3.96.86 \(\int \frac {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+(128 x-8 x^2+320 x^3-128 x^4+192 x^5) \log (x)+(-75 x^2-64 x^3+16 x^4-72 x^5) \log ^2(x)+(10 x^2+8 x^5) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+(-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7) \log (x)+(25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7) \log ^2(x)} \, dx\)

Optimal. Leaf size=28 \[ \frac {\log (x)}{16-8 x+\frac {5}{x^2+\frac {4}{4-\log (x)}}} \]

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Rubi [F]  time = 59.64, 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 {336-128 x+592 x^2-256 x^3+256 x^4-128 x^5+\left (128 x-8 x^2+320 x^3-128 x^4+192 x^5\right ) \log (x)+\left (-75 x^2-64 x^3+16 x^4-72 x^5\right ) \log ^2(x)+\left (10 x^2+8 x^5\right ) \log ^3(x)}{7056 x-5376 x^2+11776 x^3-9472 x^4+6144 x^5-4096 x^6+1024 x^7+\left (-840 x+320 x^2-3328 x^3+2688 x^4-2560 x^5+2048 x^6-512 x^7\right ) \log (x)+\left (25 x+160 x^3-80 x^4+256 x^5-256 x^6+64 x^7\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(336 - 128*x + 592*x^2 - 256*x^3 + 256*x^4 - 128*x^5 + (128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5)*Log[x
] + (-75*x^2 - 64*x^3 + 16*x^4 - 72*x^5)*Log[x]^2 + (10*x^2 + 8*x^5)*Log[x]^3)/(7056*x - 5376*x^2 + 11776*x^3
- 9472*x^4 + 6144*x^5 - 4096*x^6 + 1024*x^7 + (-840*x + 320*x^2 - 3328*x^3 + 2688*x^4 - 2560*x^5 + 2048*x^6 -
512*x^7)*Log[x] + (25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)*Log[x]^2),x]

[Out]

