3.1.94 \(\int \frac {72 x (i \pi +\log (-4+4 e^5))^2+((-288 x^2-18 x^3) (i \pi +\log (-4+4 e^5))+144 x (i \pi +\log (-4+4 e^5))^2 \log (x)) \log (\log (x))+(-864 x^2-36 x^3) (i \pi +\log (-4+4 e^5)) \log (x) \log ^2(\log (x))+(1152 x^3+72 x^4) \log (x) \log ^3(\log (x))}{-(i \pi +\log (-4+4 e^5))^3 \log (x)+12 x (i \pi +\log (-4+4 e^5))^2 \log (x) \log (\log (x))-48 x^2 (i \pi +\log (-4+4 e^5)) \log (x) \log ^2(\log (x))+64 x^3 \log (x) \log ^3(\log (x))} \, dx\)

Optimal. Leaf size=35 \[ 9 \left (-4+\frac {x}{-4+\frac {i \pi +\log \left (-4+4 e^5\right )}{x \log (\log (x))}}\right )^2 \]

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Rubi [F]  time = 7.38, 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 {72 x \left (i \pi +\log \left (-4+4 e^5\right )\right )^2+\left (\left (-288 x^2-18 x^3\right ) \left (i \pi +\log \left (-4+4 e^5\right )\right )+144 x \left (i \pi +\log \left (-4+4 e^5\right )\right )^2 \log (x)\right ) \log (\log (x))+\left (-864 x^2-36 x^3\right ) \left (i \pi +\log \left (-4+4 e^5\right )\right ) \log (x) \log ^2(\log (x))+\left (1152 x^3+72 x^4\right ) \log (x) \log ^3(\log (x))}{-\left (i \pi +\log \left (-4+4 e^5\right )\right )^3 \log (x)+12 x \left (i \pi +\log \left (-4+4 e^5\right )\right )^2 \log (x) \log (\log (x))-48 x^2 \left (i \pi +\log \left (-4+4 e^5\right )\right ) \log (x) \log ^2(\log (x))+64 x^3 \log (x) \log ^3(\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(72*x*(I*Pi + Log[-4 + 4*E^5])^2 + ((-288*x^2 - 18*x^3)*(I*Pi + Log[-4 + 4*E^5]) + 144*x*(I*Pi + Log[-4 +
4*E^5])^2*Log[x])*Log[Log[x]] + (-864*x^2 - 36*x^3)*(I*Pi + Log[-4 + 4*E^5])*Log[x]*Log[Log[x]]^2 + (1152*x^3
+ 72*x^4)*Log[x]*Log[Log[x]]^3)/(-((I*Pi + Log[-4 + 4*E^5])^3*Log[x]) + 12*x*(I*Pi + Log[-4 + 4*E^5])^2*Log[x]
*Log[Log[x]] - 48*x^2*(I*Pi + Log[-4 + 4*E^5])*Log[x]*Log[Log[x]]^2 + 64*x^3*Log[x]*Log[Log[x]]^3),x]

[Out]

