3.92.98 \(\int \frac {-6885-1701 x+1593 x^2-867 x^3-84 x^4+216 x^5+2 x^6+14 x^7+6 x^8+(864 x^2-96 x^3-182 x^4+6 x^5-34 x^6-10 x^7) \log (2)+(18 x^5+4 x^6) \log ^2(2)}{(6777-108 x-2034 x^2+116 x^3-84 x^4-69 x^5+39 x^6+5 x^7+x^8+x^9+(288 x^3+48 x^4-46 x^5-4 x^6-4 x^7-2 x^8) \log (2)+(3 x^6+x^7) \log ^2(2)) \log (\frac {2259-789 x-415 x^2+177 x^3-87 x^4+6 x^5+11 x^6-2 x^7+x^8+(96 x^3-16 x^4-10 x^5+2 x^6-2 x^7) \log (2)+x^6 \log ^2(2)}{9+6 x+x^2})} \, dx\)

Optimal. Leaf size=28 \[ \log \left (\log \left (-5+x+\left ((-4+x)^2+\frac {x^3 (-x+\log (2))}{3+x}\right )^2\right )\right ) \]

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Rubi [F]  time = 18.41, 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 {-6885-1701 x+1593 x^2-867 x^3-84 x^4+216 x^5+2 x^6+14 x^7+6 x^8+\left (864 x^2-96 x^3-182 x^4+6 x^5-34 x^6-10 x^7\right ) \log (2)+\left (18 x^5+4 x^6\right ) \log ^2(2)}{\left (6777-108 x-2034 x^2+116 x^3-84 x^4-69 x^5+39 x^6+5 x^7+x^8+x^9+\left (288 x^3+48 x^4-46 x^5-4 x^6-4 x^7-2 x^8\right ) \log (2)+\left (3 x^6+x^7\right ) \log ^2(2)\right ) \log \left (\frac {2259-789 x-415 x^2+177 x^3-87 x^4+6 x^5+11 x^6-2 x^7+x^8+\left (96 x^3-16 x^4-10 x^5+2 x^6-2 x^7\right ) \log (2)+x^6 \log ^2(2)}{9+6 x+x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-6885 - 1701*x + 1593*x^2 - 867*x^3 - 84*x^4 + 216*x^5 + 2*x^6 + 14*x^7 + 6*x^8 + (864*x^2 - 96*x^3 - 182
*x^4 + 6*x^5 - 34*x^6 - 10*x^7)*Log[2] + (18*x^5 + 4*x^6)*Log[2]^2)/((6777 - 108*x - 2034*x^2 + 116*x^3 - 84*x
^4 - 69*x^5 + 39*x^6 + 5*x^7 + x^8 + x^9 + (288*x^3 + 48*x^4 - 46*x^5 - 4*x^6 - 4*x^7 - 2*x^8)*Log[2] + (3*x^6
+ x^7)*Log[2]^2)*Log[(2259 - 789*x - 415*x^2 + 177*x^3 - 87*x^4 + 6*x^5 + 11*x^6 - 2*x^7 + x^8 + (96*x^3 - 16
*x^4 - 10*x^5 + 2*x^6 - 2*x^7)*Log[2] + x^6*Log[2]^2)/(9 + 6*x + x^2)]),x]

[Out]