(45606240*(109*(263 + 3*Sqrt[5865])^(2/3)*(2*(60977 + 789*Sqrt[5865]))^(1/3)*(14959703 + 195219*Sqrt[5865]) -
24*2^(1/3)*(142908320175 + 1866494027*Sqrt[5865]) + (263 + 3*Sqrt[5865])^(1/3)*(471983877914 + 6165236418*Sqrt
[5865])))/((263 + 3*Sqrt[5865])^(1/3)*(512*2^(2/3) - 64*(263 + 3*Sqrt[5865])^(2/3) + 2^(1/3)*(263 + 3*Sqrt[586
5])^(4/3))^2*(512*2^(2/3) + 32*(263 + 3*Sqrt[5865])^(2/3) + 2^(1/3)*(263 + 3*Sqrt[5865])^(4/3))*(96 + 1536*(2/
(263 + 3*Sqrt[5865]))^(2/3) + 2*2^(1/3)*(263 + 3*Sqrt[5865])^(2/3) + 2^(2/3)*(60977 + 789*Sqrt[5865])^(1/3))*(
(263 + 3*Sqrt[5865])^(4/3) + 16*(32*2^(1/3) + (526 + 6*Sqrt[5865])^(2/3)))*(32*2^(1/3) + (526 + 6*Sqrt[5865])^
(2/3) + 4*(263 + 3*Sqrt[5865])^(1/3)*(2 - 3*x))^2) - (34204680*2^(2/3)*(263 + 3*Sqrt[5865])^(4/3)*(5865*(46274
85 + 60977*Sqrt[5865]))^(1/3))/((32 - 2^(1/3)*(263 + 3*Sqrt[5865])^(2/3))*(512*2^(2/3) - 64*(263 + 3*Sqrt[5865
])^(2/3) + 2^(1/3)*(263 + 3*Sqrt[5865])^(4/3))*(96 + 1536*(2/(263 + 3*Sqrt[5865]))^(2/3) + 2*2^(1/3)*(263 + 3*
Sqrt[5865])^(2/3) + 2^(2/3)*(60977 + 789*Sqrt[5865])^(1/3))^2*((263 + 3*Sqrt[5865])^(4/3) + 16*(32*2^(1/3) + (
526 + 6*Sqrt[5865])^(2/3)))*(32*2^(1/3) + (526 + 6*Sqrt[5865])^(2/3) + 4*(263 + 3*Sqrt[5865])^(1/3)*(2 - 3*x))
) + (81*(2/1955)^(2/3)*(3*(17595 + 263*Sqrt[5865]))^(1/3)*(1065475 + ((8*2^(2/3)*(338215 + 8931*Sqrt[5865]) -
(526 + 6*Sqrt[5865])^(1/3)*(1065475 + 20847*Sqrt[5865]))*(2 - 3*x))/(263 + 3*Sqrt[5865])^(2/3)))/(5*(32 - 2^(1
/3)*(263 + 3*Sqrt[5865])^(2/3))*(2^(1/3)*(32/(263 + 3*Sqrt[5865])^(1/3) + (526 + 6*Sqrt[5865])^(1/3)) + 4*(2 -
3*x))^2*(32 - 512*(2/(263 + 3*Sqrt[5865]))^(2/3) - 2^(1/3)*(263 + 3*Sqrt[5865])^(2/3) + (2*2^(2/3)*(16*2^(2/3
) + (263 + 3*Sqrt[5865])^(2/3))*(2 - 3*x))/(263 + 3*Sqrt[5865])^(1/3) - 8*(2 - 3*x)^2)^2) - (9*((5865*(-17595
+ 263*Sqrt[5865]))/2)^(1/3)*(6976*(60977 + 789*Sqrt[5865]) + 8*2^(2/3)*(263 + 3*Sqrt[5865])^(1/3)*(5962301 + 8
4177*Sqrt[5865]) - 2^(1/3)*(263 + 3*Sqrt[5865])^(2/3)*(27408593 + 363573*Sqrt[5865]) + 8*(1744*2^(1/3)*(263 +
3*Sqrt[5865])^(5/3) - 1384*(60977 + 789*Sqrt[5865]) + 109*2^(2/3)*(263 + 3*Sqrt[5865])^(1/3)*(60977 + 789*Sqrt
[5865]))*(2 - 3*x)))/(32*(512*(17595 + 263*Sqrt[5865]) - 32*2^(1/3)*(263 + 3*Sqrt[5865])^(2/3)*(17595 + 263*Sq
rt[5865]) + 2^(2/3)*(263 + 3*Sqrt[5865])^(1/3)*(4627485 + 60977*Sqrt[5865]))*(2^(1/3)*(32/(263 + 3*Sqrt[5865])
^(1/3) + (526 + 6*Sqrt[5865])^(1/3)) + 4*(2 - 3*x))^2*(32 - 512*(2/(263 + 3*Sqrt[5865]))^(2/3) - 2^(1/3)*(263
+ 3*Sqrt[5865])^(2/3) + (2*2^(2/3)*(16*2^(2/3) + (263 + 3*Sqrt[5865])^(2/3))*(2 - 3*x))/(263 + 3*Sqrt[5865])^(
1/3) - 8*(2 - 3*x)^2)) - 151/(15*(5 + 16*x^2 - 8*x^3)^2) + (199*x)/(15*(5 + 16*x^2 - 8*x^3)^2) - (41*x^2)/(12*
(5 + 16*x^2 - 8*x^3)^2) + (32*x^3)/(3*(5 + 16*x^2 - 8*x^3)^2) - (24*x^4)/(5 + 16*x^2 - 8*x^3)^2 + (8*x^5)/(5 +
16*x^2 - 8*x^3)^2 + (364849920*2^(5/6)*Sqrt[3]*(1384*2^(1/3)*(60977 + 789*Sqrt[5865])^(2/3)*(223655274894737
+ 2920418259957*Sqrt[5865]) - 4*2^(2/3)*(263 + 3*Sqrt[5865])^(1/3)*(5646070386772280597 + 73724500782967305*Sq
rt[5865]) - (263 + 3*Sqrt[5865])^(2/3)*(55808*(60977 + 789*Sqrt[5865])^(1/3)*(907785402023 + 11853537315*Sqrt[