(9*(16 + x)^2)/16 + (9*(I*Pi + Log[-4*(1 - E^5)])^3*Defer[Int][x/(I*Pi*(1 - (I*Log[4*(-1 + E^5)])/Pi) - 4*x*Lo
g[Log[x]])^3, x])/8 - (9*(I*Pi + Log[-4*(1 - E^5)])*Defer[Int][x/(I*Pi*(1 - (I*Log[4*(-1 + E^5)])/Pi) - 4*x*Lo
g[Log[x]]), x])/8 - 18*(Pi - I*Log[-4*(1 - E^5)])^2*Defer[Int][(Pi*(1 - (I*Log[4*(-1 + E^5)])/Pi) + (4*I)*x*Lo
g[Log[x]])^(-2), x] - (9*(Pi - I*Log[-4*(1 - E^5)])^2*Defer[Int][x/(Pi*(1 - (I*Log[4*(-1 + E^5)])/Pi) + (4*I)*
x*Log[Log[x]])^2, x])/8 + 72*(I*Pi + Log[-4*(1 - E^5)])*Defer[Int][x/(Log[x]*(Pi*(1 - (I*Log[4*(-1 + E^5)])/Pi
) + (4*I)*x*Log[Log[x]])^2), x] + (9*(I*Pi + Log[-4*(1 - E^5)])*Defer[Int][x^2/(Log[x]*(Pi*(1 - (I*Log[4*(-1 +
E^5)])/Pi) + (4*I)*x*Log[Log[x]])^2), x])/2 + (9*(Pi - I*Log[-4*(1 - E^5)])^2*Defer[Int][x^2/(Log[x]*((-I)*Pi
*(1 - (I*Log[4*(-1 + E^5)])/Pi) + 4*x*Log[Log[x]])^3), x])/2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18 x \left (4 i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-x (16+x) \log (\log (x))\right ) \left (-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+2 \log (x) \log (\log (x)) \left (-i \pi -\log \left (4 \left (-1+e^5\right )\right )+2 x \log (\log (x))\right )\right )}{\log (x) \left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3} \, dx\\ &=18 \int \frac {x \left (4 i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-x (16+x) \log (\log (x))\right ) \left (-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+2 \log (x) \log (\log (x)) \left (-i \pi -\log \left (4 \left (-1+e^5\right )\right )+2 x \log (\log (x))\right )\right )}{\log (x) \left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3} \, dx\\ &=18 \int \left (\frac {16+x}{16}+\frac {x \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2 \left (-4 x-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{16 \log (x) \left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3}+\frac {x \left (-i \pi -\log \left (-4 \left (1-e^5\right )\right )\right )}{16 \left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )}+\frac {(16+x) \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right ) \left (4 i x-\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{16 \log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}\right ) \, dx\\ &=\frac {9}{16} (16+x)^2+\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {(16+x) \left (4 i x-\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx+\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \frac {x \left (-4 x-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{\log (x) \left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3} \, dx-\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x}{i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))} \, dx\\ &=\frac {9}{16} (16+x)^2+\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \left (\frac {16 \left (4 i x-\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}+\frac {x \left (4 i x-\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}\right ) \, dx+\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \left (\frac {x \left (-i \pi -\log \left (-4 \left (1-e^5\right )\right )\right )}{\left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3}+\frac {4 x^2}{\log (x) \left (-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 x \log (\log (x))\right )^3}\right ) \, dx-\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x}{i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))} \, dx\\ &=\frac {9}{16} (16+x)^2+\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x \left (4 i x-\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)\right )}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx+\left (18 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {4 i x-\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right ) \log (x)}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx+\frac {1}{2} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \frac {x^2}{\log (x) \left (-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 x \log (\log (x))\right )^3} \, dx-\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x}{i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))} \, dx+\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )^3\right ) \int \frac {x}{\left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3} \, dx\\ &=\frac {9}{16} (16+x)^2+\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \left (\frac {x \left (-\pi +i \log \left (-4 \left (1-e^5\right )\right )\right )}{\left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}+\frac {4 i x^2}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}\right ) \, dx+\left (18 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \left (\frac {-\pi +i \log \left (-4 \left (1-e^5\right )\right )}{\left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}+\frac {4 i x}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2}\right ) \, dx+\frac {1}{2} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \frac {x^2}{\log (x) \left (-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 x \log (\log (x))\right )^3} \, dx-\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x}{i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))} \, dx+\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )^3\right ) \int \frac {x}{\left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3} \, dx\\ &=\frac {9}{16} (16+x)^2-\frac {1}{8} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \frac {x}{\left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx+\frac {1}{2} \left (9 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \frac {x^2}{\log (x) \left (-i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 x \log (\log (x))\right )^3} \, dx-\left (18 \left (\pi -i \log \left (-4 \left (1-e^5\right )\right )\right )^2\right ) \int \frac {1}{\left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx-\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x}{i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))} \, dx+\frac {1}{2} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x^2}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx+\left (72 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )\right ) \int \frac {x}{\log (x) \left (\pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )+4 i x \log (\log (x))\right )^2} \, dx+\frac {1}{8} \left (9 \left (i \pi +\log \left (-4 \left (1-e^5\right )\right )\right )^3\right ) \int \frac {x}{\left (i \pi \left (1-\frac {i \log \left (4 \left (-1+e^5\right )\right )}{\pi }\right )-4 x \log (\log (x))\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 56, normalized size = 1.60 \begin {gather*} -\frac {9 x^2 \log (\log (x)) \left (-8 i \pi -8 \log \left (4 \left (-1+e^5\right )\right )+x (32+x) \log (\log (x))\right )}{\left (\pi -i \log \left (4 \left (-1+e^5\right )\right )+4 i x \log (\log (x))\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(72*x*(I*Pi + Log[-4 + 4*E^5])^2 + ((-288*x^2 - 18*x^3)*(I*Pi + Log[-4 + 4*E^5]) + 144*x*(I*Pi + Log
[-4 + 4*E^5])^2*Log[x])*Log[Log[x]] + (-864*x^2 - 36*x^3)*(I*Pi + Log[-4 + 4*E^5])*Log[x]*Log[Log[x]]^2 + (115
2*x^3 + 72*x^4)*Log[x]*Log[Log[x]]^3)/(-((I*Pi + Log[-4 + 4*E^5])^3*Log[x]) + 12*x*(I*Pi + Log[-4 + 4*E^5])^2*
Log[x]*Log[Log[x]] - 48*x^2*(I*Pi + Log[-4 + 4*E^5])*Log[x]*Log[Log[x]]^2 + 64*x^3*Log[x]*Log[Log[x]]^3),x]

