\(\int \frac {9765625 x^{15} (30-35 x+5 x \log (x^2))}{(2 x-3 x^2+x^2 \log (x^2)) (4-12 x+9 x^2+(4 x-6 x^2) \log (x^2)+x^2 \log ^2(x^2))^5} \, dx\) [2381]

Optimal result

Integrand size = 72, antiderivative size = 18 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 x^5}{\left (-3+\frac {2}{x}+\log \left (x^2\right )\right )^{10}} \]

[Out]

9765625/(ln(x^2)+2/x-3)^10*x^5

Rubi [F]

\[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx \]

[In]

Int[(9765625*x^15*(30 - 35*x + 5*x*Log[x^2]))/((2*x - 3*x^2 + x^2*Log[x^2])*(4 - 12*x + 9*x^2 + (4*x - 6*x^2)*
Log[x^2] + x^2*Log[x^2]^2)^5),x]

[Out]

195312500*Defer[Int][x^14/(2 - 3*x + x*Log[x^2])^11, x] - 195312500*Defer[Int][x^15/(2 - 3*x + x*Log[x^2])^11,
x] + 48828125*Defer[Int][x^14/(2 - 3*x + x*Log[x^2])^10, x]

Rubi steps \begin{align*} \text {integral}& = 9765625 \int \frac {x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx \\ & = 9765625 \int \frac {5 x^{14} \left (6-7 x+x \log \left (x^2\right )\right )}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ & = 48828125 \int \frac {x^{14} \left (6-7 x+x \log \left (x^2\right )\right )}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ & = 48828125 \int \left (-\frac {4 (-1+x) x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}}+\frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}}\right ) \, dx \\ & = 48828125 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \, dx-195312500 \int \frac {(-1+x) x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ & = 48828125 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \, dx-195312500 \int \left (-\frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}}+\frac {x^{15}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}}\right ) \, dx \\ & = 48828125 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \, dx+195312500 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx-195312500 \int \frac {x^{15}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 1.36 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 x^{15}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \]

[In]

Integrate[(9765625*x^15*(30 - 35*x + 5*x*Log[x^2]))/((2*x - 3*x^2 + x^2*Log[x^2])*(4 - 12*x + 9*x^2 + (4*x - 6
*x^2)*Log[x^2] + x^2*Log[x^2]^2)^5),x]

[Out]

(9765625*x^15)/(2 - 3*x + x*Log[x^2])^10

Maple [A] (verified)

Time = 0.96 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06

method	result	size
risch	\(\frac {9765625 x^{15}}{{\left (x \ln \left (x^{2}\right )-3 x +2\right )}^{10}}\)	\(19\)
parallelrisch	\(\frac {9765625 x^{15}}{\left (x^{2} \ln \left (x^{2}\right )^{2}-6 x^{2} \ln \left (x^{2}\right )+4 x \ln \left (x^{2}\right )+9 x^{2}-12 x +4\right )^{4} {\left (x \ln \left (x^{2}\right )-3 x +2\right )}^{2}}\)	\(57\)

[In]

int(9765625*(5*x*ln(x^2)-35*x+30)*x^15/(x^2*ln(x^2)^2+(-6*x^2+4*x)*ln(x^2)+9*x^2-12*x+4)^5/(x^2*ln(x^2)-3*x^2+
2*x),x,method=_RETURNVERBOSE)

[Out]

9765625*x^15/(x*ln(x^2)-3*x+2)^10

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 414 vs. \(2 (18) = 36\).