5865]) - 15621*(14959703 + 195219*Sqrt[5865])^(1/3)*(907785402023 + 11853537315*Sqrt[5865]) + 6976*(3684640097
+ 48110853*Sqrt[5865])^(1/3)*(907785402023 + 11853537315*Sqrt[5865]) + 128*2^(1/3)*(1720166020015171 + 224619
72209583*Sqrt[5865])) - 218*(16*2^(1/3)*(14959703 + 195219*Sqrt[5865])^(2/3)*(907785402023 + 11853537315*Sqrt[
5865]) + 128*2^(2/3)*(3684640097 + 48110853*Sqrt[5865])^(1/3)*(907785402023 + 11853537315*Sqrt[5865]) + 2^(1/3
)*(3684640097 + 48110853*Sqrt[5865])^(2/3)*(907785402023 + 11853537315*Sqrt[5865]) - 8*2^(2/3)*(14959703 + 195
219*Sqrt[5865])^(1/3)*(223655274894737 + 2920418259957*Sqrt[5865]) - 80*(55103048290629623 + 719517913526451*S
qrt[5865])))*ArcTan[(32*2^(1/3) + (526 + 6*Sqrt[5865])^(2/3) - 8*(263 + 3*Sqrt[5865])^(1/3)*(2 - 3*x))/Sqrt[6*
(512*2^(2/3) - 64*(263 + 3*Sqrt[5865])^(2/3) + 2^(1/3)*(263 + 3*Sqrt[5865])^(4/3))]])/((263 + 3*Sqrt[5865])^3*
(512*2^(2/3) - 64*(263 + 3*Sqrt[5865])^(2/3) + 2^(1/3)*(263 + 3*Sqrt[5865])^(4/3))^(5/2)*(96 + 1536*(2/(263 +
3*Sqrt[5865]))^(2/3) + 2*2^(1/3)*(263 + 3*Sqrt[5865])^(2/3) + 2^(2/3)*(60977 + 789*Sqrt[5865])^(1/3))^3*((263
+ 3*Sqrt[5865])^(4/3) + 16*(32*2^(1/3) + (526 + 6*Sqrt[5865])^(2/3)))^2) + (124416*(35190*2^(1/3)*(263 + 3*Sqr
t[5865])^(2/3)*(17128253094647805 + 223655274894737*Sqrt[5865]) - 872*2^(2/3)*(3684640097 + 48110853*Sqrt[5865
])^(1/3)*(17128253094647805 + 223655274894737*Sqrt[5865]) + 17595*(4219972562832635115 + 55103048290629623*Sqr
t[5865]) + 16*2^(2/3)*(263 + 3*Sqrt[5865])^(1/3)*(380674311274542678255 + 4970723412725763211*Sqrt[5865]))*Log
[32*2^(1/3) + (526 + 6*Sqrt[5865])^(2/3) + 4*(263 + 3*Sqrt[5865])^(1/3)*(2 - 3*x)])/((263 + 3*Sqrt[5865])^5*(3
2 - 2^(1/3)*(263 + 3*Sqrt[5865])^(2/3))*(512*2^(2/3) - 64*(263 + 3*Sqrt[5865])^(2/3) + 2^(1/3)*(263 + 3*Sqrt[5
865])^(4/3))*(96 + 1536*(2/(263 + 3*Sqrt[5865]))^(2/3) + 2*2^(1/3)*(263 + 3*Sqrt[5865])^(2/3) + 2^(2/3)*(60977
+ 789*Sqrt[5865])^(1/3))^3*((263 + 3*Sqrt[5865])^(4/3) + 16*(32*2^(1/3) + (526 + 6*Sqrt[5865])^(2/3)))) - (62
208*Sqrt[5865]*(563040*(55103048290629623 + 719517913526451*Sqrt[5865]) + 42476*2^(2/3)*(263 + 3*Sqrt[5865])^(
1/3)*(55103048290629623 + 719517913526451*Sqrt[5865]) + (263 + 3*Sqrt[5865])^(2/3)*(27904*(60977 + 789*Sqrt[58
65])^(1/3)*(223655274894737 + 2920418259957*Sqrt[5865]) + 109*(14959703 + 195219*Sqrt[5865])^(1/3)*(5510304829
0629623 + 719517913526451*Sqrt[5865]) - 64*2^(1/3)*(7972608156613239467 + 104103761258615991*Sqrt[5865])))*Log
[2^(1/3)*(45 + Sqrt[5865])*(4*2^(1/3) - (263 + 3*Sqrt[5865])^(1/3)) - 526*2^(2/3)*x - 6*2^(2/3)*Sqrt[5865]*x +
32*(263 + 3*Sqrt[5865])^(2/3)*x - 64*(2*(263 + 3*Sqrt[5865]))^(1/3)*x - 24*(263 + 3*Sqrt[5865])^(2/3)*x^2])/(
(263 + 3*Sqrt[5865])^(17/3)*(32 - 2^(1/3)*(263 + 3*Sqrt[5865])^(2/3))*(512*2^(2/3) - 64*(263 + 3*Sqrt[5865])^(
2/3) + 2^(1/3)*(263 + 3*Sqrt[5865])^(4/3))*(512*2^(2/3) + 32*(263 + 3*Sqrt[5865])^(2/3) + 2^(1/3)*(263 + 3*Sqr
t[5865])^(4/3))*(96 + 1536*(2/(263 + 3*Sqrt[5865]))^(2/3) + 2*2^(1/3)*(263 + 3*Sqrt[5865])^(2/3) + 2^(2/3)*(60