-2*Defer[Int][1/((3 + x)*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log[2]) + 3*x^
3*(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x)^2]), x] - (3*(2367 + 48*Log[2] +
263*Log[2]^2 + 765*Log[4])*Defer[Int][1/((2259 - 789*x - 415*x^2 + x^8 + 6*x^5*(1 - (5*Log[2])/3) - 87*x^4*(1
+ (16*Log[2])/87) + 177*x^3*(1 + (32*Log[2])/59) - 2*x^7*(1 + Log[2]) + 11*x^6*(1 + (Log[2]^2 + Log[4])/11))*
Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log[2]) + 3*x^3*(59 + 32*Log[2]) - x^7*
(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x)^2]), x])/(9 + Log[2]^2 + Log[64]) - (2*(3735 + 2688*Log[2
] + 415*Log[2]^2 - 99*Log[4])*Defer[Int][x/((2259 - 789*x - 415*x^2 + x^8 + 6*x^5*(1 - (5*Log[2])/3) - 87*x^4*
(1 + (16*Log[2])/87) + 177*x^3*(1 + (32*Log[2])/59) - 2*x^7*(1 + Log[2]) + 11*x^6*(1 + (Log[2]^2 + Log[4])/11)
)*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log[2]) + 3*x^3*(59 + 32*Log[2]) - x^
7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x)^2]), x])/(9 + Log[2]^2 + Log[64]) + (3*(1593 + 561*Log[
2]^2 + 96*Log[2]^3 + 155*Log[4] + 16*Log[2]*(101 + 6*Log[4]))*Defer[Int][x^2/((2259 - 789*x - 415*x^2 + x^8 +
6*x^5*(1 - (5*Log[2])/3) - 87*x^4*(1 + (16*Log[2])/87) + 177*x^3*(1 + (32*Log[2])/59) - 2*x^7*(1 + Log[2]) + 1
1*x^6*(1 + (Log[2]^2 + Log[4])/11))*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log
[2]) + 3*x^3*(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x)^2]), x])/(9 + Log[2]^
2 + Log[64]) - (4*(783 + 119*Log[2]^2 + 16*Log[2]^3 + 111*Log[4] + 4*Log[2]*(111 + 8*Log[4]))*Defer[Int][x^3/(
(2259 - 789*x - 415*x^2 + x^8 + 6*x^5*(1 - (5*Log[2])/3) - 87*x^4*(1 + (16*Log[2])/87) + 177*x^3*(1 + (32*Log[
2])/59) - 2*x^7*(1 + Log[2]) + 11*x^6*(1 + (Log[2]^2 + Log[4])/11))*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6
- 10*Log[2]) - x^4*(87 + 16*Log[2]) + 3*x^3*(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]
))/(3 + x)^2]), x])/(9 + Log[2]^2 + Log[64]) + (2*(135 - 135*Log[2] - 117*Log[2]^2 - 25*Log[2]^3 - Log[8]*Log[
64])*Defer[Int][x^4/((2259 - 789*x - 415*x^2 + x^8 + 6*x^5*(1 - (5*Log[2])/3) - 87*x^4*(1 + (16*Log[2])/87) +
177*x^3*(1 + (32*Log[2])/59) - 2*x^7*(1 + Log[2]) + 11*x^6*(1 + (Log[2]^2 + Log[4])/11))*Log[(2259 - 789*x - 4
15*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log[2]) + 3*x^3*(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(1
1 + Log[2]^2 + Log[4]))/(3 + x)^2]), x])/(9 + Log[2]^2 + Log[64]) + (2*(297 + 18*Log[2]^3 + 3*Log[2]^4 + 16*Lo
g[4] + 4*Log[2]*(55 + Log[4]) + Log[2]^2*(88 + Log[64]))*Defer[Int][x^5/((2259 - 789*x - 415*x^2 + x^8 + 6*x^5
*(1 - (5*Log[2])/3) - 87*x^4*(1 + (16*Log[2])/87) + 177*x^3*(1 + (32*Log[2])/59) - 2*x^7*(1 + Log[2]) + 11*x^6
*(1 + (Log[2]^2 + Log[4])/11))*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log[2])
+ 3*x^3*(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x)^2]), x])/(9 + Log[2]^2 + L
og[64]) - (2*(63 + 101*Log[2] + 39*Log[2]^2 + 7*Log[2]^3 + Log[16] + Log[4]*Log[32])*Defer[Int][x^6/((2259 - 7
89*x - 415*x^2 + x^8 + 6*x^5*(1 - (5*Log[2])/3) - 87*x^4*(1 + (16*Log[2])/87) + 177*x^3*(1 + (32*Log[2])/59) -
