3.46.33 \(\int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+(-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+(-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7) \log (3)) \log (x^2+2 x \log (3)+\log ^2(3))+(49152-73728 x+33792 x^2-4608 x^3+192 x^4+(36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+(36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5) \log (3)) \log (x^2+2 x \log (3)+\log ^2(3))) \log (\log (x^2+2 x \log (3)+\log ^2(3)))+(-24576+18432 x-1536 x^2+(-18432 x+16896 x^2-3456 x^3+192 x^4+(-18432+16896 x-3456 x^2+192 x^3) \log (3)) \log (x^2+2 x \log (3)+\log ^2(3))) \log ^2(\log (x^2+2 x \log (3)+\log ^2(3)))+(4096+(3072 x-512 x^2+(3072-512 x) \log (3)) \log (x^2+2 x \log (3)+\log ^2(3))) \log ^3(\log (x^2+2 x \log (3)+\log ^2(3)))}{(800 x+800 \log (3)) \log (x^2+2 x \log (3)+\log ^2(3))} \, dx\)

Optimal. Leaf size=29 \[ -5+\frac {1}{25} \left (-\frac {1}{4} (-4+x)^2+x+2 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^4 \]

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Rubi [A]  time = 0.63, antiderivative size = 24, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 3, integrand size = 385, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {6688, 12, 6686} \begin {gather*} \frac {\left (x^2-12 x-8 \log \left (\log \left ((x+\log (3))^2\right )\right )+16\right )^4}{6400} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-32768 + 73728*x - 61440*x^2 + 23040*x^3 - 3840*x^4 + 288*x^5 - 8*x^6 + (-24576*x + 59392*x^2 - 55296*x^3
+ 24960*x^4 - 5760*x^5 + 696*x^6 - 42*x^7 + x^8 + (-24576 + 59392*x - 55296*x^2 + 24960*x^3 - 5760*x^4 + 696*
x^5 - 42*x^6 + x^7)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2] + (49152 - 73728*x + 33792*x^2 - 4608*x^3 + 192*x
^4 + (36864*x - 61440*x^2 + 34560*x^3 - 7680*x^4 + 720*x^5 - 24*x^6 + (36864 - 61440*x + 34560*x^2 - 7680*x^3
+ 720*x^4 - 24*x^5)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2])*Log[Log[x^2 + 2*x*Log[3] + Log[3]^2]] + (-24576
+ 18432*x - 1536*x^2 + (-18432*x + 16896*x^2 - 3456*x^3 + 192*x^4 + (-18432 + 16896*x - 3456*x^2 + 192*x^3)*Lo
g[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2])*Log[Log[x^2 + 2*x*Log[3] + Log[3]^2]]^2 + (4096 + (3072*x - 512*x^2 +
(3072 - 512*x)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2])*Log[Log[x^2 + 2*x*Log[3] + Log[3]^2]]^3)/((800*x + 80
0*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2]),x]

[Out]

(16 - 12*x + x^2 - 8*Log[Log[(x + Log[3])^2]])^4/6400

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6686

Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[(q*y^(m + 1))/(m + 1), x] /;  !F
alseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (-8+(-6+x) (x+\log (3)) \log \left ((x+\log (3))^2\right )\right ) \left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^3}{800 (x+\log (3)) \log \left ((x+\log (3))^2\right )} \, dx\\ &=\frac {1}{800} \int \frac {\left (-8+(-6+x) (x+\log (3)) \log \left ((x+\log (3))^2\right )\right ) \left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^3}{(x+\log (3)) \log \left ((x+\log (3))^2\right )} \, dx\\ &=\frac {\left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^4}{6400}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 24, normalized size = 0.83 \begin {gather*} \frac {\left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^4}{6400} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-32768 + 73728*x - 61440*x^2 + 23040*x^3 - 3840*x^4 + 288*x^5 - 8*x^6 + (-24576*x + 59392*x^2 - 552
96*x^3 + 24960*x^4 - 5760*x^5 + 696*x^6 - 42*x^7 + x^8 + (-24576 + 59392*x - 55296*x^2 + 24960*x^3 - 5760*x^4
+ 696*x^5 - 42*x^6 + x^7)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2] + (49152 - 73728*x + 33792*x^2 - 4608*x^3 +
192*x^4 + (36864*x - 61440*x^2 + 34560*x^3 - 7680*x^4 + 720*x^5 - 24*x^6 + (36864 - 61440*x + 34560*x^2 - 768
0*x^3 + 720*x^4 - 24*x^5)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2])*Log[Log[x^2 + 2*x*Log[3] + Log[3]^2]] + (-
24576 + 18432*x - 1536*x^2 + (-18432*x + 16896*x^2 - 3456*x^3 + 192*x^4 + (-18432 + 16896*x - 3456*x^2 + 192*x
^3)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2])*Log[Log[x^2 + 2*x*Log[3] + Log[3]^2]]^2 + (4096 + (3072*x - 512*
x^2 + (3072 - 512*x)*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2])*Log[Log[x^2 + 2*x*Log[3] + Log[3]^2]]^3)/((800*
x + 800*Log[3])*Log[x^2 + 2*x*Log[3] + Log[3]^2]),x]