Time = 0.25 (sec) , antiderivative size = 414, normalized size of antiderivative = 23.00 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 \, x^{15}}{x^{10} \log \left (x^{2}\right )^{10} + 59049 \, x^{10} - 10 \, {\left (3 \, x^{10} - 2 \, x^{9}\right )} \log \left (x^{2}\right )^{9} - 393660 \, x^{9} + 45 \, {\left (9 \, x^{10} - 12 \, x^{9} + 4 \, x^{8}\right )} \log \left (x^{2}\right )^{8} + 1180980 \, x^{8} - 120 \, {\left (27 \, x^{10} - 54 \, x^{9} + 36 \, x^{8} - 8 \, x^{7}\right )} \log \left (x^{2}\right )^{7} - 2099520 \, x^{7} + 210 \, {\left (81 \, x^{10} - 216 \, x^{9} + 216 \, x^{8} - 96 \, x^{7} + 16 \, x^{6}\right )} \log \left (x^{2}\right )^{6} + 2449440 \, x^{6} - 252 \, {\left (243 \, x^{10} - 810 \, x^{9} + 1080 \, x^{8} - 720 \, x^{7} + 240 \, x^{6} - 32 \, x^{5}\right )} \log \left (x^{2}\right )^{5} - 1959552 \, x^{5} + 210 \, {\left (729 \, x^{10} - 2916 \, x^{9} + 4860 \, x^{8} - 4320 \, x^{7} + 2160 \, x^{6} - 576 \, x^{5} + 64 \, x^{4}\right )} \log \left (x^{2}\right )^{4} + 1088640 \, x^{4} - 120 \, {\left (2187 \, x^{10} - 10206 \, x^{9} + 20412 \, x^{8} - 22680 \, x^{7} + 15120 \, x^{6} - 6048 \, x^{5} + 1344 \, x^{4} - 128 \, x^{3}\right )} \log \left (x^{2}\right )^{3} - 414720 \, x^{3} + 45 \, {\left (6561 \, x^{10} - 34992 \, x^{9} + 81648 \, x^{8} - 108864 \, x^{7} + 90720 \, x^{6} - 48384 \, x^{5} + 16128 \, x^{4} - 3072 \, x^{3} + 256 \, x^{2}\right )} \log \left (x^{2}\right )^{2} + 103680 \, x^{2} - 10 \, {\left (19683 \, x^{10} - 118098 \, x^{9} + 314928 \, x^{8} - 489888 \, x^{7} + 489888 \, x^{6} - 326592 \, x^{5} + 145152 \, x^{4} - 41472 \, x^{3} + 6912 \, x^{2} - 512 \, x\right )} \log \left (x^{2}\right ) - 15360 \, x + 1024} \]

[In]

integrate(9765625*(5*x*log(x^2)-35*x+30)*x^15/(x^2*log(x^2)^2+(-6*x^2+4*x)*log(x^2)+9*x^2-12*x+4)^5/(x^2*log(x
^2)-3*x^2+2*x),x, algorithm="fricas")

[Out]

9765625*x^15/(x^10*log(x^2)^10 + 59049*x^10 - 10*(3*x^10 - 2*x^9)*log(x^2)^9 - 393660*x^9 + 45*(9*x^10 - 12*x^
9 + 4*x^8)*log(x^2)^8 + 1180980*x^8 - 120*(27*x^10 - 54*x^9 + 36*x^8 - 8*x^7)*log(x^2)^7 - 2099520*x^7 + 210*(
81*x^10 - 216*x^9 + 216*x^8 - 96*x^7 + 16*x^6)*log(x^2)^6 + 2449440*x^6 - 252*(243*x^10 - 810*x^9 + 1080*x^8 -
720*x^7 + 240*x^6 - 32*x^5)*log(x^2)^5 - 1959552*x^5 + 210*(729*x^10 - 2916*x^9 + 4860*x^8 - 4320*x^7 + 2160*
x^6 - 576*x^5 + 64*x^4)*log(x^2)^4 + 1088640*x^4 - 120*(2187*x^10 - 10206*x^9 + 20412*x^8 - 22680*x^7 + 15120*
x^6 - 6048*x^5 + 1344*x^4 - 128*x^3)*log(x^2)^3 - 414720*x^3 + 45*(6561*x^10 - 34992*x^9 + 81648*x^8 - 108864*
x^7 + 90720*x^6 - 48384*x^5 + 16128*x^4 - 3072*x^3 + 256*x^2)*log(x^2)^2 + 103680*x^2 - 10*(19683*x^10 - 11809
8*x^9 + 314928*x^8 - 489888*x^7 + 489888*x^6 - 326592*x^5 + 145152*x^4 - 41472*x^3 + 6912*x^2 - 512*x)*log(x^2
) - 15360*x + 1024)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 398 vs. \(2 (15) = 30\).