977 + 789*Sqrt[5865])^(1/3))^3) + 10*Defer[Int][Log[x]/(-5 - 16*x^2 + 8*x^3)^2, x] + 15*Defer[Int][(x*Log[x])/
(-5 - 16*x^2 + 8*x^3)^2, x] + 32*Defer[Int][(x^2*Log[x])/(-5 - 16*x^2 + 8*x^3)^2, x] + 2*Defer[Int][Log[x]/(-5
- 16*x^2 + 8*x^3), x] + Defer[Int][(x*Log[x])/(-5 - 16*x^2 + 8*x^3), x] + 336*Defer[Int][1/(x*(84 - 32*x + 64
*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] - 1024000*Defer[Int][1/((-5 - 16*x^2 + 8*x^3)^
3*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] - 2314240*Defer[Int][x/((-5 -
16*x^2 + 8*x^3)^3*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] + 1310720*De
fer[Int][x^2/((-5 - 16*x^2 + 8*x^3)^3*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^
2), x] - 125440*Defer[Int][1/((-5 - 16*x^2 + 8*x^3)^2*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x]
+ 8*x^3*Log[x])^2), x] + 204800*Defer[Int][x/((-5 - 16*x^2 + 8*x^3)^2*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x]
- 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] - 81920*Defer[Int][x^2/((-5 - 16*x^2 + 8*x^3)^2*(84 - 32*x + 64*x^2 - 3
2*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] + 5760*Defer[Int][1/((-5 - 16*x^2 + 8*x^3)*(84 - 32*x
+ 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] + 4096*Defer[Int][x/((-5 - 16*x^2 + 8*x^3)
*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] - 2048*Defer[Int][x^2/((-5 - 1
6*x^2 + 8*x^3)*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])^2), x] + 28800*Defer[In
t][1/((-5 - 16*x^2 + 8*x^3)^3*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])), x] + 1
22880*Defer[Int][x/((-5 - 16*x^2 + 8*x^3)^3*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Lo
g[x])), x] - 61440*Defer[Int][x^2/((-5 - 16*x^2 + 8*x^3)^3*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Lo
g[x] + 8*x^3*Log[x])), x] + 5120*Defer[Int][1/((-5 - 16*x^2 + 8*x^3)^2*(84 - 32*x + 64*x^2 - 32*x^3 - 5*Log[x]
- 16*x^2*Log[x] + 8*x^3*Log[x])), x] - 5120*Defer[Int][x/((-5 - 16*x^2 + 8*x^3)^2*(84 - 32*x + 64*x^2 - 32*x^
3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])), x] + 3840*Defer[Int][x^2/((-5 - 16*x^2 + 8*x^3)^2*(84 - 32*x +
64*x^2 - 32*x^3 - 5*Log[x] - 16*x^2*Log[x] + 8*x^3*Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16 \left (-21+8 x-37 x^2+16 x^3-16 x^4+8 x^5\right )+8 x \left (16-x+40 x^2-16 x^3+24 x^4\right ) \log (x)-x^2 \left (75+64 x-16 x^2+72 x^3\right ) \log ^2(x)+2 x^2 \left (5+4 x^3\right ) \log ^3(x)}{x \left (84-32 x+64 x^2-32 x^3+\left (-5-16 x^2+8 x^3\right ) \log (x)\right )^2} \, dx\\ &=\int \left (-\frac {x \left (1305-960 x+160 x^2-80 x^3+256 x^4-256 x^5+64 x^6\right )}{\left (-5-16 x^2+8 x^3\right )^3}+\frac {2 x \left (5+4 x^3\right ) \log (x)}{\left (-5-16 x^2+8 x^3\right )^2}+\frac {80 \left (-525-3160 x-45488 x^2+59992 x^3-67200 x^4+63232 x^5-32704 x^6+10752 x^7-3072 x^8+512 x^9\right )}{x \left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {640 \left (5+232 x-254 x^2+192 x^3-160 x^4+48 x^5\right )}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}\right ) \, dx\\ &=2 \int \frac {x \left (5+4 x^3\right ) \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+80 \int \frac {-525-3160 x-45488 x^2+59992 x^3-67200 x^4+63232 x^5-32704 x^6+10752 x^7-3072 x^8+512 x^9}{x \left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+640 \int \frac {5+232 x-254 x^2+192 x^3-160 x^4+48 x^5}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-\int \frac {x \left (1305-960 x+160 x^2-80 x^3+256 x^4-256 x^5+64 x^6\right )}{\left (-5-16 x^2+8 x^3\right )^3} \, dx\\ &=\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}+\frac {1}{8} \int \frac {-10440 x+7680 x^2-1280 x^3+2240 x^4-2048 x^5+3072 x^6}{\left (-5-16 x^2+8 x^3\right )^3} \, dx+2 \int \left (\frac {\left (10+15 x+32 x^2\right ) \log (x)}{2 \left (-5-16 x^2+8 x^3\right )^2}+\frac {(2+x) \log (x)}{2 \left (-5-16 x^2+8 x^3\right )}\right ) \, dx+80 \int \left (\frac {21}{5 x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}+\frac {256 \left (-50-113 x+64 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {32 \left (49-80 x+32 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}-\frac {8 \left (-45-32 x+16 x^2\right )}{5 \left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2}\right ) \, dx+640 \int \left (-\frac {3 \left (-15-64 x+32 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}+\frac {2 \left (4-4 x+3 x^2\right )}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )}\right ) \, dx\\ &=-\frac {24 x^4}{\left (5+16 x^2-8 x^3\right )^2}+\frac {8 x^5}{\left (5+16 x^2-8 x^3\right )^2}-\frac {1}{128} \int \frac {167040 x-122880 x^2+81920 x^3-35840 x^4+32768 x^5}{\left (-5-16 x^2+8 x^3\right )^3} \, dx-128 \int \frac {-45-32 x+16 x^2}{\left (-5-16 x^2+8 x^3\right ) \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+336 \int \frac {1}{x \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+1280 \int \frac {4-4 x+3 x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-1920 \int \frac {-15-64 x+32 x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )} \, dx-2560 \int \frac {49-80 x+32 x^2}{\left (-5-16 x^2+8 x^3\right )^2 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+20480 \int \frac {-50-113 x+64 x^2}{\left (-5-16 x^2+8 x^3\right )^3 \left (84-32 x+64 x^2-32 x^3-5 \log (x)-16 x^2 \log (x)+8 x^3 \log (x)\right )^2} \, dx+\int \frac {\left (10+15 x+32 x^2\right ) \log (x)}{\left (-5-16 x^2+8 x^3\right )^2} \, dx+\int \frac {(2+x) \log (x)}{-5-16 x^2+8 x^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 49, normalized size = 1.75 \begin {gather*} \frac {\log (x) \left (4+4 x^2-x^2 \log (x)\right )}{84-32 x+64 x^2-32 x^3+\left (-5-16 x^2+8 x^3\right ) \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(336 - 128*x + 592*x^2 - 256*x^3 + 256*x^4 - 128*x^5 + (128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5)
*Log[x] + (-75*x^2 - 64*x^3 + 16*x^4 - 72*x^5)*Log[x]^2 + (10*x^2 + 8*x^5)*Log[x]^3)/(7056*x - 5376*x^2 + 1177
6*x^3 - 9472*x^4 + 6144*x^5 - 4096*x^6 + 1024*x^7 + (-840*x + 320*x^2 - 3328*x^3 + 2688*x^4 - 2560*x^5 + 2048*
x^6 - 512*x^7)*Log[x] + (25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)*Log[x]^2),x]

