3.74.48 \(\int \frac {270 x^3+1431 x^4-828 x^5-21016 x^6+43992 x^7-189668 x^8+381578 x^9-382272 x^{10}+221780 x^{11}-79932 x^{12}+18236 x^{13}-2568 x^{14}+204 x^{15}-7 x^{16}+(-18 x^2-528 x^3+628 x^4-240 x^5-60 x^6+168 x^7-100 x^8+24 x^9-2 x^{10}) \log (x)+(27 x^2-24 x^3+5 x^4) \log ^2(x)}{35721 x^4-47628 x^5+874314 x^6-1479492 x^7+8243811 x^8-15734160 x^9+39581880 x^{10}-71563680 x^{11}[phone] x^{12}-141607796 x^{13}[phone] x^{14}-106050644 x^{15}[phone] x^{16}-20791560 x^{17}+5728480 x^{18}-1157680 x^{19}+169971 x^{20}-17668 x^{21}+1234 x^{22}-52 x^{23}+x^{24}+(-11340 x^3+11340 x^4-195480 x^5+268800 x^6-1160748 x^7+1862828 x^8-3083396 x^9+4295684 x^{10}-3745020 x^{11}+2041420 x^{12}-724740 x^{13}+171300 x^{14}-26848 x^{15}+2688 x^{16}-156 x^{17}+4 x^{18}) \log (x)+(1278 x^2-852 x^3+13642 x^4-14400 x^5+39390 x^6-50460 x^7+29910 x^8-9480 x^9+1674 x^{10}-156 x^{11}+6 x^{12}) \log ^2(x)+(-60 x+20 x^2-300 x^3+220 x^4-52 x^5+4 x^6) \log ^3(x)+\log ^4(x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {x}{-4+\left (5+(-5+x)^2 x^2-\frac {\log (x)}{(3-x) x}\right )^2} \]

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Rubi [F]  time = 58.69, 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 {270 x^3+1431 x^4-828 x^5-21016 x^6+43992 x^7-189668 x^8+381578 x^9-382272 x^{10}+221780 x^{11}-79932 x^{12}+18236 x^{13}-2568 x^{14}+204 x^{15}-7 x^{16}+\left (-18 x^2-528 x^3+628 x^4-240 x^5-60 x^6+168 x^7-100 x^8+24 x^9-2 x^{10}\right ) \log (x)+\left (27 x^2-24 x^3+5 x^4\right ) \log ^2(x)}{35721 x^4-47628 x^5+874314 x^6-1479492 x^7+8243811 x^8-15734160 x^9+39581880 x^{10}-71563680 x^{11}[phone] x^{12}-141607796 x^{13}[phone] x^{14}-106050644 x^{15}[phone] x^{16}-20791560 x^{17}+5728480 x^{18}-1157680 x^{19}+169971 x^{20}-17668 x^{21}+1234 x^{22}-52 x^{23}+x^{24}+\left (-11340 x^3+11340 x^4-195480 x^5+268800 x^6-1160748 x^7+1862828 x^8-3083396 x^9+4295684 x^{10}-3745020 x^{11}+2041420 x^{12}-724740 x^{13}+171300 x^{14}-26848 x^{15}+2688 x^{16}-156 x^{17}+4 x^{18}\right ) \log (x)+\left (1278 x^2-852 x^3+13642 x^4-14400 x^5+39390 x^6-50460 x^7+29910 x^8-9480 x^9+1674 x^{10}-156 x^{11}+6 x^{12}\right ) \log ^2(x)+\left (-60 x+20 x^2-300 x^3+220 x^4-52 x^5+4 x^6\right ) \log ^3(x)+\log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(270*x^3 + 1431*x^4 - 828*x^5 - 21016*x^6 + 43992*x^7 - 189668*x^8 + 381578*x^9 - 382272*x^10 + 221780*x^1
1 - 79932*x^12 + 18236*x^13 - 2568*x^14 + 204*x^15 - 7*x^16 + (-18*x^2 - 528*x^3 + 628*x^4 - 240*x^5 - 60*x^6
+ 168*x^7 - 100*x^8 + 24*x^9 - 2*x^10)*Log[x] + (27*x^2 - 24*x^3 + 5*x^4)*Log[x]^2)/(35721*x^4 - 47628*x^5 + 8
74314*x^6 - 1479492*x^7 + 8243811*x^8 - 15734160*x^9 + 39581880*x^10 - 71563680*x^11 + 106612717*x^12 - 141607
796*x^13 + 145039298*x^14 - 106050644*x^15 + 55218437*x^16 - 20791560*x^17 + 5728480*x^18 - 1157680*x^19 + 169
971*x^20 - 17668*x^21 + 1234*x^22 - 52*x^23 + x^24 + (-11340*x^3 + 11340*x^4 - 195480*x^5 + 268800*x^6 - 11607
48*x^7 + 1862828*x^8 - 3083396*x^9 + 4295684*x^10 - 3745020*x^11 + 2041420*x^12 - 724740*x^13 + 171300*x^14 -
26848*x^15 + 2688*x^16 - 156*x^17 + 4*x^18)*Log[x] + (1278*x^2 - 852*x^3 + 13642*x^4 - 14400*x^5 + 39390*x^6 -
50460*x^7 + 29910*x^8 - 9480*x^9 + 1674*x^10 - 156*x^11 + 6*x^12)*Log[x]^2 + (-60*x + 20*x^2 - 300*x^3 + 220*
x^4 - 52*x^5 + 4*x^6)*Log[x]^3 + Log[x]^4),x]