[Out]

(16 - 12*x + x^2 - 8*Log[Log[(x + Log[3])^2]])^4/6400

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fricas [B]  time = 0.66, size = 167, normalized size = 5.76 \begin {gather*} \frac {1}{6400} \, x^{8} - \frac {3}{400} \, x^{7} + \frac {29}{200} \, x^{6} - \frac {36}{25} \, x^{5} + \frac {39}{5} \, x^{4} - \frac {8}{25} \, {\left (x^{2} - 12 \, x + 16\right )} \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right )^{3} + \frac {16}{25} \, \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right )^{4} - \frac {576}{25} \, x^{3} + \frac {3}{50} \, {\left (x^{4} - 24 \, x^{3} + 176 \, x^{2} - 384 \, x + 256\right )} \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right )^{2} + \frac {928}{25} \, x^{2} - \frac {1}{200} \, {\left (x^{6} - 36 \, x^{5} + 480 \, x^{4} - 2880 \, x^{3} + 7680 \, x^{2} - 9216 \, x + 4096\right )} \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right ) - \frac {768}{25} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-512*x+3072)*log(3)-512*x^2+3072*x)*log(log(3)^2+2*x*log(3)+x^2)+4096)*log(log(log(3)^2+2*x*log(
3)+x^2))^3+(((192*x^3-3456*x^2+16896*x-18432)*log(3)+192*x^4-3456*x^3+16896*x^2-18432*x)*log(log(3)^2+2*x*log(
3)+x^2)-1536*x^2+18432*x-24576)*log(log(log(3)^2+2*x*log(3)+x^2))^2+(((-24*x^5+720*x^4-7680*x^3+34560*x^2-6144
0*x+36864)*log(3)-24*x^6+720*x^5-7680*x^4+34560*x^3-61440*x^2+36864*x)*log(log(3)^2+2*x*log(3)+x^2)+192*x^4-46
08*x^3+33792*x^2-73728*x+49152)*log(log(log(3)^2+2*x*log(3)+x^2))+((x^7-42*x^6+696*x^5-5760*x^4+24960*x^3-5529
6*x^2+59392*x-24576)*log(3)+x^8-42*x^7+696*x^6-5760*x^5+24960*x^4-55296*x^3+59392*x^2-24576*x)*log(log(3)^2+2*
x*log(3)+x^2)-8*x^6+288*x^5-3840*x^4+23040*x^3-61440*x^2+73728*x-32768)/(800*log(3)+800*x)/log(log(3)^2+2*x*lo
g(3)+x^2),x, algorithm="fricas")

[Out]

1/6400*x^8 - 3/400*x^7 + 29/200*x^6 - 36/25*x^5 + 39/5*x^4 - 8/25*(x^2 - 12*x + 16)*log(log(x^2 + 2*x*log(3) +
log(3)^2))^3 + 16/25*log(log(x^2 + 2*x*log(3) + log(3)^2))^4 - 576/25*x^3 + 3/50*(x^4 - 24*x^3 + 176*x^2 - 38
4*x + 256)*log(log(x^2 + 2*x*log(3) + log(3)^2))^2 + 928/25*x^2 - 1/200*(x^6 - 36*x^5 + 480*x^4 - 2880*x^3 + 7
680*x^2 - 9216*x + 4096)*log(log(x^2 + 2*x*log(3) + log(3)^2)) - 768/25*x