[Out]

(-9*x^2*Log[Log[x]]*((-8*I)*Pi - 8*Log[4*(-1 + E^5)] + x*(32 + x)*Log[Log[x]]))/(Pi - I*Log[4*(-1 + E^5)] + (4
*I)*x*Log[Log[x]])^2

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fricas [B]  time = 0.57, size = 69, normalized size = 1.97 \begin {gather*} -\frac {9 \, {\left (8 \, x^{2} \log \left (-4 \, e^{5} + 4\right ) \log \left (\log \relax (x)\right ) - {\left (x^{4} + 32 \, x^{3}\right )} \log \left (\log \relax (x)\right )^{2}\right )}}{16 \, x^{2} \log \left (\log \relax (x)\right )^{2} - 8 \, x \log \left (-4 \, e^{5} + 4\right ) \log \left (\log \relax (x)\right ) + \log \left (-4 \, e^{5} + 4\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^4+1152*x^3)*log(x)*log(log(x))^3+(-36*x^3-864*x^2)*log(-4*exp(5)+4)*log(x)*log(log(x))^2+(144
*x*log(-4*exp(5)+4)^2*log(x)+(-18*x^3-288*x^2)*log(-4*exp(5)+4))*log(log(x))+72*x*log(-4*exp(5)+4)^2)/(64*x^3*
log(x)*log(log(x))^3-48*x^2*log(-4*exp(5)+4)*log(x)*log(log(x))^2+12*x*log(-4*exp(5)+4)^2*log(x)*log(log(x))-l
og(-4*exp(5)+4)^3*log(x)),x, algorithm="fricas")

[Out]

-9*(8*x^2*log(-4*e^5 + 4)*log(log(x)) - (x^4 + 32*x^3)*log(log(x))^2)/(16*x^2*log(log(x))^2 - 8*x*log(-4*e^5 +
4)*log(log(x)) + log(-4*e^5 + 4)^2)

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giac [B]  time = 0.69, size = 72, normalized size = 2.06 \begin {gather*} \frac {9 \, {\left (x^{4} \log \left (\log \relax (x)\right )^{2} + 32 \, x^{3} \log \left (\log \relax (x)\right )^{2} - 8 \, x^{2} \log \left (-4 \, e^{5} + 4\right ) \log \left (\log \relax (x)\right )\right )}}{16 \, x^{2} \log \left (\log \relax (x)\right )^{2} - 8 \, x \log \left (-4 \, e^{5} + 4\right ) \log \left (\log \relax (x)\right ) + \log \left (-4 \, e^{5} + 4\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^4+1152*x^3)*log(x)*log(log(x))^3+(-36*x^3-864*x^2)*log(-4*exp(5)+4)*log(x)*log(log(x))^2+(144
*x*log(-4*exp(5)+4)^2*log(x)+(-18*x^3-288*x^2)*log(-4*exp(5)+4))*log(log(x))+72*x*log(-4*exp(5)+4)^2)/(64*x^3*
log(x)*log(log(x))^3-48*x^2*log(-4*exp(5)+4)*log(x)*log(log(x))^2+12*x*log(-4*exp(5)+4)^2*log(x)*log(log(x))-l
og(-4*exp(5)+4)^3*log(x)),x, algorithm="giac")

[Out]

9*(x^4*log(log(x))^2 + 32*x^3*log(log(x))^2 - 8*x^2*log(-4*e^5 + 4)*log(log(x)))/(16*x^2*log(log(x))^2 - 8*x*l
og(-4*e^5 + 4)*log(log(x)) + log(-4*e^5 + 4)^2)