[Out]

(Log[x]*(4 + 4*x^2 - x^2*Log[x]))/(84 - 32*x + 64*x^2 - 32*x^3 + (-5 - 16*x^2 + 8*x^3)*Log[x])

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fricas [A]  time = 0.53, size = 52, normalized size = 1.86 \begin {gather*} \frac {x^{2} \log \relax (x)^{2} - 4 \, {\left (x^{2} + 1\right )} \log \relax (x)}{32 \, x^{3} - 64 \, x^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - 5\right )} \log \relax (x) + 32 \, x - 84} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^5+10*x^2)*log(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*log(x)^2+(192*x^5-128*x^4+320*x^3-8*x^2+128*
x)*log(x)-128*x^5+256*x^4-256*x^3+592*x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*log(x)^2+(-
512*x^7+2048*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*log(x)+1024*x^7-4096*x^6+6144*x^5-9472*x^4+11776*x^
3-5376*x^2+7056*x),x, algorithm="fricas")

[Out]

(x^2*log(x)^2 - 4*(x^2 + 1)*log(x))/(32*x^3 - 64*x^2 - (8*x^3 - 16*x^2 - 5)*log(x) + 32*x - 84)

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giac [B]  time = 0.18, size = 177, normalized size = 6.32 \begin {gather*} -\frac {x^{2} \log \relax (x)}{8 \, x^{3} - 16 \, x^{2} - 5} - \frac {80 \, {\left (8 \, x^{3} - 16 \, x^{2} + 8 \, x - 21\right )}}{512 \, x^{9} \log \relax (x) - 2048 \, x^{9} - 3072 \, x^{8} \log \relax (x) + 12288 \, x^{8} + 6144 \, x^{7} \log \relax (x) - 26624 \, x^{7} - 5056 \, x^{6} \log \relax (x) + 32512 \, x^{6} + 3840 \, x^{5} \log \relax (x) - 39936 \, x^{5} - 3840 \, x^{4} \log \relax (x) + 34304 \, x^{4} + 600 \, x^{3} \log \relax (x) - 12640 \, x^{3} - 1200 \, x^{2} \log \relax (x) + 15040 \, x^{2} - 800 \, x - 125 \, \log \relax (x) + 2100} - \frac {20}{64 \, x^{6} - 256 \, x^{5} + 256 \, x^{4} - 80 \, x^{3} + 160 \, x^{2} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^5+10*x^2)*log(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*log(x)^2+(192*x^5-128*x^4+320*x^3-8*x^2+128*
x)*log(x)-128*x^5+256*x^4-256*x^3+592*x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*log(x)^2+(-
512*x^7+2048*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*log(x)+1024*x^7-4096*x^6+6144*x^5-9472*x^4+11776*x^
3-5376*x^2+7056*x),x, algorithm="giac")

[Out]

