3.6.88 \(\int \frac {-24 e^5 x^4+(432-108 x-108 x^2+27 x^3+e^{10} (-32 x^3+8 x^4)) \log (4-x)+(72 x^4+e^5 (192 x^3-48 x^4) \log (4-x)) \log (\log (4-x))+(-288 x^3+72 x^4) \log (4-x) \log ^2(\log (4-x))}{(-432 x+108 x^2-108 x^3+27 x^4+e^{10} (-16 x^4+4 x^5)) \log (4-x)+e^5 (96 x^4-24 x^5) \log (4-x) \log (\log (4-x))+(-144 x^4+36 x^5) \log (4-x) \log ^2(\log (4-x))} \, dx\)

Optimal. Leaf size=37 \[ \log \left (5 \left (-x+4 \left (\frac {3}{x}+x+x^2 \left (-\frac {e^5}{3}+\log (\log (4-x))\right )^2\right )\right )\right ) \]

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Rubi [F]  time = 16.85, 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 {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-24*E^5*x^4 + (432 - 108*x - 108*x^2 + 27*x^3 + E^10*(-32*x^3 + 8*x^4))*Log[4 - x] + (72*x^4 + E^5*(192*x
^3 - 48*x^4)*Log[4 - x])*Log[Log[4 - x]] + (-288*x^3 + 72*x^4)*Log[4 - x]*Log[Log[4 - x]]^2)/((-432*x + 108*x^
2 - 108*x^3 + 27*x^4 + E^10*(-16*x^4 + 4*x^5))*Log[4 - x] + E^5*(96*x^4 - 24*x^5)*Log[4 - x]*Log[Log[4 - x]] +
(-144*x^4 + 36*x^5)*Log[4 - x]*Log[Log[4 - x]]^2),x]

[Out]

2*Log[x] - 324*Defer[Int][1/(x*(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]
]^2)), x] - 27*Defer[Int][x/(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]]^2
), x] - 384*E^5*Defer[Int][1/(Log[4 - x]*(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[
Log[4 - x]]^2)), x] - 1536*E^5*Defer[Int][1/((-4 + x)*Log[4 - x]*(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[L
og[4 - x]] + 36*x^3*Log[Log[4 - x]]^2)), x] - 96*E^5*Defer[Int][x/(Log[4 - x]*(108 + 27*x^2 + 4*E^10*x^3 - 24*
E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]]^2)), x] - 24*E^5*Defer[Int][x^2/(Log[4 - x]*(108 + 27*x^2 + 4
*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]]^2)), x] + 1152*Defer[Int][Log[Log[4 - x]]/(Log
[4 - x]*(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]]^2)), x] + 4608*Defer[
Int][Log[Log[4 - x]]/((-4 + x)*Log[4 - x]*(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log
[Log[4 - x]]^2)), x] + 288*Defer[Int][(x*Log[Log[4 - x]])/(Log[4 - x]*(108 + 27*x^2 + 4*E^10*x^3 - 24*E^5*x^3*
Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]]^2)), x] + 72*Defer[Int][(x^2*Log[Log[4 - x]])/(Log[4 - x]*(108 + 27*x
^2 + 4*E^10*x^3 - 24*E^5*x^3*Log[Log[4 - x]] + 36*x^3*Log[Log[4 - x]]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {24 x^4 \left (e^5-3 \log (\log (4-x))\right )-(-4+x) \log (4-x) \left (-108+27 x^2+8 e^{10} x^3-48 e^5 x^3 \log (\log (4-x))+72 x^3 \log ^2(\log (4-x))\right )}{(4-x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx\\ &=\int \left (\frac {2}{x}-\frac {3 \left (8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))\right )}{(-4+x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx\\ &=2 \log (x)-3 \int \frac {8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))}{(-4+x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx\\ &=2 \log (x)-3 \int \frac {-9 \left (-48+12 x-4 x^2+x^3\right ) \log (4-x)-8 x^4 \left (e^5-3 \log (\log (4-x))\right )}{(4-x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx\\ &=2 \log (x)-3 \int \left (\frac {8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))}{4 (-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {-8 e^5 x^4+432 \log (4-x)-108 x \log (4-x)+36 x^2 \log (4-x)-9 x^3 \log (4-x)+24 x^4 \log (\log (4-x))}{4 x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx\\ &=2 \log (x)-\frac {3}{4} \int \frac {8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-\frac {3}{4} \int \frac {-8 e^5 x^4+432 \log (4-x)-108 x \log (4-x)+36 x^2 \log (4-x)-9 x^3 \log (4-x)+24 x^4 \log (\log (4-x))}{x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx\\ &=2 \log (x)-\frac {3}{4} \int \frac {-9 \left (-48+12 x-4 x^2+x^3\right ) \log (4-x)-8 x^4 \left (e^5-3 \log (\log (4-x))\right )}{(4-x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-\frac {3}{4} \int \frac {-9 \left (-48+12 x-4 x^2+x^3\right ) \log (4-x)-8 x^4 \left (e^5-3 \log (\log (4-x))\right )}{x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx\\ &=2 \log (x)-\frac {3}{4} \int \left (-\frac {108}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))}+\frac {432}{x \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {36 x}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))}-\frac {9 x^2}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))}-\frac {8 e^5 x^3}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {24 x^3 \log (\log (4-x))}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx-\frac {3}{4} \int \left (-\frac {432}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {108 x}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}-\frac {36 x^2}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {9 x^3}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {8 e^5 x^4}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}-\frac {24 x^4 \log (\log (4-x))}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx\\ &=2 \log (x)+\frac {27}{4} \int \frac {x^2}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))} \, dx-\frac {27}{4} \int \frac {x^3}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-18 \int \frac {x^3 \log (\log (4-x))}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+18 \int \frac {x^4 \log (\log (4-x))}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-27 \int \frac {x}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))} \, dx+27 \int \frac {x^2}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+81 \int \frac {1}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))} \, dx-81 \int \frac {x}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+324 \int \frac {1}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-324 \int \frac {1}{x \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+\left (6 e^5\right ) \int \frac {x^3}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-\left (6 e^5\right ) \int \frac {x^4}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.18, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-24*E^5*x^4 + (432 - 108*x - 108*x^2 + 27*x^3 + E^10*(-32*x^3 + 8*x^4))*Log[4 - x] + (72*x^4 + E^5*
(192*x^3 - 48*x^4)*Log[4 - x])*Log[Log[4 - x]] + (-288*x^3 + 72*x^4)*Log[4 - x]*Log[Log[4 - x]]^2)/((-432*x +
108*x^2 - 108*x^3 + 27*x^4 + E^10*(-16*x^4 + 4*x^5))*Log[4 - x] + E^5*(96*x^4 - 24*x^5)*Log[4 - x]*Log[Log[4 -
x]] + (-144*x^4 + 36*x^5)*Log[4 - x]*Log[Log[4 - x]]^2),x]