2*x^7*(1 + Log[2]) + 11*x^6*(1 + (Log[2]^2 + Log[4])/11))*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log
[2]) - x^4*(87 + 16*Log[2]) + 3*x^3*(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x
)^2]), x])/(9 + Log[2]^2 + Log[64]) + (24*Log[4]*Defer[Int][x^7/((2259 - 789*x - 415*x^2 + x^8 + 6*x^5*(1 - (5
*Log[2])/3) - 87*x^4*(1 + (16*Log[2])/87) + 177*x^3*(1 + (32*Log[2])/59) - 2*x^7*(1 + Log[2]) + 11*x^6*(1 + (L
og[2]^2 + Log[4])/11))*Log[(2259 - 789*x - 415*x^2 + x^8 + x^5*(6 - 10*Log[2]) - x^4*(87 + 16*Log[2]) + 3*x^3*
(59 + 32*Log[2]) - x^7*(2 + Log[4]) + x^6*(11 + Log[2]^2 + Log[4]))/(3 + x)^2]), x])/Log[64]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-6885-1701 x+1593 x^2-867 x^3-84 x^4+216 x^5+2 x^6+14 x^7+6 x^8+\left (864 x^2-96 x^3-182 x^4+6 x^5-34 x^6-10 x^7\right ) \log (2)+\left (18 x^5+4 x^6\right ) \log ^2(2)}{(3+x) \left (2259-789 x-415 x^2+x^8+6 x^5 \left (1-\frac {5 \log (2)}{3}\right )-87 x^4 \left (1+\frac {16 \log (2)}{87}\right )+177 x^3 \left (1+\frac {32 \log (2)}{59}\right )-2 x^7 (1+\log (2))+11 x^6 \left (1+\frac {1}{11} \left (\log ^2(2)+\log (4)\right )\right )\right ) \log \left (\frac {2259-789 x-415 x^2+177 x^3-87 x^4+6 x^5-2 x^7+x^8+\left (96 x^3-16 x^4-10 x^5+2 x^6-2 x^7\right ) \log (2)+11 x^6 \left (1+\frac {\log ^2(2)}{11}\right )}{9+6 x+x^2}\right )} \, dx\\ &=\int \left (-\frac {2 (3+\log (2))^2}{(3+x) \left (9+\log ^2(2)+\log (64)\right ) \log \left (\frac {2259-789 x-415 x^2+x^8+x^5 (6-10 \log (2))-x^4 (87+16 \log (2))+3 x^3 (59+32 \log (2))-x^7 (2+\log (4))+x^6 \left (11+\log ^2(2)+\log (4)\right )}{(3+x)^2}\right )}+\frac {-7470 x \left (1+\frac {2688 \log (2)+415 \log ^2(2)-99 \log (4)}{3735}\right )-7101 \left (1+\frac {48 \log (2)+263 \log ^2(2)+765 \log (4)}{2367}\right )+4779 x^2 \left (1+\frac {561 \log ^2(2)+96 \log ^3(2)+155 \log (4)+16 \log (2) (101+6 \log (4))}{1593}\right )-3132 x^3 \left (1+\frac {1}{783} \left (119 \log ^2(2)+16 \log ^3(2)+111 \log (4)+4 \log (2) (111+8 \log (4))\right )\right )-126 x^6 \left (1+\frac {1}{63} \left (101 \log (2)+39 \log ^2(2)+7 \log ^3(2)+\log (16)+\log (4) \log (32)\right )\right )+72 x^7 \left (1+\frac {1}{2} \log (2) \left (1+\frac {2 \log (2)}{9}+\frac {\log (4)}{\log (64)}\right )\right )+270 x^4 \left (1-\frac {1}{135} \log (2) \left (117 \log (2)+25 \log ^2(2)+3 (45+\log (64))\right )\right )+594 x^5 \left (1+\frac {20}{27} \log (2) \left (1+\frac {2}{5} \log (2) \left (1+\frac {9}{44} \log (2) \left (1+\frac {\log (2)}{6}+\frac {8 \log (4) \left (1+\frac {1}{4} \log (2) \left (1+\frac {\log (2) \log (64)}{\log (256)}\right )\right )}{9 \log ^3(2)}\right )\right )\right )\right )}{\left (2259-789 x-415 x^2+x^8+6 x^5 \left (1-\frac {5 \log (2)}{3}\right )-87 x^4 \left (1+\frac {16 \log (2)}{87}\right )+177 x^3 \left (1+\frac {32 \log (2)}{59}\right )-2 x^7 (1+\log (2))+11 x^6 \left (1+\frac {1}{11} \left (\log ^2(2)+\log (4)\right )\right )\right ) \left (9+\log ^2(2)+\log (64)\right ) \log \left (\frac {2259-789 x-415 x^2+x^8+x^5 (6-10 \log (2))-x^4 (87+16 \log (2))+3 