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maple [B]  time = 0.07, size = 138, normalized size = 3.94

method	result	size
risch	\(\frac {9 x^{2}}{16}+18 x -\frac {9 x \left (-16 x^{2} \ln \left (\ln \relax (x )\right ) \ln \relax (2)-8 x^{2} \ln \left (\ln \relax (x )\right ) \ln \left (1-{\mathrm e}^{5}\right )+4 x \ln \relax (2)^{2}+4 x \ln \relax (2) \ln \left (1-{\mathrm e}^{5}\right )-256 x \ln \left (\ln \relax (x )\right ) \ln \relax (2)+x \ln \left (1-{\mathrm e}^{5}\right )^{2}-128 x \ln \left (\ln \relax (x )\right ) \ln \left (1-{\mathrm e}^{5}\right )+128 \ln \relax (2)^{2}+128 \ln \relax (2) \ln \left (1-{\mathrm e}^{5}\right )+32 \ln \left (1-{\mathrm e}^{5}\right )^{2}\right )}{16 \left (-4 x \ln \left (\ln \relax (x )\right )+2 \ln \relax (2)+\ln \left (1-{\mathrm e}^{5}\right )\right )^{2}}\)	\(138\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((72*x^4+1152*x^3)*ln(x)*ln(ln(x))^3+(-36*x^3-864*x^2)*ln(-4*exp(5)+4)*ln(x)*ln(ln(x))^2+(144*x*ln(-4*exp(
5)+4)^2*ln(x)+(-18*x^3-288*x^2)*ln(-4*exp(5)+4))*ln(ln(x))+72*x*ln(-4*exp(5)+4)^2)/(64*x^3*ln(x)*ln(ln(x))^3-4
8*x^2*ln(-4*exp(5)+4)*ln(x)*ln(ln(x))^2+12*x*ln(-4*exp(5)+4)^2*ln(x)*ln(ln(x))-ln(-4*exp(5)+4)^3*ln(x)),x,meth
od=_RETURNVERBOSE)

[Out]

9/16*x^2+18*x-9/16*x*(-16*x^2*ln(ln(x))*ln(2)-8*x^2*ln(ln(x))*ln(1-exp(5))+4*x*ln(2)^2+4*x*ln(2)*ln(1-exp(5))-
256*x*ln(ln(x))*ln(2)+x*ln(1-exp(5))^2-128*x*ln(ln(x))*ln(1-exp(5))+128*ln(2)^2+128*ln(2)*ln(1-exp(5))+32*ln(1
-exp(5))^2)/(-4*x*ln(ln(x))+2*ln(2)+ln(1-exp(5)))^2

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maxima [C]  time = 0.85, size = 188, normalized size = 5.37 \begin {gather*} -\frac {9 \, {\left (8 \, {\left (i \, \pi + 2 \, \log \relax (2) + \log \left (e^{4} + e^{3} + e^{2} + e + 1\right ) + \log \left (e - 1\right )\right )} x^{2} \log \left (\log \relax (x)\right ) - {\left (x^{4} + 32 \, x^{3}\right )} \log \left (\log \relax (x)\right )^{2}\right )}}{16 \, x^{2} \log \left (\log \relax (x)\right )^{2} - 8 \, {\left (i \, \pi + 2 \, \log \relax (2) + \log \left (e^{4} + e^{3} + e^{2} + e + 1\right ) + \log \left (e - 1\right )\right )} x \log \left (\log \relax (x)\right ) - \pi ^{2} + 2 i \, \pi {\left (2 \, \log \relax (2) + \log \left (e^{4} + e^{3} + e^{2} + e + 1\right ) + \log \left (e - 1\right )\right )} + 4 \, {\left (\log \left (e^{4} + e^{3} + e^{2} + e + 1\right ) + \log \left (e - 1\right )\right )} \log \relax (2) + 4 \, \log \relax (2)^{2} + \log \left (e^{4} + e^{3} + e^{2} + e + 1\right )^{2} + 2 \, \log \left (e^{4} + e^{3} + e^{2} + e + 1\right ) \log \left (e - 1\right ) + \log \left (e - 1\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^4+1152*x^3)*log(x)*log(log(x))^3+(-36*x^3-864*x^2)*log(-4*exp(5)+4)*log(x)*log(log(x))^2+(144
*x*log(-4*exp(5)+4)^2*log(x)+(-18*x^3-288*x^2)*log(-4*exp(5)+4))*log(log(x))+72*x*log(-4*exp(5)+4)^2)/(64*x^3*
log(x)*log(log(x))^3-48*x^2*log(-4*exp(5)+4)*log(x)*log(log(x))^2+12*x*log(-4*exp(5)+4)^2*log(x)*log(log(x))-l
og(-4*exp(5)+4)^3*log(x)),x, algorithm="maxima")