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giac [B]  time = 1.92, size = 183, normalized size = 6.31 \begin {gather*} \frac {1}{6400} \, x^{8} - \frac {3}{400} \, x^{7} + \frac {29}{200} \, x^{6} - \frac {36}{25} \, x^{5} + \frac {39}{5} \, x^{4} - \frac {8}{25} \, {\left (x^{2} - 12 \, x + 16\right )} \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right )^{3} + \frac {16}{25} \, \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right )^{4} - \frac {576}{25} \, x^{3} + \frac {3}{50} \, {\left (x^{4} - 24 \, x^{3} + 176 \, x^{2} - 384 \, x + 256\right )} \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right )^{2} + \frac {928}{25} \, x^{2} - \frac {1}{200} \, {\left (x^{6} - 36 \, x^{5} + 480 \, x^{4} - 2880 \, x^{3} + 7680 \, x^{2} - 9216 \, x\right )} \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right ) - \frac {768}{25} \, x - \frac {512}{25} \, \log \left (\log \left (x^{2} + 2 \, x \log \relax (3) + \log \relax (3)^{2}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-512*x+3072)*log(3)-512*x^2+3072*x)*log(log(3)^2+2*x*log(3)+x^2)+4096)*log(log(log(3)^2+2*x*log(
3)+x^2))^3+(((192*x^3-3456*x^2+16896*x-18432)*log(3)+192*x^4-3456*x^3+16896*x^2-18432*x)*log(log(3)^2+2*x*log(
3)+x^2)-1536*x^2+18432*x-24576)*log(log(log(3)^2+2*x*log(3)+x^2))^2+(((-24*x^5+720*x^4-7680*x^3+34560*x^2-6144
0*x+36864)*log(3)-24*x^6+720*x^5-7680*x^4+34560*x^3-61440*x^2+36864*x)*log(log(3)^2+2*x*log(3)+x^2)+192*x^4-46
08*x^3+33792*x^2-73728*x+49152)*log(log(log(3)^2+2*x*log(3)+x^2))+((x^7-42*x^6+696*x^5-5760*x^4+24960*x^3-5529
6*x^2+59392*x-24576)*log(3)+x^8-42*x^7+696*x^6-5760*x^5+24960*x^4-55296*x^3+59392*x^2-24576*x)*log(log(3)^2+2*
x*log(3)+x^2)-8*x^6+288*x^5-3840*x^4+23040*x^3-61440*x^2+73728*x-32768)/(800*log(3)+800*x)/log(log(3)^2+2*x*lo
g(3)+x^2),x, algorithm="giac")

[Out]

1/6400*x^8 - 3/400*x^7 + 29/200*x^6 - 36/25*x^5 + 39/5*x^4 - 8/25*(x^2 - 12*x + 16)*log(log(x^2 + 2*x*log(3) +
log(3)^2))^3 + 16/25*log(log(x^2 + 2*x*log(3) + log(3)^2))^4 - 576/25*x^3 + 3/50*(x^4 - 24*x^3 + 176*x^2 - 38
4*x + 256)*log(log(x^2 + 2*x*log(3) + log(3)^2))^2 + 928/25*x^2 - 1/200*(x^6 - 36*x^5 + 480*x^4 - 2880*x^3 + 7
680*x^2 - 9216*x)*log(log(x^2 + 2*x*log(3) + log(3)^2)) - 768/25*x - 512/25*log(log(x^2 + 2*x*log(3) + log(3)^
2))