x^3 (59+32 \log (2))-x^7 (2+\log (4))+x^6 \left (11+\log ^2(2)+\log (4)\right )}{(3+x)^2}\right )}\right ) \, dx\\ &=-\left (2 \int \frac {1}{(3+x) \log \left (\frac {2259-789 x-415 x^2+x^8+x^5 (6-10 \log (2))-x^4 (87+16 \log (2))+3 x^3 (59+32 \log (2))-x^7 (2+\log (4))+x^6 \left (11+\log ^2(2)+\log (4)\right )}{(3+x)^2}\right )} \, dx\right )+\frac {\int \frac {-7470 x \left (1+\frac {2688 \log (2)+415 \log ^2(2)-99 \log (4)}{3735}\right )-7101 \left (1+\frac {48 \log (2)+263 \log ^2(2)+765 \log (4)}{2367}\right )+4779 x^2 \left (1+\frac {561 \log ^2(2)+96 \log ^3(2)+155 \log (4)+16 \log (2) (101+6 \log (4))}{1593}\right )-3132 x^3 \left (1+\frac {1}{783} \left (119 \log ^2(2)+16 \log ^3(2)+111 \log (4)+4 \log (2) (111+8 \log (4))\right )\right )-126 x^6 \left (1+\frac {1}{63} \left (101 \log (2)+39 \log ^2(2)+7 \log ^3(2)+\log (16)+\log (4) \log (32)\right )\right )+72 x^7 \left (1+\frac {1}{2} \log (2) \left (1+\frac {2 \log (2)}{9}+\frac {\log (4)}{\log (64)}\right )\right )+270 x^4 \left (1-\frac {1}{135} \log (2) \left (117 \log (2)+25 \log ^2(2)+3 (45+\log (64))\right )\right )+594 x^5 \left (1+\frac {20}{27} \log (2) \left (1+\frac {2}{5} \log (2) \left (1+\frac {9}{44} \log (2) \left (1+\frac {\log (2)}{6}+\frac {8 \log (4) \left (1+\frac {1}{4} \log (2) \left (1+\frac {\log (2) \log (64)}{\log (256)}\right )\right )}{9 \log ^3(2)}\right )\right )\right )\right )}{\left (2259-789 x-415 x^2+x^8+6 x^5 \left (1-\frac {5 \log (2)}{3}\right )-87 x^4 \left (1+\frac {16 \log (2)}{87}\right )+177 x^3 \left (1+\frac {32 \log (2)}{59}\right )-2 x^7 (1+\log (2))+11 x^6 \left (1+\frac {1}{11} \left (\log ^2(2)+\log (4)\right )\right )\right ) \log \left (\frac {2259-789 x-415 x^2+x^8+x^5 (6-10 \log (2))-x^4 (87+16 \log (2))+3 x^3 (59+32 \log (2))-x^7 (2+\log (4))+x^6 \left (11+\log ^2(2)+\log (4)\right )}{(3+x)^2}\right )} \, dx}{9+\log ^2(2)+\log (64)}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 7.31, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-6885-1701 x+1593 x^2-867 x^3-84 x^4+216 x^5+2 x^6+14 x^7+6 x^8+\left (864 x^2-96 x^3-182 x^4+6 x^5-34 x^6-10 x^7\right ) \log (2)+\left (18 x^5+4 x^6\right ) \log ^2(2)}{\left (6777-108 x-2034 x^2+116 x^3-84 x^4-69 x^5+39 x^6+5 x^7+x^8+x^9+\left (288 x^3+48 x^4-46 x^5-4 x^6-4 x^7-2 x^8\right ) \log (2)+\left (3 x^6+x^7\right ) \log ^2(2)\right ) \log \left (\frac {2259-789 x-415 x^2+177 x^3-87 x^4+6 x^5+11 x^6-2 x^7+x^8+\left (96 x^3-16 x^4-10 x^5+2 x^6-2 x^7\right ) \log (2)+x^6 \log ^2(2)}{9+6 x+x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-6885 - 1701*x + 1593*x^2 - 867*x^3 - 84*x^4 + 216*x^5 + 2*x^6 + 14*x^7 + 6*x^8 + (864*x^2 - 96*x^3
- 182*x^4 + 6*x^5 - 34*x^6 - 10*x^7)*Log[2] + (18*x^5 + 4*x^6)*Log[2]^2)/((6777 - 108*x - 2034*x^2 + 116*x^3
- 84*x^4 - 69*x^5 + 39*x^6 + 5*x^7 + x^8 + x^9 + (288*x^3 + 48*x^4 - 46*x^5 - 4*x^6 - 4*x^7 - 2*x^8)*Log[2] +
(3*x^6 + x^7)*Log[2]^2)*Log[(2259 - 789*x - 415*x^2 + 177*x^3 - 87*x^4 + 6*x^5 + 11*x^6 - 2*x^7 + x^8 + (96*x^
3 - 16*x^4 - 10*x^5 + 2*x^6 - 2*x^7)*Log[2] + x^6*Log[2]^2)/(9 + 6*x + x^2)]),x]