[Out]

(3*Defer[Int][x/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 - 7*Defer[Int][x^2/(-9*x + 3
*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x] + (27*Defer[Int][x^3/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 1
3*x^5 + x^6 + Log[x])^2, x])/4 - (681*Defer[Int][x^4/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^
2, x])/4 + (885*Defer[Int][x^5/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 - (415*Defer[
Int][x^6/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 + (83*Defer[Int][x^7/(-9*x + 3*x^2
- 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 - (3*Defer[Int][x^8/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x
^5 + x^6 + Log[x])^2, x])/2 - (3*Defer[Int][x/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x]), x])/2
+ (3*Defer[Int][x^2/(-9*x + 3*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x]), x])/4 - (3*Defer[Int][x/(-21*x +
7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 + 16*Defer[Int][x^2/(-21*x + 7*x^2 - 75*x^3 + 55*x^
4 - 13*x^5 + x^6 + Log[x])^2, x] - (63*Defer[Int][x^3/(-21*x + 7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x]
)^2, x])/4 + (689*Defer[Int][x^4/(-21*x + 7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 - (885*Def
er[Int][x^5/(-21*x + 7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 + (415*Defer[Int][x^6/(-21*x +
7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x])^2, x])/4 - (83*Defer[Int][x^7/(-21*x + 7*x^2 - 75*x^3 + 55*x^
4 - 13*x^5 + x^6 + Log[x])^2, x])/4 + (3*Defer[Int][x^8/(-21*x + 7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[
x])^2, x])/2 + (3*Defer[Int][x/(-21*x + 7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x]), x])/2 - (3*Defer[Int
][x^2/(-21*x + 7*x^2 - 75*x^3 + 55*x^4 - 13*x^5 + x^6 + Log[x]), x])/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(3-x) x^2 \left ((-3+x)^2 x \left (10+63 x+29 x^2-770 x^3+852 x^4-5915 x^5+7905 x^6-4250 x^7+1110 x^8-141 x^9+7 x^{10}\right )+2 \left (-3-89 x+75 x^2-15 x^3-15 x^4+23 x^5-9 x^6+x^7\right ) \log (x)+(9-5 x) \log ^2(x)\right )}{\left ((-3+x)^2 x^2 \left (21+250 x^2-100 x^3+635 x^4-500 x^5+150 x^6-20 x^7+x^8\right )+2 x \left (-15+5 x-75 x^2+55 x^3-13 x^4+x^5\right ) \log (x)+\log ^2(x)\right )^2} \, dx\\ &=\int \left (-\frac {x \left (-3+28 x-27 x^2+681 x^3-885 x^4+415 x^5-83 x^6+6 x^7\right )}{4 \left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {3 (-2+x) x}{4 \left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )}+\frac {x \left (-3+64 x-63 x^2+689 x^3-885 x^4+415 x^5-83 x^6+6 x^7\right )}{4 \left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {3 (-2+x) x}{4 \left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )}\right ) \, dx\\ &=-\left (\frac {1}{4} \int \frac {x \left (-3+28 x-27 x^2+681 x^3-885 x^4+415 x^5-83 x^6+6 x^7\right )}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx\right )+\frac {1}{4} \int \frac {x \left (-3+64 x-63 x^2+689 x^3-885 x^4+415 x^5-83 x^6+6 x^7\right )}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {3}{4} \int \frac {(-2+x) x}{-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)} \, dx-\frac {3}{4} \int \frac {(-2+x) x}{-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)} \, dx\\ &=-\left (\frac {1}{4} \int \left (-\frac {3 x}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {28 x^2}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {27 x^3}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {681 x^4}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {885 x^5}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {415 x^6}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {83 x^7}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {6 x^8}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}\right ) \, dx\right )+\frac {1}{4} \int \left (-\frac {3 x}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {64 