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maple [F]  time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (\left (-512 x +3072\right ) \ln \relax (3)-512 x^{2}+3072 x \right ) \ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )+4096\right ) \ln \left (\ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )\right )^{3}+\left (\left (\left (192 x^{3}-3456 x^{2}+16896 x -18432\right ) \ln \relax (3)+192 x^{4}-3456 x^{3}+16896 x^{2}-18432 x \right ) \ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )-1536 x^{2}+18432 x -24576\right ) \ln \left (\ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )\right )^{2}+\left (\left (\left (-24 x^{5}+720 x^{4}-7680 x^{3}+34560 x^{2}-61440 x +36864\right ) \ln \relax (3)-24 x^{6}+720 x^{5}-7680 x^{4}+34560 x^{3}-61440 x^{2}+36864 x \right ) \ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )+192 x^{4}-4608 x^{3}+33792 x^{2}-73728 x +49152\right ) \ln \left (\ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )\right )+\left (\left (x^{7}-42 x^{6}+696 x^{5}-5760 x^{4}+24960 x^{3}-55296 x^{2}+59392 x -24576\right ) \ln \relax (3)+x^{8}-42 x^{7}+696 x^{6}-5760 x^{5}+24960 x^{4}-55296 x^{3}+59392 x^{2}-24576 x \right ) \ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )-8 x^{6}+288 x^{5}-3840 x^{4}+23040 x^{3}-61440 x^{2}+73728 x -32768}{\left (800 \ln \relax (3)+800 x \right ) \ln \left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-512*x+3072)*ln(3)-512*x^2+3072*x)*ln(ln(3)^2+2*x*ln(3)+x^2)+4096)*ln(ln(ln(3)^2+2*x*ln(3)+x^2))^3+(((
192*x^3-3456*x^2+16896*x-18432)*ln(3)+192*x^4-3456*x^3+16896*x^2-18432*x)*ln(ln(3)^2+2*x*ln(3)+x^2)-1536*x^2+1
8432*x-24576)*ln(ln(ln(3)^2+2*x*ln(3)+x^2))^2+(((-24*x^5+720*x^4-7680*x^3+34560*x^2-61440*x+36864)*ln(3)-24*x^
6+720*x^5-7680*x^4+34560*x^3-61440*x^2+36864*x)*ln(ln(3)^2+2*x*ln(3)+x^2)+192*x^4-4608*x^3+33792*x^2-73728*x+4
9152)*ln(ln(ln(3)^2+2*x*ln(3)+x^2))+((x^7-42*x^6+696*x^5-5760*x^4+24960*x^3-55296*x^2+59392*x-24576)*ln(3)+x^8
-42*x^7+696*x^6-5760*x^5+24960*x^4-55296*x^3+59392*x^2-24576*x)*ln(ln(3)^2+2*x*ln(3)+x^2)-8*x^6+288*x^5-3840*x
^4+23040*x^3-61440*x^2+73728*x-32768)/(800*ln(3)+800*x)/ln(ln(3)^2+2*x*ln(3)+x^2),x)

[Out]

int(((((-512*x+3072)*ln(3)-512*x^2+3072*x)*ln(ln(3)^2+2*x*ln(3)+x^2)+4096)*ln(ln(ln(3)^2+2*x*ln(3)+x^2))^3+(((
192*x^3-3456*x^2+16896*x-18432)*ln(3)+192*x^4-3456*x^3+16896*x^2-18432*x)*ln(ln(3)^2+2*x*ln(3)+x^2)-1536*x^2+1
8432*x-24576)*ln(ln(ln(3)^2+2*x*ln(3)+x^2))^2+(((-24*x^5+720*x^4-7680*x^3+34560*x^2-61440*x+36864)*ln(3)-24*x^
6+720*x^5-7680*x^4+34560*x^3-61440*x^2+36864*x)*ln(ln(3)^2+2*x*ln(3)+x^2)+192*x^4-4608*x^3+33792*x^2-73728*x+4
9152)*ln(ln(ln(3)^2+2*x*ln(3)+x^2))+((x^7-42*x^6+696*x^5-5760*x^4+24960*x^3-55296*x^2+59392*x-24576)*ln(3)+x^8
-42*x^7+696*x^6-5760*x^5+24960*x^4-55296*x^3+59392*x^2-24576*x)*ln(ln(3)^2+2*x*ln(3)+x^2)-8*x^6+288*x^5-3840*x
^4+23040*x^3-61440*x^2+73728*x-32768)/(800*ln(3)+800*x)/ln(ln(3)^2+2*x*ln(3)+x^2),x)