-x^2*log(x)/(8*x^3 - 16*x^2 - 5) - 80*(8*x^3 - 16*x^2 + 8*x - 21)/(512*x^9*log(x) - 2048*x^9 - 3072*x^8*log(x)
+ 12288*x^8 + 6144*x^7*log(x) - 26624*x^7 - 5056*x^6*log(x) + 32512*x^6 + 3840*x^5*log(x) - 39936*x^5 - 3840*
x^4*log(x) + 34304*x^4 + 600*x^3*log(x) - 12640*x^3 - 1200*x^2*log(x) + 15040*x^2 - 800*x - 125*log(x) + 2100)
- 20/(64*x^6 - 256*x^5 + 256*x^4 - 80*x^3 + 160*x^2 + 25)

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maple [B]  time = 0.05, size = 135, normalized size = 4.82

method	result	size
risch	\(-\frac {x^{2} \ln \relax (x )}{8 x^{3}-16 x^{2}-5}-\frac {20}{64 x^{6}-256 x^{5}+256 x^{4}-80 x^{3}+160 x^{2}+25}-\frac {80 \left (8 x^{3}-16 x^{2}+8 x -21\right )}{\left (64 x^{6}-256 x^{5}+256 x^{4}-80 x^{3}+160 x^{2}+25\right ) \left (8 x^{3} \ln \relax (x )-16 x^{2} \ln \relax (x )-32 x^{3}+64 x^{2}-5 \ln \relax (x )-32 x +84\right )}\)	\(135\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((8*x^5+10*x^2)*ln(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*ln(x)^2+(192*x^5-128*x^4+320*x^3-8*x^2+128*x)*ln(x)
-128*x^5+256*x^4-256*x^3+592*x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*ln(x)^2+(-512*x^7+20
48*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*ln(x)+1024*x^7-4096*x^6+6144*x^5-9472*x^4+11776*x^3-5376*x^2+
7056*x),x,method=_RETURNVERBOSE)

[Out]

-x^2/(8*x^3-16*x^2-5)*ln(x)-20/(64*x^6-256*x^5+256*x^4-80*x^3+160*x^2+25)-80*(8*x^3-16*x^2+8*x-21)/(64*x^6-256
*x^5+256*x^4-80*x^3+160*x^2+25)/(8*x^3*ln(x)-16*x^2*ln(x)-32*x^3+64*x^2-5*ln(x)-32*x+84)

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maxima [A]  time = 0.40, size = 52, normalized size = 1.86 \begin {gather*} \frac {x^{2} \log \relax (x)^{2} - 4 \, {\left (x^{2} + 1\right )} \log \relax (x)}{32 \, x^{3} - 64 \, x^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - 5\right )} \log \relax (x) + 32 \, x - 84} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^5+10*x^2)*log(x)^3+(-72*x^5+16*x^4-64*x^3-75*x^2)*log(x)^2+(192*x^5-128*x^4+320*x^3-8*x^2+128*
x)*log(x)-128*x^5+256*x^4-256*x^3+592*x^2-128*x+336)/((64*x^7-256*x^6+256*x^5-80*x^4+160*x^3+25*x)*log(x)^2+(-
512*x^7+2048*x^6-2560*x^5+2688*x^4-3328*x^3+320*x^2-840*x)*log(x)+1024*x^7-4096*x^6+6144*x^5-9472*x^4+11776*x^
3-5376*x^2+7056*x),x, algorithm="maxima")

[Out]