x^2}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {63 x^3}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {689 x^4}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {885 x^5}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {415 x^6}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}-\frac {83 x^7}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}+\frac {6 x^8}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2}\right ) \, dx+\frac {3}{4} \int \left (-\frac {2 x}{-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)}+\frac {x^2}{-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)}\right ) \, dx-\frac {3}{4} \int \left (-\frac {2 x}{-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)}+\frac {x^2}{-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)}\right ) \, dx\\ &=\frac {3}{4} \int \frac {x}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {3}{4} \int \frac {x^2}{-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)} \, dx-\frac {3}{4} \int \frac {x}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {3}{4} \int \frac {x^2}{-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)} \, dx-\frac {3}{2} \int \frac {x^8}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {3}{2} \int \frac {x}{-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)} \, dx+\frac {3}{2} \int \frac {x^8}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {3}{2} \int \frac {x}{-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)} \, dx+\frac {27}{4} \int \frac {x^3}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-7 \int \frac {x^2}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {63}{4} \int \frac {x^3}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+16 \int \frac {x^2}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {83}{4} \int \frac {x^7}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {83}{4} \int \frac {x^7}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {415}{4} \int \frac {x^6}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {415}{4} \int \frac {x^6}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {681}{4} \int \frac {x^4}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {689}{4} \int \frac {x^4}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx+\frac {885}{4} \int \frac {x^5}{\left (-9 x+3 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx-\frac {885}{4} \int \frac {x^5}{\left (-21 x+7 x^2-75 x^3+55 x^4-13 x^5+x^6+\log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.16, size = 88, normalized size = 2.67 \begin {gather*} \frac {(-3+x)^2 x^3}{(-3+x)^2 x^2 \left (21+250 x^2-100 x^3+635 x^4-500 x^5+150 x^6-20 x^7+x^8\right )+2 x \left (-15+5 x-75 x^2+55 x^3-13 x^4+x^5\right ) \log (x)+\log ^2(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(270*x^3 + 1431*x^4 - 828*x^5 - 21016*x^6 + 43992*x^7 - 189668*x^8 + 381578*x^9 - 382272*x^10 + 2217
80*x^11 - 79932*x^12 + 18236*x^13 - 2568*x^14 + 204*x^15 - 7*x^16 + (-18*x^2 - 528*x^3 + 628*x^4 - 240*x^5 - 6
0*x^6 + 168*x^7 - 100*x^8 + 24*x^9 - 2*x^10)*Log[x] + (27*x^2 - 24*x^3 + 5*x^4)*Log[x]^2)/(35721*x^4 - 47628*x
^5 + 874314*x^6 - 1479492*x^7 + 8243811*x^8 - 15734160*x^9 + 39581880*x^10 - 71563680*x^11 + 106612717*x^12 -
141607796*x^13 + 145039298*x^14 - 106050644*x^15 + 55218437*x^16 - 20791560*x^17 + 5728480*x^18 - 1157680*x^19
+ 169971*x^20 - 17668*x^21 + 1234*x^22 - 52*x^23 + x^24 + (-11340*x^3 + 11340*x^4 - 195480*x^5 + 268800*x^6 -
1160748*x^7 + 1862828*x^8 - 3083396*x^9 + 4295684*x^10 - 3745020*x^11 + 2041420*x^12 - 724740*x^13 + 171300*x
^14 - 26848*x^15 + 2688*x^16 - 156*x^17 + 4*x^18)*Log[x] + (1278*x^2 - 852*x^3 + 13642*x^4 - 14400*x^5 + 39390
*x^6 - 50460*x^7 + 29910*x^8 - 9480*x^9 + 1674*x^10 - 156*x^11 + 6*x^12)*Log[x]^2 + (-60*x + 20*x^2 - 300*x^3
+ 220*x^4 - 52*x^5 + 4*x^6)*Log[x]^3 + Log[x]^4),x]