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maxima [B]  time = 0.53, size = 264, normalized size = 9.10 \begin {gather*} \frac {1}{6400} \, x^{8} - \frac {3}{400} \, x^{7} - \frac {1}{200} \, x^{6} {\left (\log \relax (2) - 29\right )} + \frac {9}{50} \, x^{5} {\left (\log \relax (2) - 8\right )} + \frac {3}{50} \, {\left (\log \relax (2)^{2} - 40 \, \log \relax (2) + 130\right )} x^{4} - \frac {36}{25} \, {\left (\log \relax (2)^{2} - 10 \, \log \relax (2) + 16\right )} x^{3} - \frac {8}{25} \, {\left (x^{2} - 12 \, x - 8 \, \log \relax (2) + 16\right )} \log \left (\log \left (x + \log \relax (3)\right )\right )^{3} + \frac {16}{25} \, \log \left (\log \left (x + \log \relax (3)\right )\right )^{4} - \frac {8}{25} \, {\left (\log \relax (2)^{3} - 33 \, \log \relax (2)^{2} + 120 \, \log \relax (2) - 116\right )} x^{2} + \frac {3}{50} \, {\left (x^{4} - 24 \, x^{3} - 16 \, x^{2} {\left (\log \relax (2) - 11\right )} + 192 \, x {\left (\log \relax (2) - 2\right )} + 64 \, \log \relax (2)^{2} - 256 \, \log \relax (2) + 256\right )} \log \left (\log \left (x + \log \relax (3)\right )\right )^{2} + \frac {96}{25} \, {\left (\log \relax (2)^{3} - 6 \, \log \relax (2)^{2} + 12 \, \log \relax (2) - 8\right )} x - \frac {1}{200} \, {\left (x^{6} - 36 \, x^{5} - 24 \, x^{4} {\left (\log \relax (2) - 20\right )} + 576 \, x^{3} {\left (\log \relax (2) - 5\right )} + 192 \, {\left (\log \relax (2)^{2} - 22 \, \log \relax (2) + 40\right )} x^{2} - 512 \, \log \relax (2)^{3} - 2304 \, {\left (\log \relax (2)^{2} - 4 \, \log \relax (2) + 4\right )} x + 3072 \, \log \relax (2)^{2} - 6144 \, \log \relax (2)\right )} \log \left (\log \left (x + \log \relax (3)\right )\right ) - \frac {512}{25} \, \log \left (\log \left (x + \log \relax (3)\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-512*x+3072)*log(3)-512*x^2+3072*x)*log(log(3)^2+2*x*log(3)+x^2)+4096)*log(log(log(3)^2+2*x*log(
3)+x^2))^3+(((192*x^3-3456*x^2+16896*x-18432)*log(3)+192*x^4-3456*x^3+16896*x^2-18432*x)*log(log(3)^2+2*x*log(
3)+x^2)-1536*x^2+18432*x-24576)*log(log(log(3)^2+2*x*log(3)+x^2))^2+(((-24*x^5+720*x^4-7680*x^3+34560*x^2-6144
0*x+36864)*log(3)-24*x^6+720*x^5-7680*x^4+34560*x^3-61440*x^2+36864*x)*log(log(3)^2+2*x*log(3)+x^2)+192*x^4-46
08*x^3+33792*x^2-73728*x+49152)*log(log(log(3)^2+2*x*log(3)+x^2))+((x^7-42*x^6+696*x^5-5760*x^4+24960*x^3-5529
6*x^2+59392*x-24576)*log(3)+x^8-42*x^7+696*x^6-5760*x^5+24960*x^4-55296*x^3+59392*x^2-24576*x)*log(log(3)^2+2*
x*log(3)+x^2)-8*x^6+288*x^5-3840*x^4+23040*x^3-61440*x^2+73728*x-32768)/(800*log(3)+800*x)/log(log(3)^2+2*x*lo
g(3)+x^2),x, algorithm="maxima")

[Out]

1/6400*x^8 - 3/400*x^7 - 1/200*x^6*(log(2) - 29) + 9/50*x^5*(log(2) - 8) + 3/50*(log(2)^2 - 40*log(2) + 130)*x
^4 - 36/25*(log(2)^2 - 10*log(2) + 16)*x^3 - 8/25*(x^2 - 12*x - 8*log(2) + 16)*log(log(x + log(3)))^3 + 16/25*
log(log(x + log(3)))^4 - 8/25*(log(2)^3 - 33*log(2)^2 + 120*log(2) - 116)*x^2 + 3/50*(x^4 - 24*x^3 - 16*x^2*(l
og(2) - 11) + 192*x*(log(2) - 2) + 64*log(2)^2 - 256*log(2) + 256)*log(log(x + log(3)))^2 + 96/25*(log(2)^3 -
6*log(2)^2 + 12*log(2) - 8)*x - 1/200*(x^6 - 36*x^5 - 24*x^4*(log(2) - 20) + 576*x^3*(log(2) - 5) + 192*(log(2
)^2 - 22*log(2) + 40)*x^2 - 512*log(2)^3 - 2304*(log(2)^2 - 4*log(2) + 4)*x + 3072*log(2)^2 - 6144*log(2))*log
(log(x + log(3))) - 512/25*log(log(x + log(3)))

