∫ 72+(72−6x−384x3+192x4−24x5) log(x)+(−6x+384x3−384x4+72x5) log2(x)+(−64x4+48x5−4104x6+5120x7−2304x8+448x9−32x10) log3(x)___ −27+(432x3−216x4+27x5) log(x)+(−2304x6+2304x7−864x8+144x9−9x10) log2(x)+(4096x9−6144x10+3840x11−1280x12+240x13−24x14+x15) log3(x) dx

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

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Rubi [F] time = 5.75, 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+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx \end {gather*}

Int[(72 + (72 - 6*x - 384*x^3 + 192*x^4 - 24*x^5)*Log[x] + (-6*x + 384*x^3 - 384*x^4 + 72*x^5)*Log[x]^2 + (-64

*x^4 + 48*x^5 - 4104*x^6 + 5120*x^7 - 2304*x^8 + 448*x^9 - 32*x^10)*Log[x]^3)/(-27 + (432*x^3 - 216*x^4 + 27*x

^5)*Log[x] + (-2304*x^6 + 2304*x^7 - 864*x^8 + 144*x^9 - 9*x^10)*Log[x]^2 + (4096*x^9 - 6144*x^10 + 3840*x^11

1/(256*(4 - x)^4) + 1/(256*(4 - x)^3) + 1029/(2048*(4 - x)^2) + 1029/(4096*(4 - x)) + 1/(256*x^4) + 1/(256*x^3

) + 1029/(2048*x^2) + 1029/(4096*x) - 24*Defer[Int][(3 - (-4 + x)^2*x^3*Log[x])^(-2), x] - (27*Defer[Int][1/((

-4 + x)^5*(3 - (-4 + x)^2*x^3*Log[x])^2), x])/64 - (4653*Defer[Int][1/((-4 + x)^3*(3 - (-4 + x)^2*x^3*Log[x])^

2), x])/512 + (17211*Defer[Int][1/((-4 + x)*(3 - (-4 + x)^2*x^3*Log[x])^2), x])/16384 - (9*Defer[Int][1/(x^5*(

3 - (-4 + x)^2*x^3*Log[x])^2), x])/16 - (117*Defer[Int][1/(x^4*(3 - (-4 + x)^2*x^3*Log[x])^2), x])/256 - (1404

9*Defer[Int][1/(x^3*(3 - (-4 + x)^2*x^3*Log[x])^2), x])/1024 - (20283*Defer[Int][1/(x^2*(3 - (-4 + x)^2*x^3*Lo

g[x])^2), x])/4096 - (17211*Defer[Int][1/(x*(3 - (-4 + x)^2*x^3*Log[x])^2), x])/16384 - (81*Defer[Int][1/(x^5*

(-3 + (-4 + x)^2*x^3*Log[x])^3), x])/128 - (135*Defer[Int][1/(x^4*(-3 + (-4 + x)^2*x^3*Log[x])^3), x])/256 - (

135*Defer[Int][1/(x^3*(-3 + (-4 + x)^2*x^3*Log[x])^3), x])/512 - (5013*Defer[Int][1/(x^2*(-3 + (-4 + x)^2*x^3*

Log[x])^3), x])/4096 - (19377*Defer[Int][1/(x*(-3 + (-4 + x)^2*x^3*Log[x])^3), x])/32768 - (21*Defer[Int][1/(x

^5*(-3 + (-4 + x)^2*x^3*Log[x])), x])/128 - (33*Defer[Int][1/(x^4*(-3 + (-4 + x)^2*x^3*Log[x])), x])/256 - (19

35*Defer[Int][1/(x^3*(-3 + (-4 + x)^2*x^3*Log[x])), x])/256 - (9291*Defer[Int][1/(x^2*(-3 + (-4 + x)^2*x^3*Log

[x])), x])/4096 - (9321*Defer[Int][1/(x*(-3 + (-4 + x)^2*x^3*Log[x])), x])/32768 - (27*Defer[Int][1/((-4 + x)^