[Out]

Integrate[(-6885 - 1701*x + 1593*x^2 - 867*x^3 - 84*x^4 + 216*x^5 + 2*x^6 + 14*x^7 + 6*x^8 + (864*x^2 - 96*x^3
- 182*x^4 + 6*x^5 - 34*x^6 - 10*x^7)*Log[2] + (18*x^5 + 4*x^6)*Log[2]^2)/((6777 - 108*x - 2034*x^2 + 116*x^3
- 84*x^4 - 69*x^5 + 39*x^6 + 5*x^7 + x^8 + x^9 + (288*x^3 + 48*x^4 - 46*x^5 - 4*x^6 - 4*x^7 - 2*x^8)*Log[2] +
(3*x^6 + x^7)*Log[2]^2)*Log[(2259 - 789*x - 415*x^2 + 177*x^3 - 87*x^4 + 6*x^5 + 11*x^6 - 2*x^7 + x^8 + (96*x^
3 - 16*x^4 - 10*x^5 + 2*x^6 - 2*x^7)*Log[2] + x^6*Log[2]^2)/(9 + 6*x + x^2)]), x]

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fricas [B]  time = 0.63, size = 87, normalized size = 3.11 \begin {gather*} \log \left (\log \left (\frac {x^{8} + x^{6} \log \relax (2)^{2} - 2 \, x^{7} + 11 \, x^{6} + 6 \, x^{5} - 87 \, x^{4} + 177 \, x^{3} - 415 \, x^{2} - 2 \, {\left (x^{7} - x^{6} + 5 \, x^{5} + 8 \, x^{4} - 48 \, x^{3}\right )} \log \relax (2) - 789 \, x + 2259}{x^{2} + 6 \, x + 9}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6+18*x^5)*log(2)^2+(-10*x^7-34*x^6+6*x^5-182*x^4-96*x^3+864*x^2)*log(2)+6*x^8+14*x^7+2*x^6+216
*x^5-84*x^4-867*x^3+1593*x^2-1701*x-6885)/((x^7+3*x^6)*log(2)^2+(-2*x^8-4*x^7-4*x^6-46*x^5+48*x^4+288*x^3)*log
(2)+x^9+x^8+5*x^7+39*x^6-69*x^5-84*x^4+116*x^3-2034*x^2-108*x+6777)/log((x^6*log(2)^2+(-2*x^7+2*x^6-10*x^5-16*
x^4+96*x^3)*log(2)+x^8-2*x^7+11*x^6+6*x^5-87*x^4+177*x^3-415*x^2-789*x+2259)/(x^2+6*x+9)),x, algorithm="fricas
")

[Out]

log(log((x^8 + x^6*log(2)^2 - 2*x^7 + 11*x^6 + 6*x^5 - 87*x^4 + 177*x^3 - 415*x^2 - 2*(x^7 - x^6 + 5*x^5 + 8*x
^4 - 48*x^3)*log(2) - 789*x + 2259)/(x^2 + 6*x + 9)))

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giac [B]  time = 0.26, size = 95, normalized size = 3.39 \begin {gather*} \log \left (-\log \left (x^{8} - 2 \, x^{7} \log \relax (2) + x^{6} \log \relax (2)^{2} - 2 \, x^{7} + 2 \, x^{6} \log \relax (2) + 11 \, x^{6} - 10 \, x^{5} \log \relax (2) + 6 \, x^{5} - 16 \, x^{4} \log \relax (2) - 87 \, x^{4} + 96 \, x^{3} \log \relax (2) + 177 \, x^{3} - 415 \, x^{2} - 789 \, x + 2259\right ) + \log \left (x^{2} + 6 \, x + 9\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6+18*x^5)*log(2)^2+(-10*x^7-34*x^6+6*x^5-182*x^4-96*x^3+864*x^2)*log(2)+6*x^8+14*x^7+2*x^6+216
*x^5-84*x^4-867*x^3+1593*x^2-1701*x-6885)/((x^7+3*x^6)*log(2)^2+(-2*x^8-4*x^7-4*x^6-46*x^5+48*x^4+288*x^3)*log
(2)+x^9+x^8+5*x^7+39*x^6-69*x^5-84*x^4+116*x^3-2034*x^2-108*x+6777)/log((x^6*log(2)^2+(-2*x^7+2*x^6-10*x^5-16*
x^4+96*x^3)*log(2)+x^8-2*x^7+11*x^6+6*x^5-87*x^4+177*x^3-415*x^2-789*x+2259)/(x^2+6*x+9)),x, algorithm="giac")