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mupad [B]  time = 4.39, size = 187, normalized size = 6.45 \begin {gather*} \frac {16\,{\ln \left (\ln \left (x^2+2\,\ln \relax (3)\,x+{\ln \relax (3)}^2\right )\right )}^4}{25}-\frac {512\,\ln \left (\ln \left (x^2+2\,\ln \relax (3)\,x+{\ln \relax (3)}^2\right )\right )}{25}-{\ln \left (\ln \left (x^2+2\,\ln \relax (3)\,x+{\ln \relax (3)}^2\right )\right )}^3\,\left (\frac {8\,x^2}{25}-\frac {96\,x}{25}+\frac {128}{25}\right )-\frac {768\,x}{25}+{\ln \left (\ln \left (x^2+2\,\ln \relax (3)\,x+{\ln \relax (3)}^2\right )\right )}^2\,\left (\frac {3\,x^4}{50}-\frac {36\,x^3}{25}+\frac {264\,x^2}{25}-\frac {576\,x}{25}+\frac {384}{25}\right )+\ln \left (\ln \left (x^2+2\,\ln \relax (3)\,x+{\ln \relax (3)}^2\right )\right )\,\left (-\frac {x^6}{200}+\frac {9\,x^5}{50}-\frac {12\,x^4}{5}+\frac {72\,x^3}{5}-\frac {192\,x^2}{5}+\frac {1152\,x}{25}\right )+\frac {928\,x^2}{25}-\frac {576\,x^3}{25}+\frac {39\,x^4}{5}-\frac {36\,x^5}{25}+\frac {29\,x^6}{200}-\frac {3\,x^7}{400}+\frac {x^8}{6400} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(log(2*x*log(3) + log(3)^2 + x^2))*(73728*x + log(2*x*log(3) + log(3)^2 + x^2)*(61440*x^2 - 36864*x -
34560*x^3 + 7680*x^4 - 720*x^5 + 24*x^6 + log(3)*(61440*x - 34560*x^2 + 7680*x^3 - 720*x^4 + 24*x^5 - 36864))
- 33792*x^2 + 4608*x^3 - 192*x^4 - 49152) - log(2*x*log(3) + log(3)^2 + x^2)*(59392*x^2 - 24576*x - 55296*x^3
+ 24960*x^4 - 5760*x^5 + 696*x^6 - 42*x^7 + x^8 + log(3)*(59392*x - 55296*x^2 + 24960*x^3 - 5760*x^4 + 696*x^
5 - 42*x^6 + x^7 - 24576)) - 73728*x - log(log(2*x*log(3) + log(3)^2 + x^2))^2*(18432*x + log(2*x*log(3) + log
(3)^2 + x^2)*(log(3)*(16896*x - 3456*x^2 + 192*x^3 - 18432) - 18432*x + 16896*x^2 - 3456*x^3 + 192*x^4) - 1536
*x^2 - 24576) + log(log(2*x*log(3) + log(3)^2 + x^2))^3*(log(2*x*log(3) + log(3)^2 + x^2)*(log(3)*(512*x - 307
2) - 3072*x + 512*x^2) - 4096) + 61440*x^2 - 23040*x^3 + 3840*x^4 - 288*x^5 + 8*x^6 + 32768)/(log(2*x*log(3) +
log(3)^2 + x^2)*(800*x + 800*log(3))),x)

[Out]

(16*log(log(2*x*log(3) + log(3)^2 + x^2))^4)/25 - (512*log(log(2*x*log(3) + log(3)^2 + x^2)))/25 - log(log(2*x
*log(3) + log(3)^2 + x^2))^3*((8*x^2)/25 - (96*x)/25 + 128/25) - (768*x)/25 + log(log(2*x*log(3) + log(3)^2 +
x^2))^2*((264*x^2)/25 - (576*x)/25 - (36*x^3)/25 + (3*x^4)/50 + 384/25) + log(log(2*x*log(3) + log(3)^2 + x^2)
)*((1152*x)/25 - (192*x^2)/5 + (72*x^3)/5 - (12*x^4)/5 + (9*x^5)/50 - x^6/200) + (928*x^2)/25 - (576*x^3)/25 +
(39*x^4)/5 - (36*x^5)/25 + (29*x^6)/200 - (3*x^7)/400 + x^8/6400