5*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])^3), x])/64 + (135*Defer[Int][1/((-4 + x)^4*(-3 + 16*x^3*Log

[x] - 8*x^4*Log[x] + x^5*Log[x])^3), x])/512 - (135*Defer[Int][1/((-4 + x)^3*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x

] + x^5*Log[x])^3), x])/2048 - (9351*Defer[Int][1/((-4 + x)^2*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])

^3), x])/8192 + (19377*Defer[Int][1/((-4 + x)*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])^3), x])/32768 +

(9*Defer[Int][1/((-4 + x)^4*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])^2), x])/32 + (3*Defer[Int][1/((-

4 + x)^2*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])^2), x])/4 - (9*Defer[Int][1/((-4 + x)^5*(-3 + 16*x^3

*Log[x] - 8*x^4*Log[x] + x^5*Log[x])), x])/64 + (51*Defer[Int][1/((-4 + x)^4*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x

] + x^5*Log[x])), x])/512 - (12363*Defer[Int][1/((-4 + x)^3*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])),

x])/2048 + (9261*Defer[Int][1/((-4 + x)^2*(-3 + 16*x^3*Log[x] - 8*x^4*Log[x] + x^5*Log[x])), x])/8192 + (9321

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-72+6 \left (-12+x+64 x^3-32 x^4+4 x^5\right ) \log (x)-6 x \left (-1+64 x^2-64 x^3+12 x^4\right ) \log ^2(x)+8 x^4 \left (8-6 x+513 x^2-640 x^3+288 x^4-56 x^5+4 x^6\right ) \log ^3(x)}{\left (3-(-4+x)^2 x^3 \log (x)\right )^3} \, dx\\ &=\int \left (-\frac {8 \left (-2+x-128 x^2+128 x^3-40 x^4+4 x^5\right )}{(-4+x)^5 x^5}-\frac {18 \left (-36+15 x-64 x^3+48 x^4-12 x^5+x^6\right )}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}-\frac {6 \left (-96+42 x-2304 x^2+2048 x^3-576 x^4-4048 x^5+5121 x^6-2560 x^7+640 x^8-80 x^9+4 x^{10}\right )}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}-\frac {6 \left (-28+13 x-1280 x^2+1216 x^3-368 x^4+36 x^5\right )}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}\right ) \, dx\\ &=-\left (6 \int \frac {-96+42 x-2304 x^2+2048 x^3-576 x^4-4048 x^5+5121 x^6-2560 x^7+640 x^8-80 x^9+4 x^{10}}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2} \, dx\right )-6 \int \frac {-28+13 x-1280 x^2+1216 x^3-368 x^4+36 x^5}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )} \, dx-8 \int \frac {-2+x-128 x^2+128 x^3-40 x^4+4 x^5}{(-4+x)^5 x^5} \, dx-18 \int \frac {-36+15 x-64 x^3+48 x^4-12 x^5+x^6}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A] time = 0.08, size = 41, normalized size = 1.46 \begin {gather*} \frac {x \log (x) \left (-24+\left (x+128 x^3-64 x^4+8 x^5\right ) \log (x)\right )}{\left (-3+(-4+x)^2 x^3 \log (x)\right )^2} \end {gather*}

Integrate[(72 + (72 - 6*x - 384*x^3 + 192*x^4 - 24*x^5)*Log[x] + (-6*x + 384*x^3 - 384*x^4 + 72*x^5)*Log[x]^2

+ (-64*x^4 + 48*x^5 - 4104*x^6 + 5120*x^7 - 2304*x^8 + 448*x^9 - 32*x^10)*Log[x]^3)/(-27 + (432*x^3 - 216*x^4

+ 27*x^5)*Log[x] + (-2304*x^6 + 2304*x^7 - 864*x^8 + 144*x^9 - 9*x^10)*Log[x]^2 + (4096*x^9 - 6144*x^10 + 3840