[Out]

log(-log(x^8 - 2*x^7*log(2) + x^6*log(2)^2 - 2*x^7 + 2*x^6*log(2) + 11*x^6 - 10*x^5*log(2) + 6*x^5 - 16*x^4*lo
g(2) - 87*x^4 + 96*x^3*log(2) + 177*x^3 - 415*x^2 - 789*x + 2259) + log(x^2 + 6*x + 9))

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maple [B]  time = 0.54, size = 89, normalized size = 3.18

method	result	size
norman	\(\ln \left (\ln \left (\frac {x^{6} \ln \relax (2)^{2}+\left (-2 x^{7}+2 x^{6}-10 x^{5}-16 x^{4}+96 x^{3}\right ) \ln \relax (2)+x^{8}-2 x^{7}+11 x^{6}+6 x^{5}-87 x^{4}+177 x^{3}-415 x^{2}-789 x +2259}{x^{2}+6 x +9}\right )\right )\)	\(89\)
risch	\(\ln \left (\ln \left (\frac {x^{6} \ln \relax (2)^{2}+\left (-2 x^{7}+2 x^{6}-10 x^{5}-16 x^{4}+96 x^{3}\right ) \ln \relax (2)+x^{8}-2 x^{7}+11 x^{6}+6 x^{5}-87 x^{4}+177 x^{3}-415 x^{2}-789 x +2259}{x^{2}+6 x +9}\right )\right )\)	\(89\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6+18*x^5)*ln(2)^2+(-10*x^7-34*x^6+6*x^5-182*x^4-96*x^3+864*x^2)*ln(2)+6*x^8+14*x^7+2*x^6+216*x^5-84*
x^4-867*x^3+1593*x^2-1701*x-6885)/((x^7+3*x^6)*ln(2)^2+(-2*x^8-4*x^7-4*x^6-46*x^5+48*x^4+288*x^3)*ln(2)+x^9+x^
8+5*x^7+39*x^6-69*x^5-84*x^4+116*x^3-2034*x^2-108*x+6777)/ln((x^6*ln(2)^2+(-2*x^7+2*x^6-10*x^5-16*x^4+96*x^3)*
ln(2)+x^8-2*x^7+11*x^6+6*x^5-87*x^4+177*x^3-415*x^2-789*x+2259)/(x^2+6*x+9)),x,method=_RETURNVERBOSE)

[Out]

ln(ln((x^6*ln(2)^2+(-2*x^7+2*x^6-10*x^5-16*x^4+96*x^3)*ln(2)+x^8-2*x^7+11*x^6+6*x^5-87*x^4+177*x^3-415*x^2-789
*x+2259)/(x^2+6*x+9)))

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maxima [B]  time = 0.62, size = 78, normalized size = 2.79 \begin {gather*} \log \left (\log \left (x^{8} - 2 \, x^{7} {\left (\log \relax (2) + 1\right )} + {\left (\log \relax (2)^{2} + 2 \, \log \relax (2) + 11\right )} x^{6} - 2 \, x^{5} {\left (5 \, \log \relax (2) - 3\right )} - x^{4} {\left (16 \, \log \relax (2) + 87\right )} + 3 \, x^{3} {\left (32 \, \log \relax (2) + 59\right )} - 415 \, x^{2} - 789 \, x + 2259\right ) - 2 \, \log \left (x + 3\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6+18*x^5)*log(2)^2+(-10*x^7-34*x^6+6*x^5-182*x^4-96*x^3+864*x^2)*log(2)+6*x^8+14*x^7+2*x^6+216
*x^5-84*x^4-867*x^3+1593*x^2-1701*x-6885)/((x^7+3*x^6)*log(2)^2+(-2*x^8-4*x^7-4*x^6-46*x^5+48*x^4+288*x^3)*log
(2)+x^9+x^8+5*x^7+39*x^6-69*x^5-84*x^4+116*x^3-2034*x^2-108*x+6777)/log((x^6*log(2)^2+(-2*x^7+2*x^6-10*x^5-16*
x^4+96*x^3)*log(2)+x^8-2*x^7+11*x^6+6*x^5-87*x^4+177*x^3-415*x^2-789*x+2259)/(x^2+6*x+9)),x, algorithm="maxima
")