Time = 1.39 (sec) , antiderivative size = 398, normalized size of antiderivative = 22.11 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 x^{15}}{x^{10} \log {\left (x^{2} \right )}^{10} + 59049 x^{10} - 393660 x^{9} + 1180980 x^{8} - 2099520 x^{7} + 2449440 x^{6} - 1959552 x^{5} + 1088640 x^{4} - 414720 x^{3} + 103680 x^{2} - 15360 x + \left (- 30 x^{10} + 20 x^{9}\right ) \log {\left (x^{2} \right )}^{9} + \left (405 x^{10} - 540 x^{9} + 180 x^{8}\right ) \log {\left (x^{2} \right )}^{8} + \left (- 3240 x^{10} + 6480 x^{9} - 4320 x^{8} + 960 x^{7}\right ) \log {\left (x^{2} \right )}^{7} + \left (17010 x^{10} - 45360 x^{9} + 45360 x^{8} - 20160 x^{7} + 3360 x^{6}\right ) \log {\left (x^{2} \right )}^{6} + \left (- 61236 x^{10} + 204120 x^{9} - 272160 x^{8} + 181440 x^{7} - 60480 x^{6} + 8064 x^{5}\right ) \log {\left (x^{2} \right )}^{5} + \left (153090 x^{10} - 612360 x^{9} + 1020600 x^{8} - 907200 x^{7} + 453600 x^{6} - 120960 x^{5} + 13440 x^{4}\right ) \log {\left (x^{2} \right )}^{4} + \left (- 262440 x^{10} + 1224720 x^{9} - 2449440 x^{8} + 2721600 x^{7} - 1814400 x^{6} + 725760 x^{5} - 161280 x^{4} + 15360 x^{3}\right ) \log {\left (x^{2} \right )}^{3} + \left (295245 x^{10} - 1574640 x^{9} + 3674160 x^{8} - 4898880 x^{7} + 4082400 x^{6} - 2177280 x^{5} + 725760 x^{4} - 138240 x^{3} + 11520 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (- 196830 x^{10} + 1180980 x^{9} - 3149280 x^{8} + 4898880 x^{7} - 4898880 x^{6} + 3265920 x^{5} - 1451520 x^{4} + 414720 x^{3} - 69120 x^{2} + 5120 x\right ) \log {\left (x^{2} \right )} + 1024} \]

[In]

integrate(9765625*(5*x*ln(x**2)-35*x+30)*x**15/(x**2*ln(x**2)**2+(-6*x**2+4*x)*ln(x**2)+9*x**2-12*x+4)**5/(x**
2*ln(x**2)-3*x**2+2*x),x)

[Out]