[Out]

((-3 + x)^2*x^3)/((-3 + x)^2*x^2*(21 + 250*x^2 - 100*x^3 + 635*x^4 - 500*x^5 + 150*x^6 - 20*x^7 + x^8) + 2*x*(
-15 + 5*x - 75*x^2 + 55*x^3 - 13*x^4 + x^5)*Log[x] + Log[x]^2)

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fricas [B]  time = 0.58, size = 106, normalized size = 3.21 \begin {gather*} \frac {x^{5} - 6 \, x^{4} + 9 \, x^{3}}{x^{12} - 26 \, x^{11} + 279 \, x^{10} - 1580 \, x^{9} + 4985 \, x^{8} - 8410 \, x^{7} + 6565 \, x^{6} - 2400 \, x^{5} + 2271 \, x^{4} - 126 \, x^{3} + 189 \, x^{2} + 2 \, {\left (x^{6} - 13 \, x^{5} + 55 \, x^{4} - 75 \, x^{3} + 5 \, x^{2} - 15 \, x\right )} \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^4-24*x^3+27*x^2)*log(x)^2+(-2*x^10+24*x^9-100*x^8+168*x^7-60*x^6-240*x^5+628*x^4-528*x^3-18*x^
2)*log(x)-7*x^16+204*x^15-2568*x^14+18236*x^13-79932*x^12+221780*x^11-382272*x^10+381578*x^9-189668*x^8+43992*
x^7-21016*x^6-828*x^5+1431*x^4+270*x^3)/(35721*x^4+874314*x^6-47628*x^5+log(x)^4-1479492*x^7+8243811*x^8+39581
880*x^10-15734160*x^9-106050644*x^15+55218437*x^16-71563680*x^11+106612717*x^12-141607796*x^13+145039298*x^14-
20791560*x^17+169971*x^20-1157680*x^19+5728480*x^18+(4*x^18-156*x^17+2688*x^16-26848*x^15+171300*x^14-724740*x
^13+2041420*x^12-3745020*x^11+4295684*x^10-3083396*x^9+1862828*x^8-1160748*x^7+268800*x^6-195480*x^5+11340*x^4
-11340*x^3)*log(x)+(4*x^6-52*x^5+220*x^4-300*x^3+20*x^2-60*x)*log(x)^3+(6*x^12-156*x^11+1674*x^10-9480*x^9+299
10*x^8-50460*x^7+39390*x^6-14400*x^5+13642*x^4-852*x^3+1278*x^2)*log(x)^2+x^24-52*x^23+1234*x^22-17668*x^21),x
, algorithm="fricas")

[Out]

(x^5 - 6*x^4 + 9*x^3)/(x^12 - 26*x^11 + 279*x^10 - 1580*x^9 + 4985*x^8 - 8410*x^7 + 6565*x^6 - 2400*x^5 + 2271
*x^4 - 126*x^3 + 189*x^2 + 2*(x^6 - 13*x^5 + 55*x^4 - 75*x^3 + 5*x^2 - 15*x)*log(x) + log(x)^2)