[Out]

-9*(8*(I*pi + 2*log(2) + log(e^4 + e^3 + e^2 + e + 1) + log(e - 1))*x^2*log(log(x)) - (x^4 + 32*x^3)*log(log(x
))^2)/(16*x^2*log(log(x))^2 - 8*(I*pi + 2*log(2) + log(e^4 + e^3 + e^2 + e + 1) + log(e - 1))*x*log(log(x)) -
pi^2 + 2*I*pi*(2*log(2) + log(e^4 + e^3 + e^2 + e + 1) + log(e - 1)) + 4*(log(e^4 + e^3 + e^2 + e + 1) + log(e
- 1))*log(2) + 4*log(2)^2 + log(e^4 + e^3 + e^2 + e + 1)^2 + 2*log(e^4 + e^3 + e^2 + e + 1)*log(e - 1) + log(
e - 1)^2)

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mupad [B]  time = 3.99, size = 3724, normalized size = 106.40 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(x))*(log(4 - 4*exp(5))*(288*x^2 + 18*x^3) - 144*x*log(4 - 4*exp(5))^2*log(x)) - 72*x*log(4 - 4*ex
p(5))^2 - log(log(x))^3*log(x)*(1152*x^3 + 72*x^4) + log(log(x))^2*log(4 - 4*exp(5))*log(x)*(864*x^2 + 36*x^3)
)/(log(4 - 4*exp(5))^3*log(x) - 64*x^3*log(log(x))^3*log(x) + 48*x^2*log(log(x))^2*log(4 - 4*exp(5))*log(x) -
12*x*log(log(x))*log(4 - 4*exp(5))^2*log(x)),x)

[Out]