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sympy [B]  time = 1.19, size = 236, normalized size = 8.14 \begin {gather*} \frac {x^{8}}{6400} - \frac {3 x^{7}}{400} + \frac {29 x^{6}}{200} - \frac {36 x^{5}}{25} + \frac {39 x^{4}}{5} - \frac {576 x^{3}}{25} + \frac {928 x^{2}}{25} - \frac {768 x}{25} + \left (- \frac {8 x^{2}}{25} + \frac {96 x}{25} - \frac {128}{25}\right ) \log {\left (\log {\left (x^{2} + 2 x \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )} \right )}^{3} + \left (\frac {3 x^{4}}{50} - \frac {36 x^{3}}{25} + \frac {264 x^{2}}{25} - \frac {576 x}{25} + \frac {384}{25}\right ) \log {\left (\log {\left (x^{2} + 2 x \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )} \right )}^{2} + \left (- \frac {x^{6}}{200} + \frac {9 x^{5}}{50} - \frac {12 x^{4}}{5} + \frac {72 x^{3}}{5} - \frac {192 x^{2}}{5} + \frac {1152 x}{25}\right ) \log {\left (\log {\left (x^{2} + 2 x \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )} \right )} + \frac {16 \log {\left (\log {\left (x^{2} + 2 x \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )} \right )}^{4}}{25} - \frac {512 \log {\left (\log {\left (x^{2} + 2 x \log {\relax (3 )} + \log {\relax (3 )}^{2} \right )} \right )}}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-512*x+3072)*ln(3)-512*x**2+3072*x)*ln(ln(3)**2+2*x*ln(3)+x**2)+4096)*ln(ln(ln(3)**2+2*x*ln(3)+x
**2))**3+(((192*x**3-3456*x**2+16896*x-18432)*ln(3)+192*x**4-3456*x**3+16896*x**2-18432*x)*ln(ln(3)**2+2*x*ln(
3)+x**2)-1536*x**2+18432*x-24576)*ln(ln(ln(3)**2+2*x*ln(3)+x**2))**2+(((-24*x**5+720*x**4-7680*x**3+34560*x**2
-61440*x+36864)*ln(3)-24*x**6+720*x**5-7680*x**4+34560*x**3-61440*x**2+36864*x)*ln(ln(3)**2+2*x*ln(3)+x**2)+19
2*x**4-4608*x**3+33792*x**2-73728*x+49152)*ln(ln(ln(3)**2+2*x*ln(3)+x**2))+((x**7-42*x**6+696*x**5-5760*x**4+2
4960*x**3-55296*x**2+59392*x-24576)*ln(3)+x**8-42*x**7+696*x**6-5760*x**5+24960*x**4-55296*x**3+59392*x**2-245
76*x)*ln(ln(3)**2+2*x*ln(3)+x**2)-8*x**6+288*x**5-3840*x**4+23040*x**3-61440*x**2+73728*x-32768)/(800*ln(3)+80
0*x)/ln(ln(3)**2+2*x*ln(3)+x**2),x)

[Out]

x**8/6400 - 3*x**7/400 + 29*x**6/200 - 36*x**5/25 + 39*x**4/5 - 576*x**3/25 + 928*x**2/25 - 768*x/25 + (-8*x**
2/25 + 96*x/25 - 128/25)*log(log(x**2 + 2*x*log(3) + log(3)**2))**3 + (3*x**4/50 - 36*x**3/25 + 264*x**2/25 -
576*x/25 + 384/25)*log(log(x**2 + 2*x*log(3) + log(3)**2))**2 + (-x**6/200 + 9*x**5/50 - 12*x**4/5 + 72*x**3/5
- 192*x**2/5 + 1152*x/25)*log(log(x**2 + 2*x*log(3) + log(3)**2)) + 16*log(log(x**2 + 2*x*log(3) + log(3)**2)
)**4/25 - 512*log(log(x**2 + 2*x*log(3) + log(3)**2))/25

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