(x^2*log(x)^2 - 4*(x^2 + 1)*log(x))/(32*x^3 - 64*x^2 - (8*x^3 - 16*x^2 - 5)*log(x) + 32*x - 84)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \relax (x)\,\left (192\,x^5-128\,x^4+320\,x^3-8\,x^2+128\,x\right )-128\,x+{\ln \relax (x)}^3\,\left (8\,x^5+10\,x^2\right )+592\,x^2-256\,x^3+256\,x^4-128\,x^5-{\ln \relax (x)}^2\,\left (72\,x^5-16\,x^4+64\,x^3+75\,x^2\right )+336}{7056\,x-\ln \relax (x)\,\left (512\,x^7-2048\,x^6+2560\,x^5-2688\,x^4+3328\,x^3-320\,x^2+840\,x\right )-5376\,x^2+11776\,x^3-9472\,x^4+6144\,x^5-4096\,x^6+1024\,x^7+{\ln \relax (x)}^2\,\left (64\,x^7-256\,x^6+256\,x^5-80\,x^4+160\,x^3+25\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5) - 128*x + log(x)^3*(10*x^2 + 8*x^5) + 592*x^2 - 256*
x^3 + 256*x^4 - 128*x^5 - log(x)^2*(75*x^2 + 64*x^3 - 16*x^4 + 72*x^5) + 336)/(7056*x - log(x)*(840*x - 320*x^
2 + 3328*x^3 - 2688*x^4 + 2560*x^5 - 2048*x^6 + 512*x^7) - 5376*x^2 + 11776*x^3 - 9472*x^4 + 6144*x^5 - 4096*x
^6 + 1024*x^7 + log(x)^2*(25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)),x)

[Out]

int((log(x)*(128*x - 8*x^2 + 320*x^3 - 128*x^4 + 192*x^5) - 128*x + log(x)^3*(10*x^2 + 8*x^5) + 592*x^2 - 256*
x^3 + 256*x^4 - 128*x^5 - log(x)^2*(75*x^2 + 64*x^3 - 16*x^4 + 72*x^5) + 336)/(7056*x - log(x)*(840*x - 320*x^
2 + 3328*x^3 - 2688*x^4 + 2560*x^5 - 2048*x^6 + 512*x^7) - 5376*x^2 + 11776*x^3 - 9472*x^4 + 6144*x^5 - 4096*x
^6 + 1024*x^7 + log(x)^2*(25*x + 160*x^3 - 80*x^4 + 256*x^5 - 256*x^6 + 64*x^7)), x)

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sympy [B]  time = 0.68, size = 153, normalized size = 5.46 \begin {gather*} - \frac {x^{2} \log {\relax (x )}}{8 x^{3} - 16 x^{2} - 5} + \frac {- 640 x^{3} + 1280 x^{2} - 640 x + 1680}{- 2048 x^{9} + 12288 x^{8} - 26624 x^{7} + 32512 x^{6} - 39936 x^{5} + 34304 x^{4} - 12640 x^{3} + 15040 x^{2} - 800 x + \left (512 x^{9} - 3072 x^{8} + 6144 x^{7} - 5056 x^{6} + 3840 x^{5} - 3840 x^{4} + 600 x^{3} - 1200 x^{2} - 125\right ) \log {\relax (x )} + 2100} - \frac {20}{64 x^{6} - 256 x^{5} + 256 x^{4} - 80 x^{3} + 160 x^{2} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x**5+10*x**2)*ln(x)**3+(-72*x**5+16*x**4-64*x**3-75*x**2)*ln(x)**2+(192*x**5-128*x**4+320*x**3-8
*x**2+128*x)*ln(x)-128*x**5+256*x**4-256*x**3+592*x**2-128*x+336)/((64*x**7-256*x**6+256*x**5-80*x**4+160*x**3
+25*x)*ln(x)**2+(-512*x**7+2048*x**6-2560*x**5+2688*x**4-3328*x**3+320*x**2-840*x)*ln(x)+1024*x**7-4096*x**6+6
144*x**5-9472*x**4+11776*x**3-5376*x**2+7056*x),x)

[Out]

-x**2*log(x)/(8*x**3 - 16*x**2 - 5) + (-640*x**3 + 1280*x**2 - 640*x + 1680)/(-2048*x**9 + 12288*x**8 - 26624*
x**7 + 32512*x**6 - 39936*x**5 + 34304*x**4 - 12640*x**3 + 15040*x**2 - 800*x + (512*x**9 - 3072*x**8 + 6144*x
**7 - 5056*x**6 + 3840*x**5 - 3840*x**4 + 600*x**3 - 1200*x**2 - 125)*log(x) + 2100) - 20/(64*x**6 - 256*x**5
+ 256*x**4 - 80*x**3 + 160*x**2 + 25)

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