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giac [B]  time = 1.74, size = 115, normalized size = 3.48 \begin {gather*} \frac {x^{5} - 6 \, x^{4} + 9 \, x^{3}}{x^{12} - 26 \, x^{11} + 279 \, x^{10} - 1580 \, x^{9} + 4985 \, x^{8} - 8410 \, x^{7} + 2 \, x^{6} \log \relax (x) + 6565 \, x^{6} - 26 \, x^{5} \log \relax (x) - 2400 \, x^{5} + 110 \, x^{4} \log \relax (x) + 2271 \, x^{4} - 150 \, x^{3} \log \relax (x) - 126 \, x^{3} + 10 \, x^{2} \log \relax (x) + 189 \, x^{2} - 30 \, x \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^4-24*x^3+27*x^2)*log(x)^2+(-2*x^10+24*x^9-100*x^8+168*x^7-60*x^6-240*x^5+628*x^4-528*x^3-18*x^
2)*log(x)-7*x^16+204*x^15-2568*x^14+18236*x^13-79932*x^12+221780*x^11-382272*x^10+381578*x^9-189668*x^8+43992*
x^7-21016*x^6-828*x^5+1431*x^4+270*x^3)/(35721*x^4+874314*x^6-47628*x^5+log(x)^4-1479492*x^7+8243811*x^8+39581
880*x^10-15734160*x^9-106050644*x^15+55218437*x^16-71563680*x^11+106612717*x^12-141607796*x^13+145039298*x^14-
20791560*x^17+169971*x^20-1157680*x^19+5728480*x^18+(4*x^18-156*x^17+2688*x^16-26848*x^15+171300*x^14-724740*x
^13+2041420*x^12-3745020*x^11+4295684*x^10-3083396*x^9+1862828*x^8-1160748*x^7+268800*x^6-195480*x^5+11340*x^4
-11340*x^3)*log(x)+(4*x^6-52*x^5+220*x^4-300*x^3+20*x^2-60*x)*log(x)^3+(6*x^12-156*x^11+1674*x^10-9480*x^9+299
10*x^8-50460*x^7+39390*x^6-14400*x^5+13642*x^4-852*x^3+1278*x^2)*log(x)^2+x^24-52*x^23+1234*x^22-17668*x^21),x
, algorithm="giac")

[Out]

(x^5 - 6*x^4 + 9*x^3)/(x^12 - 26*x^11 + 279*x^10 - 1580*x^9 + 4985*x^8 - 8410*x^7 + 2*x^6*log(x) + 6565*x^6 -
26*x^5*log(x) - 2400*x^5 + 110*x^4*log(x) + 2271*x^4 - 150*x^3*log(x) - 126*x^3 + 10*x^2*log(x) + 189*x^2 - 30
*x*log(x) + log(x)^2)

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maple [B]  time = 0.04, size = 113, normalized size = 3.42

method	result	size
risch	\(\frac {x^{3} \left (x^{2}-6 x +9\right )}{x^{12}-26 x^{11}+279 x^{10}-1580 x^{9}+4985 x^{8}+2 x^{6} \ln \relax (x )-8410 x^{7}-26 x^{5} \ln \relax (x )+6565 x^{6}+110 x^{4} \ln \relax (x )-2400 x^{5}-150 x^{3} \ln \relax (x )+2271 x^{4}+10 x^{2} \ln \relax (x )-126 x^{3}+\ln \relax (x )^{2}-30 x \ln \relax (x )+189 x^{2}}\)	\(113\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*x^4-24*x^3+27*x^2)*ln(x)^2+(-2*x^10+24*x^9-100*x^8+168*x^7-60*x^6-240*x^5+628*x^4-528*x^3-18*x^2)*ln(x
)-7*x^16+204*x^15-2568*x^14+18236*x^13-79932*x^12+221780*x^11-382272*x^10+381578*x^9-189668*x^8+43992*x^7-2101
6*x^6-828*x^5+1431*x^4+270*x^3)/(169971*x^20-1157680*x^19+5728480*x^18-20791560*x^17-71563680*x^11+106612717*x
^12-141607796*x^13+145039298*x^14+55218437*x^16-106050644*x^15-1479492*x^7+8243811*x^8+39581880*x^10-15734160*
x^9+ln(x)^4+874314*x^6-47628*x^5+35721*x^4+(4*x^18-156*x^17+2688*x^16-26848*x^15+171300*x^14-724740*x^13+20414
20*x^12-3745020*x^11+4295684*x^10-3083396*x^9+1862828*x^8-1160748*x^7+268800*x^6-195480*x^5+11340*x^4-11340*x^
3)*ln(x)+(4*x^6-52*x^5+220*x^4-300*x^3+20*x^2-60*x)*ln(x)^3+(6*x^12-156*x^11+1674*x^10-9480*x^9+29910*x^8-5046
0*x^7+39390*x^6-14400*x^5+13642*x^4-852*x^3+1278*x^2)*ln(x)^2+x^24-52*x^23+1234*x^22-17668*x^21),x,method=_RET
URNVERBOSE)