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fricas [B] time = 0.69, size = 82, normalized size = 2.93 \begin {gather*} \frac {{\left (8 \, x^{6} - 64 \, x^{5} + 128 \, x^{4} + x^{2}\right )} \log \relax (x)^{2} - 24 \, x \log \relax (x)}{{\left (x^{10} - 16 \, x^{9} + 96 \, x^{8} - 256 \, x^{7} + 256 \, x^{6}\right )} \log \relax (x)^{2} - 6 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \relax (x) + 9} \end {gather*}

integrate(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*log(x)^3+(72*x^5-384*x^4+384*x^3-6*x)*l

og(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+72)*log(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096

*x^9)*log(x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*log(x)^2+(27*x^5-216*x^4+432*x^3)*log(x)-27),x, alg

((8*x^6 - 64*x^5 + 128*x^4 + x^2)*log(x)^2 - 24*x*log(x))/((x^10 - 16*x^9 + 96*x^8 - 256*x^7 + 256*x^6)*log(x)

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giac [B] time = 0.23, size = 283, normalized size = 10.11 \begin {gather*} \frac {3 \, {\left (8 \, x^{9} \log \relax (x) - 128 \, x^{8} \log \relax (x) + 768 \, x^{7} \log \relax (x) - 2048 \, x^{6} \log \relax (x) + 2050 \, x^{5} \log \relax (x) - 16 \, x^{4} \log \relax (x) - 24 \, x^{4} + 32 \, x^{3} \log \relax (x) + 192 \, x^{3} - 384 \, x^{2} - 3\right )}}{x^{18} \log \relax (x)^{2} - 32 \, x^{17} \log \relax (x)^{2} + 448 \, x^{16} \log \relax (x)^{2} - 3584 \, x^{15} \log \relax (x)^{2} + 17920 \, x^{14} \log \relax (x)^{2} - 57344 \, x^{13} \log \relax (x)^{2} - 6 \, x^{13} \log \relax (x) + 114688 \, x^{12} \log \relax (x)^{2} + 144 \, x^{12} \log \relax (x) - 131072 \, x^{11} \log \relax (x)^{2} - 1440 \, x^{11} \log \relax (x) + 65536 \, x^{10} \log \relax (x)^{2} + 7680 \, x^{10} \log \relax (x) - 23040 \, x^{9} \log \relax (x) + 36864 \, x^{8} \log \relax (x) + 9 \, x^{8} - 24576 \, x^{7} \log \relax (x) - 144 \, x^{7} + 864 \, x^{6} - 2304 \, x^{5} + 2304 \, x^{4}} - \frac {1029 \, x^{3} - 14406 \, x^{2} + 65872 \, x - 98864}{4096 \, {\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )}} + \frac {1029 \, x^{3} + 2058 \, x^{2} + 16 \, x + 16}{4096 \, x^{4}} \end {gather*}

integrate(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*log(x)^3+(72*x^5-384*x^4+384*x^3-6*x)*l

og(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+72)*log(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096

*x^9)*log(x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*log(x)^2+(27*x^5-216*x^4+432*x^3)*log(x)-27),x, alg

3*(8*x^9*log(x) - 128*x^8*log(x) + 768*x^7*log(x) - 2048*x^6*log(x) + 2050*x^5*log(x) - 16*x^4*log(x) - 24*x^4

+ 32*x^3*log(x) + 192*x^3 - 384*x^2 - 3)/(x^18*log(x)^2 - 32*x^17*log(x)^2 + 448*x^16*log(x)^2 - 3584*x^15*lo

g(x)^2 + 17920*x^14*log(x)^2 - 57344*x^13*log(x)^2 - 6*x^13*log(x) + 114688*x^12*log(x)^2 + 144*x^12*log(x) -

131072*x^11*log(x)^2 - 1440*x^11*log(x) + 65536*x^10*log(x)^2 + 7680*x^10*log(x) - 23040*x^9*log(x) + 36864*x^