x*((39*log(4 - 4*exp(5)))/32 + 18) + (159*log(4 - 4*exp(5))^2*log(x))/128 - ((9*log(4 - 4*exp(5))^2*(64*x + 16
*log(4 - 4*exp(5))*log(x) + x*log(4 - 4*exp(5))*log(x)))/(256*x*(4*x + log(4 - 4*exp(5))*log(x))) - (9*log(log
(x))*log(4 - 4*exp(5))*(64*x + 16*log(4 - 4*exp(5))*log(x) + 4*x^2 + 3*x*log(4 - 4*exp(5))*log(x)))/(64*(4*x +
log(4 - 4*exp(5))*log(x))) + (9*x^2*log(log(x))^2*log(4 - 4*exp(5))*log(x))/(16*(4*x + log(4 - 4*exp(5))*log(
x))))/(log(4 - 4*exp(5))^2/(16*x^2) + log(log(x))^2 - (log(log(x))*log(4 - 4*exp(5)))/(2*x)) - log(x)^2*(((135
*x^2*log(4 - 4*exp(5))^5)/8 + (297*x^3*log(4 - 4*exp(5))^4)/8 + 27*x^4*log(4 - 4*exp(5))^3 + (135*x*log(4 - 4*
exp(5))^6)/64 + (27*log(4 - 4*exp(5))^7)/256)/(160*x^2*log(4 - 4*exp(5))^3 + 640*x^3*log(4 - 4*exp(5))^2 + 20*
x*log(4 - 4*exp(5))^4 + 1280*x^4*log(4 - 4*exp(5)) + 1024*x^5 + log(4 - 4*exp(5))^5) - (27*log(4 - 4*exp(5))^2
)/256) + (8040*x^2*log(4 - 4*exp(5))^5 + 20976*x^3*log(4 - 4*exp(5))^4 + 18432*x^4*log(4 - 4*exp(5))^3 + 1239*
x*log(4 - 4*exp(5))^6 + (279*log(4 - 4*exp(5))^7)/4)/(20480*x^2*log(4 - 4*exp(5))^3 + 81920*x^3*log(4 - 4*exp(
5))^2 + 2560*x*log(4 - 4*exp(5))^4 + 163840*x^4*log(4 - 4*exp(5)) + 131072*x^5 + 128*log(4 - 4*exp(5))^5) + ((
9*log(4 - 4*exp(5))*(4*log(4 - 4*exp(5))^3*log(x)^3 + 256*x^3 + 16*x^4 + 48*x*log(4 - 4*exp(5))^2*log(x)^2 - x
^2*log(4 - 4*exp(5))^2*log(x) + 4*x^2*log(4 - 4*exp(5))^2*log(x)^2 + 192*x^2*log(4 - 4*exp(5))*log(x) + 16*x^3
*log(4 - 4*exp(5))*log(x)))/(16*(4*x + log(4 - 4*exp(5))*log(x))^3) - (9*x^2*log(log(x))^2*log(x)*(2*x^2*log(4
- 4*exp(5)) + x*log(4 - 4*exp(5))^2*log(x)^2 + 2*x^2*log(4 - 4*exp(5))*log(x)))/(2*(4*x + log(4 - 4*exp(5))*l
og(x))^3) + (9*x^2*log(log(x))*log(x)*(3*log(4 - 4*exp(5))^3*log(x)^2 + 8*x*log(4 - 4*exp(5))^2 - 16*x^2*log(4
- 4*exp(5))))/(16*(4*x + log(4 - 4*exp(5))*log(x))^3))/(log(log(x)) - log(4 - 4*exp(5))/(4*x)) - ((3*x*(x^2*l
og(4 - 4*exp(5))^3 + 88*x^4*log(4 - 4*exp(5)) + 320*x^5))/(4*log(4 - 4*exp(5))*(4*x + log(4 - 4*exp(5)))^3) +
(3*x*log(x)^2*(9*x^2*log(4 - 4*exp(5))^2 + 188*x^3*log(4 - 4*exp(5)) + 384*x^4))/(8*(4*x + log(4 - 4*exp(5)))^
3) + (27*x^3*log(4 - 4*exp(5))*log(x)^3*(8*x + 3*log(4 - 4*exp(5))))/(8*(4*x + log(4 - 4*exp(5)))^3) + (3*x*lo
g(x)*(32*x^3*log(4 - 4*exp(5))^2 - 3*x^2*log(4 - 4*exp(5))^3 + 256*x^4*log(4 - 4*exp(5)) + 256*x^5))/(4*log(4
- 4*exp(5))*(4*x + log(4 - 4*exp(5)))^3))/((16*x^2)/log(4 - 4*exp(5))^2 + log(x)^2 + (8*x*log(x))/log(4 - 4*ex
p(5))) - ((3*x*(5*x^3*log(4 - 4*exp(5))^3 + 206*x^4*log(4 - 4*exp(5))^2 + 976*x^5*log(4 - 4*exp(5)) + 1216*x^6
))/(4*x + log(4 - 4*exp(5)))^5 + (12*x*log(x)*(22*x^3*log(4 - 4*exp(5))^3 + 159*x^4*log(4 - 4*exp(5))^2 + 320*
x^5*log(4 - 4*exp(5)) + 192*x^6))/(4*x + log(4 - 4*exp(5)))^5 + (3*x*log(4 - 4*exp(5))*log(x)^2*(27*x^2*log(4
- 4*exp(5))^3 + 323*x^3*log(4 - 4*exp(5))^2 + 884*x^4*log(4 - 4*exp(5)) + 768*x^5))/(2*(4*x + log(4 - 4*exp(5)