9765625*x**15/(x**10*log(x**2)**10 + 59049*x**10 - 393660*x**9 + 1180980*x**8 - 2099520*x**7 + 2449440*x**6 -
1959552*x**5 + 1088640*x**4 - 414720*x**3 + 103680*x**2 - 15360*x + (-30*x**10 + 20*x**9)*log(x**2)**9 + (405*
x**10 - 540*x**9 + 180*x**8)*log(x**2)**8 + (-3240*x**10 + 6480*x**9 - 4320*x**8 + 960*x**7)*log(x**2)**7 + (1
7010*x**10 - 45360*x**9 + 45360*x**8 - 20160*x**7 + 3360*x**6)*log(x**2)**6 + (-61236*x**10 + 204120*x**9 - 27
2160*x**8 + 181440*x**7 - 60480*x**6 + 8064*x**5)*log(x**2)**5 + (153090*x**10 - 612360*x**9 + 1020600*x**8 -
907200*x**7 + 453600*x**6 - 120960*x**5 + 13440*x**4)*log(x**2)**4 + (-262440*x**10 + 1224720*x**9 - 2449440*x
**8 + 2721600*x**7 - 1814400*x**6 + 725760*x**5 - 161280*x**4 + 15360*x**3)*log(x**2)**3 + (295245*x**10 - 157
4640*x**9 + 3674160*x**8 - 4898880*x**7 + 4082400*x**6 - 2177280*x**5 + 725760*x**4 - 138240*x**3 + 11520*x**2
)*log(x**2)**2 + (-196830*x**10 + 1180980*x**9 - 3149280*x**8 + 4898880*x**7 - 4898880*x**6 + 3265920*x**5 - 1
451520*x**4 + 414720*x**3 - 69120*x**2 + 5120*x)*log(x**2) + 1024)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 395 vs. \(2 (18) = 36\).

Time = 0.46 (sec) , antiderivative size = 395, normalized size of antiderivative = 21.94 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 \, x^{15}}{1024 \, x^{10} \log \left (x\right )^{10} + 59049 \, x^{10} - 5120 \, {\left (3 \, x^{10} - 2 \, x^{9}\right )} \log \left (x\right )^{9} - 393660 \, x^{9} + 11520 \, {\left (9 \, x^{10} - 12 \, x^{9} + 4 \, x^{8}\right )} \log \left (x\right )^{8} + 1180980 \, x^{8} - 15360 \, {\left (27 \, x^{10} - 54 \, x^{9} + 36 \, x^{8} - 8 \, x^{7}\right )} \log \left (x\right )^{7} - 2099520 \, x^{7} + 13440 \, {\left (81 \, x^{10} - 216 \, x^{9} + 216 \, x^{8} - 96 \, x^{7} + 16 \, x^{6}\right )} \log \left (x\right )^{6} + 2449440 \, x^{6} - 8064 \, {\left (243 \, x^{10} - 810 \, x^{9} + 1080 \, x^{8} - 720 \, x^{7} + 240 \, x^{6} - 32 \, x^{5}\right )} \log \left (x\right )^{5} - 1959552 \, x^{5} + 3360 \, {\left (729 \, x^{10} - 2916 \, x^{9} + 4860 \, x^{8} - 4320 \, x^{7} + 2160 \, x^{6} - 576 \, x^{5} + 64 \, x^{4}\right )} \log \left (x\right )^{4} + 1088640 \, x^{4} - 960 \, {\left (2187 \, x^{10} - 10206 \, x^{9} + 20412 \, x^{8} - 22680 \, x^{7} + 15120 \, x^{6} - 6048 \, x^{5} + 1344 \, x^{4} - 128 \, x^{3}\right )} \log \left (x\right )^{3} - 414720 \, x^{3} + 180 \, {\left (6561 \, x^{10} - 34992 \, x^{9} + 81648 \, x^{8} - 108864 \, x^{7} + 90720 \, x^{6} - 48384 \, x^{5} + 16128 \, x^{4} - 3072 \, x^{3} + 256 \, x^{2}\right )} \log \left (x\right )^{2} + 103680 \, x^{2} - 20 \, {\left (19683 \, x^{10} - 118098 \, x^{9} + 314928 \, x^{8} - 489888 \, x^{7} + 489888 \, x^{6} - 326592 \, x^{5} + 145152 \, x^{4} - 41472 \, x^{3} + 6912 \, x^{2} - 512 \, x\right )} \log \left (x\right ) - 15360 \, x + 1024} \]

[In]

integrate(9765625*(5*x*log(x^2)-35*x+30)*x^15/(x^2*log(x^2)^2+(-6*x^2+4*x)*log(x^2)+9*x^2-12*x+4)^5/(x^2*log(x
^2)-3*x^2+2*x),x, algorithm="maxima")