[Out]

x^3*(x^2-6*x+9)/(x^12-26*x^11+279*x^10-1580*x^9+4985*x^8+2*x^6*ln(x)-8410*x^7-26*x^5*ln(x)+6565*x^6+110*x^4*ln
(x)-2400*x^5-150*x^3*ln(x)+2271*x^4+10*x^2*ln(x)-126*x^3+ln(x)^2-30*x*ln(x)+189*x^2)

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maxima [B]  time = 0.46, size = 106, normalized size = 3.21 \begin {gather*} \frac {x^{5} - 6 \, x^{4} + 9 \, x^{3}}{x^{12} - 26 \, x^{11} + 279 \, x^{10} - 1580 \, x^{9} + 4985 \, x^{8} - 8410 \, x^{7} + 6565 \, x^{6} - 2400 \, x^{5} + 2271 \, x^{4} - 126 \, x^{3} + 189 \, x^{2} + 2 \, {\left (x^{6} - 13 \, x^{5} + 55 \, x^{4} - 75 \, x^{3} + 5 \, x^{2} - 15 \, x\right )} \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^4-24*x^3+27*x^2)*log(x)^2+(-2*x^10+24*x^9-100*x^8+168*x^7-60*x^6-240*x^5+628*x^4-528*x^3-18*x^
2)*log(x)-7*x^16+204*x^15-2568*x^14+18236*x^13-79932*x^12+221780*x^11-382272*x^10+381578*x^9-189668*x^8+43992*
x^7-21016*x^6-828*x^5+1431*x^4+270*x^3)/(35721*x^4+874314*x^6-47628*x^5+log(x)^4-1479492*x^7+8243811*x^8+39581
880*x^10-15734160*x^9-106050644*x^15+55218437*x^16-71563680*x^11+106612717*x^12-141607796*x^13+145039298*x^14-
20791560*x^17+169971*x^20-1157680*x^19+5728480*x^18+(4*x^18-156*x^17+2688*x^16-26848*x^15+171300*x^14-724740*x
^13+2041420*x^12-3745020*x^11+4295684*x^10-3083396*x^9+1862828*x^8-1160748*x^7+268800*x^6-195480*x^5+11340*x^4
-11340*x^3)*log(x)+(4*x^6-52*x^5+220*x^4-300*x^3+20*x^2-60*x)*log(x)^3+(6*x^12-156*x^11+1674*x^10-9480*x^9+299
10*x^8-50460*x^7+39390*x^6-14400*x^5+13642*x^4-852*x^3+1278*x^2)*log(x)^2+x^24-52*x^23+1234*x^22-17668*x^21),x
, algorithm="maxima")

[Out]