))^5) + (27*x^3*log(4 - 4*exp(5))^2*log(x)^3*(32*x*log(4 - 4*exp(5)) + 32*x^2 + 9*log(4 - 4*exp(5))^2))/(8*(4*
x + log(4 - 4*exp(5)))^5))/(log(x) + (4*x)/log(4 - 4*exp(5))) - ((27*x^3*log(x)^3)/(4*(4*x + log(4 - 4*exp(5))
)) - (3*x*(x^3*log(4 - 4*exp(5)) - 8*x^4))/(log(4 - 4*exp(5))^2*(4*x + log(4 - 4*exp(5)))) + (3*x*log(x)*(x^2*
log(4 - 4*exp(5))^2 + 4*x^3*log(4 - 4*exp(5)) + 16*x^4))/(2*log(4 - 4*exp(5))^2*(4*x + log(4 - 4*exp(5)))) - (
3*x*log(x)^2*(3*x^2*log(4 - 4*exp(5)) - 16*x^3))/(2*log(4 - 4*exp(5))*(4*x + log(4 - 4*exp(5)))))/((64*x^3)/lo
g(4 - 4*exp(5))^3 + log(x)^3 + (12*x*log(x)^2)/log(4 - 4*exp(5)) + (48*x^2*log(x))/log(4 - 4*exp(5))^2) + (9*x
^2)/16 - (log(log(x))*(log(x)*(64*x^6*(((27*x^2*log(4 - 4*exp(5)))/4 + 18*x^3)/(2*x^3*log(4 - 4*exp(5)) + 8*x^
4) - ((27*x^2*log(4 - 4*exp(5)))/4 + 27*x^3)/(2*x^3*log(4 - 4*exp(5)) + 8*x^4)) + x*log(4 - 4*exp(5))*((24*x^2
*(3*x^2*log(4 - 4*exp(5)) - 20*x^3))/(4*x*log(4 - 4*exp(5)) + log(4 - 4*exp(5))^2) - (3*x*(x^2*log(4 - 4*exp(5
))^2 - 32*x^4))/(4*x*log(4 - 4*exp(5)) + log(4 - 4*exp(5))^2)) - 48*x^5*log(4 - 4*exp(5))*((54*x^2*log(4 - 4*e
xp(5))^2 + (27*x*log(4 - 4*exp(5))^3)/4 + 108*x^3*log(4 - 4*exp(5)))/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(
4 - 4*exp(5))) - ((27*x*log(4 - 4*exp(5))^3)/4 - (189*x^2*log(4 - 4*exp(5))^2)/2 + 90*x^3*log(4 - 4*exp(5)) +
2304*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) - ((81*x^2*log(4 - 4*exp(5))^2)/2 + 162*x^3*
log(4 - 4*exp(5)))/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) + (252*x^3*log(4 - 4*exp(5)) - 108*
x^2*log(4 - 4*exp(5))^2 + 1728*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5)))) + (6*x^4*log(4 -
4*exp(5))*(6*x - log(4 - 4*exp(5))))/(4*x + log(4 - 4*exp(5))) + (24*x^3*log(4 - 4*exp(5))*(3*x^2*log(4 - 4*ex
p(5)) - 20*x^3))/(4*x*log(4 - 4*exp(5)) + log(4 - 4*exp(5))^2)) + log(x)^3*((12*x^4*log(4 - 4*exp(5))^2)/(4*x
+ log(4 - 4*exp(5))) + 12*x^4*log(4 - 4*exp(5))^2*(((27*x^2*log(4 - 4*exp(5)))/4 + 18*x^3)/(2*x^3*log(4 - 4*ex
p(5)) + 8*x^4) - ((27*x^2*log(4 - 4*exp(5)))/4 + 27*x^3)/(2*x^3*log(4 - 4*exp(5)) + 8*x^4)) - x^3*log(4 - 4*ex
p(5))^3*((54*x^2*log(4 - 4*exp(5))^2 + (27*x*log(4 - 4*exp(5))^3)/4 + 108*x^3*log(4 - 4*exp(5)))/(24*x^3*log(4
- 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) - ((27*x*log(4 - 4*exp(5))^3)/4 - (189*x^2*log(4 - 4*exp(5))^2)/2 +
90*x^3*log(4 - 4*exp(5)) + 2304*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) - ((81*x^2*log(4
- 4*exp(5))^2)/2 + 162*x^3*log(4 - 4*exp(5)))/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) + (252*
x^3*log(4 - 4*exp(5)) - 108*x^2*log(4 - 4*exp(5))^2 + 1728*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4
*exp(5))))) + log(x)^2*(48*x^5*log(4 - 4*exp(5))*(((27*x^2*log(4 - 4*exp(5)))/4 + 18*x^3)/(2*x^3*log(4 - 4*exp
(5)) + 8*x^4) - ((27*x^2*log(4 - 4*exp(5)))/4 + 27*x^3)/(2*x^3*log(4 - 4*exp(5)) + 8*x^4)) - 12*x^4*log(4 - 4*