[Out]

Integrate[(-24*E^5*x^4 + (432 - 108*x - 108*x^2 + 27*x^3 + E^10*(-32*x^3 + 8*x^4))*Log[4 - x] + (72*x^4 + E^5*
(192*x^3 - 48*x^4)*Log[4 - x])*Log[Log[4 - x]] + (-288*x^3 + 72*x^4)*Log[4 - x]*Log[Log[4 - x]]^2)/((-432*x +
108*x^2 - 108*x^3 + 27*x^4 + E^10*(-16*x^4 + 4*x^5))*Log[4 - x] + E^5*(96*x^4 - 24*x^5)*Log[4 - x]*Log[Log[4 -
x]] + (-144*x^4 + 36*x^5)*Log[4 - x]*Log[Log[4 - x]]^2), x]

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fricas [A]  time = 0.65, size = 53, normalized size = 1.43 \begin {gather*} 2 \, \log \relax (x) + \log \left (-\frac {24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) - 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} - 4 \, x^{3} e^{10} - 27 \, x^{2} - 108}{x^{3}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)*exp(5)*log(-x+4)+72*x^4)*log(log(-x+
4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-108*x^2-108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*lo
g(log(-x+4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x^4)*exp(5)^2+27*x^4-108*x^3+108*x^
2-432*x)*log(-x+4)),x, algorithm="fricas")

[Out]

2*log(x) + log(-(24*x^3*e^5*log(log(-x + 4)) - 36*x^3*log(log(-x + 4))^2 - 4*x^3*e^10 - 27*x^2 - 108)/x^3)

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giac [A]  time = 1.24, size = 48, normalized size = 1.30 \begin {gather*} \log \left (-24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) + 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} + 4 \, x^{3} e^{10} + 27 \, x^{2} + 108\right ) - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)*exp(5)*log(-x+4)+72*x^4)*log(log(-x+
4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-108*x^2-108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*lo
g(log(-x+4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x^4)*exp(5)^2+27*x^4-108*x^3+108*x^
2-432*x)*log(-x+4)),x, algorithm="giac")

[Out]

log(-24*x^3*e^5*log(log(-x + 4)) + 36*x^3*log(log(-x + 4))^2 + 4*x^3*e^10 + 27*x^2 + 108) - log(x)

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maple [A]  time = 0.18, size = 47, normalized size = 1.27

method	result	size
risch	\(2 \ln \relax (x )+\ln \left (\ln \left (\ln \left (-x +4\right )\right )^{2}-\frac {2 \,{\mathrm e}^{5} \ln \left (\ln \left (-x +4\right )\right )}{3}+\frac {4 x^{3} {\mathrm e}^{10}+27 x^{2}+108}{36 x^{3}}\right )\)	\(47\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((72*x^4-288*x^3)*ln(-x+4)*ln(ln(-x+4))^2+((-48*x^4+192*x^3)*exp(5)*ln(-x+4)+72*x^4)*ln(ln(-x+4))+((8*x^4-
32*x^3)*exp(5)^2+27*x^3-108*x^2-108*x+432)*ln(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*ln(-x+4)*ln(ln(-x+4))^2+(
-24*x^5+96*x^4)*exp(5)*ln(-x+4)*ln(ln(-x+4))+((4*x^5-16*x^4)*exp(5)^2+27*x^4-108*x^3+108*x^2-432*x)*ln(-x+4)),
x,method=_RETURNVERBOSE)