(x^5 - 6*x^4 + 9*x^3)/(x^12 - 26*x^11 + 279*x^10 - 1580*x^9 + 4985*x^8 - 8410*x^7 + 6565*x^6 - 2400*x^5 + 2271
*x^4 - 126*x^3 + 189*x^2 + 2*(x^6 - 13*x^5 + 55*x^4 - 75*x^3 + 5*x^2 - 15*x)*log(x) + log(x)^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \relax (x)\,\left (2\,x^{10}-24\,x^9+100\,x^8-168\,x^7+60\,x^6+240\,x^5-628\,x^4+528\,x^3+18\,x^2\right )-{\ln \relax (x)}^2\,\left (5\,x^4-24\,x^3+27\,x^2\right )-270\,x^3-1431\,x^4+828\,x^5+21016\,x^6-43992\,x^7+189668\,x^8-381578\,x^9+382272\,x^{10}-221780\,x^{11}+79932\,x^{12}-18236\,x^{13}+2568\,x^{14}-204\,x^{15}+7\,x^{16}}{{\ln \relax (x)}^4-\ln \relax (x)\,\left (-4\,x^{18}+156\,x^{17}-2688\,x^{16}+26848\,x^{15}-171300\,x^{14}+724740\,x^{13}-2041420\,x^{12}+3745020\,x^{11}-4295684\,x^{10}+3083396\,x^9-1862828\,x^8+1160748\,x^7-268800\,x^6+195480\,x^5-11340\,x^4+11340\,x^3\right )+{\ln \relax (x)}^2\,\left (6\,x^{12}-156\,x^{11}+1674\,x^{10}-9480\,x^9+29910\,x^8-50460\,x^7+39390\,x^6-14400\,x^5+13642\,x^4-852\,x^3+1278\,x^2\right )+35721\,x^4-47628\,x^5+874314\,x^6-1479492\,x^7+8243811\,x^8-15734160\,x^9+39581880\,x^{10}-71563680\,x^{11}[phone]\,x^{12}-141607796\,x^{13}[phone]\,x^{14}-106050644\,x^{15}[phone]\,x^{16}-20791560\,x^{17}+5728480\,x^{18}-1157680\,x^{19}+169971\,x^{20}-17668\,x^{21}+1234\,x^{22}-52\,x^{23}+x^{24}-{\ln \relax (x)}^3\,\left (-4\,x^6+52\,x^5-220\,x^4+300\,x^3-20\,x^2+60\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)*(18*x^2 + 528*x^3 - 628*x^4 + 240*x^5 + 60*x^6 - 168*x^7 + 100*x^8 - 24*x^9 + 2*x^10) - log(x)^2*
(27*x^2 - 24*x^3 + 5*x^4) - 270*x^3 - 1431*x^4 + 828*x^5 + 21016*x^6 - 43992*x^7 + 189668*x^8 - 381578*x^9 + 3
82272*x^10 - 221780*x^11 + 79932*x^12 - 18236*x^13 + 2568*x^14 - 204*x^15 + 7*x^16)/(log(x)^4 - log(x)*(11340*
x^3 - 11340*x^4 + 195480*x^5 - 268800*x^6 + 1160748*x^7 - 1862828*x^8 + 3083396*x^9 - 4295684*x^10 + 3745020*x
^11 - 2041420*x^12 + 724740*x^13 - 171300*x^14 + 26848*x^15 - 2688*x^16 + 156*x^17 - 4*x^18) + log(x)^2*(1278*
x^2 - 852*x^3 + 13642*x^4 - 14400*x^5 + 39390*x^6 - 50460*x^7 + 29910*x^8 - 9480*x^9 + 1674*x^10 - 156*x^11 +
6*x^12) + 35721*x^4 - 47628*x^5 + 874314*x^6 - 1479492*x^7 + 8243811*x^8 - 15734160*x^9 + 39581880*x^10 - 7156
3680*x^11 + 106612717*x^12 - 141607796*x^13 + 145039298*x^14 - 106050644*x^15 + 55218437*x^16 - 20791560*x^17
+ 5728480*x^18 - 1157680*x^19 + 169971*x^20 - 17668*x^21 + 1234*x^22 - 52*x^23 + x^24 - log(x)^3*(60*x - 20*x^
2 + 300*x^3 - 220*x^4 + 52*x^5 - 4*x^6)),x)