[Out]

log(log(x^8 - 2*x^7*(log(2) + 1) + (log(2)^2 + 2*log(2) + 11)*x^6 - 2*x^5*(5*log(2) - 3) - x^4*(16*log(2) + 87
) + 3*x^3*(32*log(2) + 59) - 415*x^2 - 789*x + 2259) - 2*log(x + 3))

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mupad [B]  time = 9.94, size = 89, normalized size = 3.18 \begin {gather*} \ln \left (\ln \left (\frac {x^6\,{\ln \relax (2)}^2-789\,x-\ln \relax (2)\,\left (2\,x^7-2\,x^6+10\,x^5+16\,x^4-96\,x^3\right )-415\,x^2+177\,x^3-87\,x^4+6\,x^5+11\,x^6-2\,x^7+x^8+2259}{x^2+6\,x+9}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1593*x^2 - log(2)*(96*x^3 - 864*x^2 + 182*x^4 - 6*x^5 + 34*x^6 + 10*x^7) - 1701*x - 867*x^3 - 84*x^4 + 21
6*x^5 + 2*x^6 + 14*x^7 + 6*x^8 + log(2)^2*(18*x^5 + 4*x^6) - 6885)/(log((x^6*log(2)^2 - 789*x - log(2)*(16*x^4
- 96*x^3 + 10*x^5 - 2*x^6 + 2*x^7) - 415*x^2 + 177*x^3 - 87*x^4 + 6*x^5 + 11*x^6 - 2*x^7 + x^8 + 2259)/(6*x +
x^2 + 9))*(log(2)^2*(3*x^6 + x^7) - log(2)*(46*x^5 - 48*x^4 - 288*x^3 + 4*x^6 + 4*x^7 + 2*x^8) - 108*x - 2034
*x^2 + 116*x^3 - 84*x^4 - 69*x^5 + 39*x^6 + 5*x^7 + x^8 + x^9 + 6777)),x)

[Out]

log(log((x^6*log(2)^2 - 789*x - log(2)*(16*x^4 - 96*x^3 + 10*x^5 - 2*x^6 + 2*x^7) - 415*x^2 + 177*x^3 - 87*x^4
+ 6*x^5 + 11*x^6 - 2*x^7 + x^8 + 2259)/(6*x + x^2 + 9)))

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sympy [B]  time = 5.00, size = 87, normalized size = 3.11 \begin {gather*} \log {\left (\log {\left (\frac {x^{8} - 2 x^{7} + x^{6} \log {\relax (2 )}^{2} + 11 x^{6} + 6 x^{5} - 87 x^{4} + 177 x^{3} - 415 x^{2} - 789 x + \left (- 2 x^{7} + 2 x^{6} - 10 x^{5} - 16 x^{4} + 96 x^{3}\right ) \log {\relax (2 )} + 2259}{x^{2} + 6 x + 9} \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**6+18*x**5)*ln(2)**2+(-10*x**7-34*x**6+6*x**5-182*x**4-96*x**3+864*x**2)*ln(2)+6*x**8+14*x**7+
2*x**6+216*x**5-84*x**4-867*x**3+1593*x**2-1701*x-6885)/((x**7+3*x**6)*ln(2)**2+(-2*x**8-4*x**7-4*x**6-46*x**5
+48*x**4+288*x**3)*ln(2)+x**9+x**8+5*x**7+39*x**6-69*x**5-84*x**4+116*x**3-2034*x**2-108*x+6777)/ln((x**6*ln(2
)**2+(-2*x**7+2*x**6-10*x**5-16*x**4+96*x**3)*ln(2)+x**8-2*x**7+11*x**6+6*x**5-87*x**4+177*x**3-415*x**2-789*x
+2259)/(x**2+6*x+9)),x)

[Out]

log(log((x**8 - 2*x**7 + x**6*log(2)**2 + 11*x**6 + 6*x**5 - 87*x**4 + 177*x**3 - 415*x**2 - 789*x + (-2*x**7
+ 2*x**6 - 10*x**5 - 16*x**4 + 96*x**3)*log(2) + 2259)/(x**2 + 6*x + 9)))

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