*exp(x)^2-204800*e

xp(x)*x^2+40960000*x^4)*log(4*log(2))^4+((25600*exp(x)*x^3-10240000*x^5)*log(x)-25600*exp(x)*x^4+10240000*x^6)

*log(4*log(2))^3+((-800*exp(x)*x^4+960000*x^6)*log(x)^2+(1600*x^5*exp(x)-1920000*x^7)*log(x)-800*x^6*exp(x)+96

0000*x^8)*log(4*log(2))^2+(-40000*x^7*log(x)^3+120000*x^8*log(x)^2-120000*x^9*log(x)+40000*x^10)*log(4*log(2))

+625*x^8*log(x)^4-2500*x^9*log(x)^3+3750*x^10*log(x)^2-2500*x^11*log(x)+625*x^12),x, algorithm="maxima")

[Out]

-16*(4*log(2)^2 + 4*log(2)*log(log(2)) + log(log(2))^2)*x/(25*x^6 + 25*x^4*log(x)^2 + 800*x^4*(2*log(2) + log(

log(2))) + 6400*(4*log(2)^2 + 4*log(2)*log(log(2)) + log(log(2))^2)*x^2 - 16*(4*log(2)^2 + 4*log(2)*log(log(2)

) + log(log(2))^2)*e^x - 50*(x^5 + 16*x^3*(2*log(2) + log(log(2))))*log(x))

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\ln \left (4\,\ln \relax (2)\right )}^4\,\left ({\mathrm {e}}^x\,\left (256\,x-256\right )-102400\,x^2\right )-{\ln \left (4\,\ln \relax (2)\right )}^2\,\left (\ln \relax (x)\,\left (800\,x^4-3200\,x^5\right )+1200\,x^4\,{\ln \relax (x)}^2-800\,x^5+2000\,x^6\right )+{\ln \left (4\,\ln \relax (2)\right )}^3\,\left (25600\,x^3\,\ln \relax (x)+12800\,x^3-38400\,x^4\right )}{{\ln \left (4\,\ln \relax (2)\right )}^4\,\left (256\,{\mathrm {e}}^{2\,x}-204800\,x^2\,{\mathrm {e}}^x+40960000\,x^4\right )-\ln \left (4\,\ln \relax (2)\right )\,\left (-40000\,x^{10}+120000\,x^9\,\ln \relax (x)-120000\,x^8\,{\ln \relax (x)}^2+40000\,x^7\,{\ln \relax (x)}^3\right )-2500\,x^{11}\,\ln \relax (x)+625\,x^8\,{\ln \relax (x)}^4-2500\,x^9\,{\ln \relax (x)}^3+3750\,x^{10}\,{\ln \relax (x)}^2+{\ln \left (4\,\ln \relax (2)\right )}^3\,\left (10240000\,x^6-25600\,x^4\,{\mathrm {e}}^x+\ln \relax (x)\,\left (25600\,x^3\,{\mathrm {e}}^x-10240000\,x^5\right )\right )+625\,x^{12}-{\ln \left (4\,\ln \relax (2)\right )}^2\,\left (800\,x^6\,{\mathrm {e}}^x+{\ln \relax (x)}^2\,\left (800\,x^4\,{\mathrm {e}}^x-960000\,x^6\right )-960000\,x^8-\ln \relax (x)\,\left (1600\,x^5\,{\mathrm {e}}^x-1920000\,x^7\right )\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(4*log(2))^4*(exp(x)*(256*x - 256) - 102400*x^2) - log(4*log(2))^2*(log(x)*(800*x^4 - 3200*x^5) + 120

0*x^4*log(x)^2 - 800*x^5 + 2000*x^6) + log(4*log(2))^3*(25600*x^3*log(x) + 12800*x^3 - 38400*x^4))/(log(4*log(

2))^4*(256*exp(2*x) - 204800*x^2*exp(x) + 40960000*x^4) - log(4*log(2))*(120000*x^9*log(x) + 40000*x^7*log(x)^

3 - 120000*x^8*log(x)^2 - 40000*x^10) - 2500*x^11*log(x) + 625*x^8*log(x)^4 - 2500*x^9*log(x)^3 + 3750*x^10*lo

g(x)^2 + log(4*log(2))^3*(10240000*x^6 - 25600*x^4*exp(x) + log(x)*(25600*x^3*exp(x) - 10240000*x^5)) + 625*x^