exp(5))^2*((54*x^2*log(4 - 4*exp(5))^2 + (27*x*log(4 - 4*exp(5))^3)/4 + 108*x^3*log(4 - 4*exp(5)))/(24*x^3*log
(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) - ((27*x*log(4 - 4*exp(5))^3)/4 - (189*x^2*log(4 - 4*exp(5))^2)/2
+ 90*x^3*log(4 - 4*exp(5)) + 2304*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) - ((81*x^2*log
(4 - 4*exp(5))^2)/2 + 162*x^3*log(4 - 4*exp(5)))/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) + (25
2*x^3*log(4 - 4*exp(5)) - 108*x^2*log(4 - 4*exp(5))^2 + 1728*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 -
4*exp(5)))) + (3*x^4*log(4 - 4*exp(5))*(4*x + 9*log(4 - 4*exp(5))))/(4*x + log(4 - 4*exp(5))) + (6*x^2*log(4
- 4*exp(5))^2*(3*x^2*log(4 - 4*exp(5)) - 20*x^3))/(4*x*log(4 - 4*exp(5)) + log(4 - 4*exp(5))^2)) + log(x)^4*((
9*x^3*log(4 - 4*exp(5))^3)/(2*(4*x + log(4 - 4*exp(5)))) + x^3*log(4 - 4*exp(5))^3*(((27*x^2*log(4 - 4*exp(5))
)/4 + 18*x^3)/(2*x^3*log(4 - 4*exp(5)) + 8*x^4) - ((27*x^2*log(4 - 4*exp(5)))/4 + 27*x^3)/(2*x^3*log(4 - 4*exp
(5)) + 8*x^4))) + 4*x^2*((24*x^2*(3*x^2*log(4 - 4*exp(5)) - 20*x^3))/(4*x*log(4 - 4*exp(5)) + log(4 - 4*exp(5)
)^2) - (3*x*(x^2*log(4 - 4*exp(5))^2 - 32*x^4))/(4*x*log(4 - 4*exp(5)) + log(4 - 4*exp(5))^2)) - 64*x^6*((54*x
^2*log(4 - 4*exp(5))^2 + (27*x*log(4 - 4*exp(5))^3)/4 + 108*x^3*log(4 - 4*exp(5)))/(24*x^3*log(4 - 4*exp(5))^2
+ 96*x^4*log(4 - 4*exp(5))) - ((27*x*log(4 - 4*exp(5))^3)/4 - (189*x^2*log(4 - 4*exp(5))^2)/2 + 90*x^3*log(4
- 4*exp(5)) + 2304*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) - ((81*x^2*log(4 - 4*exp(5))^2
)/2 + 162*x^3*log(4 - 4*exp(5)))/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5))) + (252*x^3*log(4 - 4*
exp(5)) - 108*x^2*log(4 - 4*exp(5))^2 + 1728*x^4)/(24*x^3*log(4 - 4*exp(5))^2 + 96*x^4*log(4 - 4*exp(5)))) + (
12*x^5*log(4 - 4*exp(5)))/(4*x + log(4 - 4*exp(5)))))/(log(4 - 4*exp(5))^3*log(x)^3 + 64*x^3 + 12*x*log(4 - 4*
exp(5))^2*log(x)^2 + 48*x^2*log(4 - 4*exp(5))*log(x)) - (log(x)*((795*x^2*log(4 - 4*exp(5))^5)/4 + (5955*x^3*l
og(4 - 4*exp(5))^4)/8 + 1119*x^4*log(4 - 4*exp(5))^3 + (795*x*log(4 - 4*exp(5))^6)/32 - 1152*x^6*log(4 - 4*exp
(5)) + (159*log(4 - 4*exp(5))^7)/128))/(160*x^2*log(4 - 4*exp(5))^3 + 640*x^3*log(4 - 4*exp(5))^2 + 20*x*log(4
- 4*exp(5))^4 + 1280*x^4*log(4 - 4*exp(5)) + 1024*x^5 + log(4 - 4*exp(5))^5)

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sympy [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(((72*x**4+1152*x**3)*ln(x)*ln(ln(x))**3+(-36*x**3-864*x**2)*ln(-4*exp(5)+4)*ln(x)*ln(ln(x))**2+(144*
x*ln(-4*exp(5)+4)**2*ln(x)+(-18*x**3-288*x**2)*ln(-4*exp(5)+4))*ln(ln(x))+72*x*ln(-4*exp(5)+4)**2)/(64*x**3*ln
(x)*ln(ln(x))**3-48*x**2*ln(-4*exp(5)+4)*ln(x)*ln(ln(x))**2+12*x*ln(-4*exp(5)+4)**2*ln(x)*ln(ln(x))-ln(-4*exp(
5)+4)**3*ln(x)),x)

[Out]

Timed out

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