[Out]

9765625*x^15/(1024*x^10*log(x)^10 + 59049*x^10 - 5120*(3*x^10 - 2*x^9)*log(x)^9 - 393660*x^9 + 11520*(9*x^10 -
12*x^9 + 4*x^8)*log(x)^8 + 1180980*x^8 - 15360*(27*x^10 - 54*x^9 + 36*x^8 - 8*x^7)*log(x)^7 - 2099520*x^7 + 1
3440*(81*x^10 - 216*x^9 + 216*x^8 - 96*x^7 + 16*x^6)*log(x)^6 + 2449440*x^6 - 8064*(243*x^10 - 810*x^9 + 1080*
x^8 - 720*x^7 + 240*x^6 - 32*x^5)*log(x)^5 - 1959552*x^5 + 3360*(729*x^10 - 2916*x^9 + 4860*x^8 - 4320*x^7 + 2
160*x^6 - 576*x^5 + 64*x^4)*log(x)^4 + 1088640*x^4 - 960*(2187*x^10 - 10206*x^9 + 20412*x^8 - 22680*x^7 + 1512
0*x^6 - 6048*x^5 + 1344*x^4 - 128*x^3)*log(x)^3 - 414720*x^3 + 180*(6561*x^10 - 34992*x^9 + 81648*x^8 - 108864
*x^7 + 90720*x^6 - 48384*x^5 + 16128*x^4 - 3072*x^3 + 256*x^2)*log(x)^2 + 103680*x^2 - 20*(19683*x^10 - 118098
*x^9 + 314928*x^8 - 489888*x^7 + 489888*x^6 - 326592*x^5 + 145152*x^4 - 41472*x^3 + 6912*x^2 - 512*x)*log(x) -
15360*x + 1024)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 758 vs. \(2 (18) = 36\).

Time = 0.36 (sec) , antiderivative size = 758, normalized size of antiderivative = 42.11 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\text {Too large to display} \]

[In]

integrate(9765625*(5*x*log(x^2)-35*x+30)*x^15/(x^2*log(x^2)^2+(-6*x^2+4*x)*log(x^2)+9*x^2-12*x+4)^5/(x^2*log(x
^2)-3*x^2+2*x),x, algorithm="giac")

[Out]

9765625*(x^16 - x^15)/(x^11*log(x^2)^10 - 30*x^11*log(x^2)^9 - x^10*log(x^2)^10 + 405*x^11*log(x^2)^8 + 50*x^1
0*log(x^2)^9 - 3240*x^11*log(x^2)^7 - 945*x^10*log(x^2)^8 - 20*x^9*log(x^2)^9 + 17010*x^11*log(x^2)^6 + 9720*x
^10*log(x^2)^7 + 720*x^9*log(x^2)^8 - 61236*x^11*log(x^2)^5 - 62370*x^10*log(x^2)^6 - 10800*x^9*log(x^2)^7 - 1
80*x^8*log(x^2)^8 + 153090*x^11*log(x^2)^4 + 265356*x^10*log(x^2)^5 + 90720*x^9*log(x^2)^6 + 5280*x^8*log(x^2)
^7 - 262440*x^11*log(x^2)^3 - 765450*x^10*log(x^2)^4 - 476280*x^9*log(x^2)^5 - 65520*x^8*log(x^2)^6 - 960*x^7*
log(x^2)^7 + 295245*x^11*log(x^2)^2 + 1487160*x^10*log(x^2)^3 + 1632960*x^9*log(x^2)^4 + 453600*x^8*log(x^2)^5
+ 23520*x^7*log(x^2)^6 - 196830*x^11*log(x^2) - 1869885*x^10*log(x^2)^2 - 3674160*x^9*log(x^2)^3 - 1927800*x^
8*log(x^2)^4 - 241920*x^7*log(x^2)^5 - 3360*x^6*log(x^2)^6 + 59049*x^11 + 1377810*x^10*log(x^2) + 5248800*x^9*
log(x^2)^2 + 5171040*x^8*log(x^2)^3 + 1360800*x^7*log(x^2)^4 + 68544*x^6*log(x^2)^5 - 452709*x^10 - 4330260*x^
9*log(x^2) - 8573040*x^8*log(x^2)^2 - 4536000*x^7*log(x^2)^3 - 574560*x^6*log(x^2)^4 - 8064*x^5*log(x^2)^5 + 1
574640*x^9 + 8048160*x^8*log(x^2) + 8981280*x^7*log(x^2)^2 + 2540160*x^6*log(x^2)^3 + 134400*x^5*log(x^2)^4 -
3280500*x^8 - 9797760*x^7*log(x^2) - 6259680*x^6*log(x^2)^2 - 887040*x^5*log(x^2)^3 - 13440*x^4*log(x^2)^4 + 4
548960*x^7 + 8164800*x^6*log(x^2) + 2903040*x^5*log(x^2)^2 + 176640*x^4*log(x^2)^3 - 4408992*x^6 - 4717440*x^5
*log(x^2) - 864000*x^4*log(x^2)^2 - 15360*x^3*log(x^2)^3 + 3048192*x^5 + 1866240*x^4*log(x^2) + 149760*x^3*log
(x^2)^2 - 1503360*x^4 - 483840*x^3*log(x^2) - 11520*x^2*log(x^2)^2 + 518400*x^3 + 74240*x^2*log(x^2) - 119040*
x^2 - 5120*x*log(x^2) + 16384*x - 1024)