12 - log(4*log(2))^2*(800*x^6*exp(x) + log(x)^2*(800*x^4*exp(x) - 960000*x^6) - 960000*x^8 - log(x)*(1600*x^5*

exp(x) - 1920000*x^7))),x)

[Out]

int(-(log(4*log(2))^4*(exp(x)*(256*x - 256) - 102400*x^2) - log(4*log(2))^2*(log(x)*(800*x^4 - 3200*x^5) + 120

0*x^4*log(x)^2 - 800*x^5 + 2000*x^6) + log(4*log(2))^3*(25600*x^3*log(x) + 12800*x^3 - 38400*x^4))/(log(4*log(

2))^4*(256*exp(2*x) - 204800*x^2*exp(x) + 40960000*x^4) - log(4*log(2))*(120000*x^9*log(x) + 40000*x^7*log(x)^

3 - 120000*x^8*log(x)^2 - 40000*x^10) - 2500*x^11*log(x) + 625*x^8*log(x)^4 - 2500*x^9*log(x)^3 + 3750*x^10*lo

g(x)^2 + log(4*log(2))^3*(10240000*x^6 - 25600*x^4*exp(x) + log(x)*(25600*x^3*exp(x) - 10240000*x^5)) + 625*x^

12 - log(4*log(2))^2*(800*x^6*exp(x) + log(x)^2*(800*x^4*exp(x) - 960000*x^6) - 960000*x^8 - log(x)*(1600*x^5*

exp(x) - 1920000*x^7))), x)

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sympy [B] time = 2.33, size = 162, normalized size = 4.91 \begin {gather*} \frac {64 x \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )} + 16 x \log {\left (\log {\relax (2 )} \right )}^{2} + 64 x \log {\relax (2 )}^{2}}{- 25 x^{6} + 50 x^{5} \log {\relax (x )} - 25 x^{4} \log {\relax (x )}^{2} - 1600 x^{4} \log {\relax (2 )} - 800 x^{4} \log {\left (\log {\relax (2 )} \right )} + 800 x^{3} \log {\relax (x )} \log {\left (\log {\relax (2 )} \right )} + 1600 x^{3} \log {\relax (2 )} \log {\relax (x )} - 25600 x^{2} \log {\relax (2 )}^{2} - 6400 x^{2} \log {\left (\log {\relax (2 )} \right )}^{2} - 25600 x^{2} \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )} + \left (64 \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )} + 16 \log {\left (\log {\relax (2 )} \right )}^{2} + 64 \log {\relax (2 )}^{2}\right ) e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-256*x+256)*exp(x)+102400*x**2)*ln(4*ln(2))**4+(-25600*x**3*ln(x)+38400*x**4-12800*x**3)*ln(4*ln(

2))**3+(1200*x**4*ln(x)**2+(-3200*x**5+800*x**4)*ln(x)+2000*x**6-800*x**5)*ln(4*ln(2))**2)/((256*exp(x)**2-204

800*exp(x)*x**2+40960000*x**4)*ln(4*ln(2))**4+((25600*exp(x)*x**3-10240000*x**5)*ln(x)-25600*exp(x)*x**4+10240

000*x**6)*ln(4*ln(2))**3+((-800*exp(x)*x**4+960000*x**6)*ln(x)**2+(1600*x**5*exp(x)-1920000*x**7)*ln(x)-800*x*

*6*exp(x)+960000*x**8)*ln(4*ln(2))**2+(-40000*x**7*ln(x)**3+120000*x**8*ln(x)**2-120000*x**9*ln(x)+40000*x**10

)*ln(4*ln(2))+625*x**8*ln(x)**4-2500*x**9*ln(x)**3+3750*x**10*ln(x)**2-2500*x**11*ln(x)+625*x**12),x)

[Out]

(64*x*log(2)*log(log(2)) + 16*x*log(log(2))**2 + 64*x*log(2)**2)/(-25*x**6 + 50*x**5*log(x) - 25*x**4*log(x)**

2 - 1600*x**4*log(2) - 800*x**4*log(log(2)) + 800*x**3*log(x)*log(log(2)) + 1600*x**3*log(2)*log(x) - 25600*x*

*2*log(2)**2 - 6400*x**2*log(log(2))**2 - 25600*x**2*log(2)*log(log(2)) + (64*log(2)*log(log(2)) + 16*log(log(

2))**2 + 64*log(2)**2)*exp(x))

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