8*log(x) + 9*x^8 - 24576*x^7*log(x) - 144*x^7 + 864*x^6 - 2304*x^5 + 2304*x^4) - 1/4096*(1029*x^3 - 14406*x^2

+ 65872*x - 98864)/(x^4 - 16*x^3 + 96*x^2 - 256*x + 256) + 1/4096*(1029*x^3 + 2058*x^2 + 16*x + 16)/x^4

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method	result	size

risch	\(\frac {8 x^{4}-64 x^{3}+128 x^{2}+1}{\left (x^{4}-16 x^{3}+96 x^{2}-256 x +256\right ) x^{4}}+\frac {24 x^{9} \ln \relax (x )-384 x^{8} \ln \relax (x )+2304 x^{7} \ln \relax (x )-6144 x^{6} \ln \relax (x )+6150 x^{5} \ln \relax (x )-48 x^{4} \ln \relax (x )-72 x^{4}+96 x^{3} \ln \relax (x )+576 x^{3}-1152 x^{2}-9}{\left (x -4\right ) \left (x^{3}-12 x^{2}+48 x -64\right ) \left (x^{5} \ln \relax (x )-8 x^{4} \ln \relax (x )+16 x^{3} \ln \relax (x )-3\right )^{2} x^{4}}\)	\(158\)

int(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*ln(x)^3+(72*x^5-384*x^4+384*x^3-6*x)*ln(x)^2+

(-24*x^5+192*x^4-384*x^3-6*x+72)*ln(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096*x^9)*ln(

x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*ln(x)^2+(27*x^5-216*x^4+432*x^3)*ln(x)-27),x,method=_RETURNVE

(8*x^4-64*x^3+128*x^2+1)/(x^4-16*x^3+96*x^2-256*x+256)/x^4+3*(8*x^9*ln(x)-128*x^8*ln(x)+768*x^7*ln(x)-2048*x^6

*ln(x)+2050*x^5*ln(x)-16*x^4*ln(x)-24*x^4+32*x^3*ln(x)+192*x^3-384*x^2-3)/(x-4)/(x^3-12*x^2+48*x-64)/(x^5*ln(x

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maxima [B] time = 0.43, size = 82, normalized size = 2.93 \begin {gather*} \frac {{\left (8 \, x^{6} - 64 \, x^{5} + 128 \, x^{4} + x^{2}\right )} \log \relax (x)^{2} - 24 \, x \log \relax (x)}{{\left (x^{10} - 16 \, x^{9} + 96 \, x^{8} - 256 \, x^{7} + 256 \, x^{6}\right )} \log \relax (x)^{2} - 6 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \relax (x) + 9} \end {gather*}

integrate(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*log(x)^3+(72*x^5-384*x^4+384*x^3-6*x)*l

og(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+72)*log(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096

*x^9)*log(x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*log(x)^2+(27*x^5-216*x^4+432*x^3)*log(x)-27),x, alg

((8*x^6 - 64*x^5 + 128*x^4 + x^2)*log(x)^2 - 24*x*log(x))/((x^10 - 16*x^9 + 96*x^8 - 256*x^7 + 256*x^6)*log(x)

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int -\frac {\left (32\,x^{10}-448\,x^9+2304\,x^8-5120\,x^7+4104\,x^6-48\,x^5+64\,x^4\right )\,{\ln \relax (x)}^3+\left (-72\,x^5+384\,x^4-384\,x^3+6\,x\right )\,{\ln \relax (x)}^2+\left (24\,x^5-192\,x^4+384\,x^3+6\,x-72\right )\,\ln \relax (x)-72}{\left (-x^{15}+24\,x^{14}-240\,x^{13}+1280\,x^{12}-3840\,x^{11}+6144\,x^{10}-4096\,x^9\right )\,{\ln \relax (x)}^3+\left (9\,x^{10}-144\,x^9+864\,x^8-2304\,x^7+2304\,x^6\right )\,{\ln \relax (x)}^2+\left (-27\,x^5+216\,x^4-432\,x^3\right )\,\ln \relax (x)+27} \,d x \end {gather*}

int((log(x)*(6*x + 384*x^3 - 192*x^4 + 24*x^5 - 72) + log(x)^2*(6*x - 384*x^3 + 384*x^4 - 72*x^5) + log(x)^3*(