[Out]

2*ln(x)+ln(ln(ln(-x+4))^2-2/3*exp(5)*ln(ln(-x+4))+1/36*(4*x^3*exp(10)+27*x^2+108)/x^3)

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maxima [A]  time = 0.56, size = 53, normalized size = 1.43 \begin {gather*} 2 \, \log \relax (x) + \log \left (-\frac {24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) - 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} - 4 \, x^{3} e^{10} - 27 \, x^{2} - 108}{36 \, x^{3}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)*exp(5)*log(-x+4)+72*x^4)*log(log(-x+
4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-108*x^2-108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*lo
g(log(-x+4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x^4)*exp(5)^2+27*x^4-108*x^3+108*x^
2-432*x)*log(-x+4)),x, algorithm="maxima")

[Out]

2*log(x) + log(-1/36*(24*x^3*e^5*log(log(-x + 4)) - 36*x^3*log(log(-x + 4))^2 - 4*x^3*e^10 - 27*x^2 - 108)/x^3
)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \left (4-x\right )\,\left (108\,x+{\mathrm {e}}^{10}\,\left (32\,x^3-8\,x^4\right )+108\,x^2-27\,x^3-432\right )-\ln \left (\ln \left (4-x\right )\right )\,\left (72\,x^4+{\mathrm {e}}^5\,\ln \left (4-x\right )\,\left (192\,x^3-48\,x^4\right )\right )+24\,x^4\,{\mathrm {e}}^5+{\ln \left (\ln \left (4-x\right )\right )}^2\,\ln \left (4-x\right )\,\left (288\,x^3-72\,x^4\right )}{\ln \left (4-x\right )\,\left (144\,x^4-36\,x^5\right )\,{\ln \left (\ln \left (4-x\right )\right )}^2-{\mathrm {e}}^5\,\ln \left (4-x\right )\,\left (96\,x^4-24\,x^5\right )\,\ln \left (\ln \left (4-x\right )\right )+\ln \left (4-x\right )\,\left (432\,x+{\mathrm {e}}^{10}\,\left (16\,x^4-4\,x^5\right )-108\,x^2+108\,x^3-27\,x^4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(4 - x)*(108*x + exp(10)*(32*x^3 - 8*x^4) + 108*x^2 - 27*x^3 - 432) - log(log(4 - x))*(72*x^4 + exp(5)
*log(4 - x)*(192*x^3 - 48*x^4)) + 24*x^4*exp(5) + log(log(4 - x))^2*log(4 - x)*(288*x^3 - 72*x^4))/(log(4 - x)
*(432*x + exp(10)*(16*x^4 - 4*x^5) - 108*x^2 + 108*x^3 - 27*x^4) + log(log(4 - x))^2*log(4 - x)*(144*x^4 - 36*
x^5) - log(log(4 - x))*exp(5)*log(4 - x)*(96*x^4 - 24*x^5)),x)

[Out]

int((log(4 - x)*(108*x + exp(10)*(32*x^3 - 8*x^4) + 108*x^2 - 27*x^3 - 432) - log(log(4 - x))*(72*x^4 + exp(5)
*log(4 - x)*(192*x^3 - 48*x^4)) + 24*x^4*exp(5) + log(log(4 - x))^2*log(4 - x)*(288*x^3 - 72*x^4))/(log(4 - x)
*(432*x + exp(10)*(16*x^4 - 4*x^5) - 108*x^2 + 108*x^3 - 27*x^4) + log(log(4 - x))^2*log(4 - x)*(144*x^4 - 36*
x^5) - log(log(4 - x))*exp(5)*log(4 - x)*(96*x^4 - 24*x^5)), x)

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sympy [A]  time = 0.86, size = 48, normalized size = 1.30 \begin {gather*} 2 \log {\relax (x )} + \log {\left (\log {\left (\log {\left (4 - x \right )} \right )}^{2} - \frac {2 e^{5} \log {\left (\log {\left (4 - x \right )} \right )}}{3} + \frac {4 x^{3} e^{10} + 27 x^{2} + 108}{36 x^{3}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x**4-288*x**3)*ln(-x+4)*ln(ln(-x+4))**2+((-48*x**4+192*x**3)*exp(5)*ln(-x+4)+72*x**4)*ln(ln(-x+
4))+((8*x**4-32*x**3)*exp(5)**2+27*x**3-108*x**2-108*x+432)*ln(-x+4)-24*x**4*exp(5))/((36*x**5-144*x**4)*ln(-x
+4)*ln(ln(-x+4))**2+(-24*x**5+96*x**4)*exp(5)*ln(-x+4)*ln(ln(-x+4))+((4*x**5-16*x**4)*exp(5)**2+27*x**4-108*x*
*3+108*x**2-432*x)*ln(-x+4)),x)

[Out]

2*log(x) + log(log(log(4 - x))**2 - 2*exp(5)*log(log(4 - x))/3 + (4*x**3*exp(10) + 27*x**2 + 108)/(36*x**3))

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