Mupad [B] (verification not implemented)

Time = 10.71 (sec) , antiderivative size = 192, normalized size of antiderivative = 10.67 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=-\frac {9765625\,\left (x^{15}-x^{16}\right )}{\left (x-1\right )\,\left ({\left (3\,x-2\right )}^{10}+x^{10}\,{\ln \left (x^2\right )}^{10}-10\,x^9\,{\ln \left (x^2\right )}^9\,\left (3\,x-2\right )+45\,x^2\,{\ln \left (x^2\right )}^2\,{\left (3\,x-2\right )}^8-120\,x^3\,{\ln \left (x^2\right )}^3\,{\left (3\,x-2\right )}^7+210\,x^4\,{\ln \left (x^2\right )}^4\,{\left (3\,x-2\right )}^6-252\,x^5\,{\ln \left (x^2\right )}^5\,{\left (3\,x-2\right )}^5+210\,x^6\,{\ln \left (x^2\right )}^6\,{\left (3\,x-2\right )}^4-120\,x^7\,{\ln \left (x^2\right )}^7\,{\left (3\,x-2\right )}^3+45\,x^8\,{\ln \left (x^2\right )}^8\,{\left (3\,x-2\right )}^2-10\,x\,\ln \left (x^2\right )\,{\left (3\,x-2\right )}^9\right )} \]

[In]

int((9765625*x^15*(5*x*log(x^2) - 35*x + 30))/((2*x + x^2*log(x^2) - 3*x^2)*(log(x^2)*(4*x - 6*x^2) - 12*x + 9
*x^2 + x^2*log(x^2)^2 + 4)^5),x)

[Out]

-(9765625*(x^15 - x^16))/((x - 1)*((3*x - 2)^10 + x^10*log(x^2)^10 - 10*x^9*log(x^2)^9*(3*x - 2) + 45*x^2*log(
x^2)^2*(3*x - 2)^8 - 120*x^3*log(x^2)^3*(3*x - 2)^7 + 210*x^4*log(x^2)^4*(3*x - 2)^6 - 252*x^5*log(x^2)^5*(3*x
- 2)^5 + 210*x^6*log(x^2)^6*(3*x - 2)^4 - 120*x^7*log(x^2)^7*(3*x - 2)^3 + 45*x^8*log(x^2)^8*(3*x - 2)^2 - 10
*x*log(x^2)*(3*x - 2)^9))