64*x^4 - 48*x^5 + 4104*x^6 - 5120*x^7 + 2304*x^8 - 448*x^9 + 32*x^10) - 72)/(log(x)^2*(2304*x^6 - 2304*x^7 + 8

64*x^8 - 144*x^9 + 9*x^10) - log(x)^3*(4096*x^9 - 6144*x^10 + 3840*x^11 - 1280*x^12 + 240*x^13 - 24*x^14 + x^1

-int(-(log(x)*(6*x + 384*x^3 - 192*x^4 + 24*x^5 - 72) + log(x)^2*(6*x - 384*x^3 + 384*x^4 - 72*x^5) + log(x)^3

*(64*x^4 - 48*x^5 + 4104*x^6 - 5120*x^7 + 2304*x^8 - 448*x^9 + 32*x^10) - 72)/(log(x)^2*(2304*x^6 - 2304*x^7 +

864*x^8 - 144*x^9 + 9*x^10) - log(x)^3*(4096*x^9 - 6144*x^10 + 3840*x^11 - 1280*x^12 + 240*x^13 - 24*x^14 + x

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sympy [B] time = 0.82, size = 209, normalized size = 7.46 \begin {gather*} - \frac {- 8 x^{4} + 64 x^{3} - 128 x^{2} - 1}{x^{8} - 16 x^{7} + 96 x^{6} - 256 x^{5} + 256 x^{4}} + \frac {- 72 x^{4} + 576 x^{3} - 1152 x^{2} + \left (24 x^{9} - 384 x^{8} + 2304 x^{7} - 6144 x^{6} + 6150 x^{5} - 48 x^{4} + 96 x^{3}\right ) \log {\relax (x )} - 9}{9 x^{8} - 144 x^{7} + 864 x^{6} - 2304 x^{5} + 2304 x^{4} + \left (- 6 x^{13} + 144 x^{12} - 1440 x^{11} + 7680 x^{10} - 23040 x^{9} + 36864 x^{8} - 24576 x^{7}\right ) \log {\relax (x )} + \left (x^{18} - 32 x^{17} + 448 x^{16} - 3584 x^{15} + 17920 x^{14} - 57344 x^{13} + 114688 x^{12} - 131072 x^{11} + 65536 x^{10}\right ) \log {\relax (x )}^{2}} \end {gather*}

integrate(((-32*x**10+448*x**9-2304*x**8+5120*x**7-4104*x**6+48*x**5-64*x**4)*ln(x)**3+(72*x**5-384*x**4+384*x

**3-6*x)*ln(x)**2+(-24*x**5+192*x**4-384*x**3-6*x+72)*ln(x)+72)/((x**15-24*x**14+240*x**13-1280*x**12+3840*x**

11-6144*x**10+4096*x**9)*ln(x)**3+(-9*x**10+144*x**9-864*x**8+2304*x**7-2304*x**6)*ln(x)**2+(27*x**5-216*x**4+

-(-8*x**4 + 64*x**3 - 128*x**2 - 1)/(x**8 - 16*x**7 + 96*x**6 - 256*x**5 + 256*x**4) + (-72*x**4 + 576*x**3 -

1152*x**2 + (24*x**9 - 384*x**8 + 2304*x**7 - 6144*x**6 + 6150*x**5 - 48*x**4 + 96*x**3)*log(x) - 9)/(9*x**8 -

144*x**7 + 864*x**6 - 2304*x**5 + 2304*x**4 + (-6*x**13 + 144*x**12 - 1440*x**11 + 7680*x**10 - 23040*x**9 +

36864*x**8 - 24576*x**7)*log(x) + (x**18 - 32*x**17 + 448*x**16 - 3584*x**15 + 17920*x**14 - 57344*x**13 + 114

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