[Out]

int(-(log(x)*(18*x^2 + 528*x^3 - 628*x^4 + 240*x^5 + 60*x^6 - 168*x^7 + 100*x^8 - 24*x^9 + 2*x^10) - log(x)^2*
(27*x^2 - 24*x^3 + 5*x^4) - 270*x^3 - 1431*x^4 + 828*x^5 + 21016*x^6 - 43992*x^7 + 189668*x^8 - 381578*x^9 + 3
82272*x^10 - 221780*x^11 + 79932*x^12 - 18236*x^13 + 2568*x^14 - 204*x^15 + 7*x^16)/(log(x)^4 - log(x)*(11340*
x^3 - 11340*x^4 + 195480*x^5 - 268800*x^6 + 1160748*x^7 - 1862828*x^8 + 3083396*x^9 - 4295684*x^10 + 3745020*x
^11 - 2041420*x^12 + 724740*x^13 - 171300*x^14 + 26848*x^15 - 2688*x^16 + 156*x^17 - 4*x^18) + log(x)^2*(1278*
x^2 - 852*x^3 + 13642*x^4 - 14400*x^5 + 39390*x^6 - 50460*x^7 + 29910*x^8 - 9480*x^9 + 1674*x^10 - 156*x^11 +
6*x^12) + 35721*x^4 - 47628*x^5 + 874314*x^6 - 1479492*x^7 + 8243811*x^8 - 15734160*x^9 + 39581880*x^10 - 7156
3680*x^11 + 106612717*x^12 - 141607796*x^13 + 145039298*x^14 - 106050644*x^15 + 55218437*x^16 - 20791560*x^17
+ 5728480*x^18 - 1157680*x^19 + 169971*x^20 - 17668*x^21 + 1234*x^22 - 52*x^23 + x^24 - log(x)^3*(60*x - 20*x^
2 + 300*x^3 - 220*x^4 + 52*x^5 - 4*x^6)), x)

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sympy [B]  time = 0.55, size = 104, normalized size = 3.15 \begin {gather*} \frac {x^{5} - 6 x^{4} + 9 x^{3}}{x^{12} - 26 x^{11} + 279 x^{10} - 1580 x^{9} + 4985 x^{8} - 8410 x^{7} + 6565 x^{6} - 2400 x^{5} + 2271 x^{4} - 126 x^{3} + 189 x^{2} + \left (2 x^{6} - 26 x^{5} + 110 x^{4} - 150 x^{3} + 10 x^{2} - 30 x\right ) \log {\relax (x )} + \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x**4-24*x**3+27*x**2)*ln(x)**2+(-2*x**10+24*x**9-100*x**8+168*x**7-60*x**6-240*x**5+628*x**4-528
*x**3-18*x**2)*ln(x)-7*x**16+204*x**15-2568*x**14+18236*x**13-79932*x**12+221780*x**11-382272*x**10+381578*x**
9-189668*x**8+43992*x**7-21016*x**6-828*x**5+1431*x**4+270*x**3)/(35721*x**4+874314*x**6-47628*x**5+ln(x)**4-1
479492*x**7+8243811*x**8+39581880*x**10-15734160*x**9-106050644*x**15+55218437*x**16-71563680*x**11+106612717*
x**12-141607796*x**13+145039298*x**14-20791560*x**17+169971*x**20-1157680*x**19+5728480*x**18+(4*x**18-156*x**
17+2688*x**16-26848*x**15+171300*x**14-724740*x**13+2041420*x**12-3745020*x**11+4295684*x**10-3083396*x**9+186
2828*x**8-1160748*x**7+268800*x**6-195480*x**5+11340*x**4-11340*x**3)*ln(x)+(4*x**6-52*x**5+220*x**4-300*x**3+
20*x**2-60*x)*ln(x)**3+(6*x**12-156*x**11+1674*x**10-9480*x**9+29910*x**8-50460*x**7+39390*x**6-14400*x**5+136
42*x**4-852*x**3+1278*x**2)*ln(x)**2+x**24-52*x**23+1234*x**22-17668*x**21),x)

[Out]

(x**5 - 6*x**4 + 9*x**3)/(x**12 - 26*x**11 + 279*x**10 - 1580*x**9 + 4985*x**8 - 8410*x**7 + 6565*x**6 - 2400*
x**5 + 2271*x**4 - 126*x**3 + 189*x**2 + (2*x**6 - 26*x**5 + 110*x**4 - 150*x**3 + 10*x**2 - 30*x)*log(x) + lo
g(x)**2)

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