3.21.94 \(\int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+(2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}) \log (x)+(458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}) \log ^2(x)}{x^8} \, dx\)

Optimal. Leaf size=28 \[ 1-x \left (3+x+\frac {\left (4+x-x^2\right )^4 (3+\log (x))}{x^4}\right )^2 \]

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Rubi [B]  time = 0.99, antiderivative size = 341, normalized size of antiderivative = 12.18, number of steps used = 57, number of rules used = 7, integrand size = 247, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {14, 2357, 2295, 2304, 2301, 2296, 2305} \begin {gather*} -9 x^9+x^9 \left (-\log ^2(x)\right )-6 x^9 \log (x)+72 x^8+8 x^8 \log ^2(x)+48 x^8 \log (x)+36 x^7-\frac {589824}{x^7}+4 x^7 \log ^2(x)-\frac {65536 \log ^2(x)}{x^7}+24 x^7 \log (x)-\frac {393216 \log (x)}{x^7}-1518 x^6-\frac {1179648}{x^6}-168 x^6 \log ^2(x)-\frac {131072 \log ^2(x)}{x^6}-1010 x^6 \log (x)-\frac {786432 \log (x)}{x^6}+1392 x^5+\frac {147456}{x^5}+154 x^5 \log ^2(x)+\frac {16384 \log ^2(x)}{x^5}+926 x^5 \log (x)+\frac {98304 \log (x)}{x^5}+14748 x^4+\frac {1548288}{x^4}+1624 x^4 \log ^2(x)+\frac {172032 \log ^2(x)}{x^4}+9788 x^4 \log (x)+\frac {1032192 \log (x)}{x^4}-18481 x^3+\frac {350208}{x^3}-2044 x^3 \log ^2(x)+\frac {39424 \log ^2(x)}{x^3}-12292 x^3 \log (x)+\frac {235008 \log (x)}{x^3}-87708 x^2-\frac {941568}{x^2}-9624 x^2 \log ^2(x)-\frac {103936 \log ^2(x)}{x^2}-58106 x^2 \log (x)-\frac {625664 \log (x)}{x^2}+102972 x-\frac {292992}{x}+11423 x \log ^2(x)+38496 \log ^2(x)-\frac {32704 \log ^2(x)}{x}+68596 x \log (x)+232352 \log (x)-\frac {195776 \log (x)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3735552 + 6291456*x - 638976*x^2 - 5160960*x^3 - 815616*x^4 + 1257472*x^5 + 97216*x^6 + 232352*x^7 + 1715
68*x^8 - 233522*x^9 - 67735*x^10 + 68780*x^11 + 7886*x^12 - 10118*x^13 + 276*x^14 + 624*x^15 - 87*x^16 + (2621
440 + 4456448*x - 458752*x^2 - 3784704*x^3 - 626176*x^4 + 1043456*x^5 + 130368*x^6 + 76992*x^7 + 91442*x^8 - 1
35460*x^9 - 40964*x^10 + 42400*x^11 + 4938*x^12 - 6396*x^13 + 176*x^14 + 400*x^15 - 56*x^16)*Log[x] + (458752
+ 786432*x - 81920*x^2 - 688128*x^3 - 118272*x^4 + 207872*x^5 + 32704*x^6 + 11423*x^8 - 19248*x^9 - 6132*x^10
+ 6496*x^11 + 770*x^12 - 1008*x^13 + 28*x^14 + 64*x^15 - 9*x^16)*Log[x]^2)/x^8,x]

[Out]

-589824/x^7 - 1179648/x^6 + 147456/x^5 + 1548288/x^4 + 350208/x^3 - 941568/x^2 - 292992/x + 102972*x - 87708*x
^2 - 18481*x^3 + 14748*x^4 + 1392*x^5 - 1518*x^6 + 36*x^7 + 72*x^8 - 9*x^9 + 232352*Log[x] - (393216*Log[x])/x
^7 - (786432*Log[x])/x^6 + (98304*Log[x])/x^5 + (1032192*Log[x])/x^4 + (235008*Log[x])/x^3 - (625664*Log[x])/x
^2 - (195776*Log[x])/x + 68596*x*Log[x] - 58106*x^2*Log[x] - 12292*x^3*Log[x] + 9788*x^4*Log[x] + 926*x^5*Log[
x] - 1010*x^6*Log[x] + 24*x^7*Log[x] + 48*x^8*Log[x] - 6*x^9*Log[x] + 38496*Log[x]^2 - (65536*Log[x]^2)/x^7 -
(131072*Log[x]^2)/x^6 + (16384*Log[x]^2)/x^5 + (172032*Log[x]^2)/x^4 + (39424*Log[x]^2)/x^3 - (103936*Log[x]^2
)/x^2 - (32704*Log[x]^2)/x + 11423*x*Log[x]^2 - 9624*x^2*Log[x]^2 - 2044*x^3*Log[x]^2 + 1624*x^4*Log[x]^2 + 15
4*x^5*Log[x]^2 - 168*x^6*Log[x]^2 + 4*x^7*Log[x]^2 + 8*x^8*Log[x]^2 - x^9*Log[x]^2

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2296

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rule 2301

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2305

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Lo
g[c*x^n])^p)/(d*(m + 1)), x] - Dist[(b*n*p)/(m + 1), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2357

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}}{x^8}-\frac {2 \left (-4-x+x^2\right )^3 \left (20480+19456 x-6656 x^2-6272 x^3+180 x^4-1599 x^5+409 x^6+958 x^7-184 x^8-116 x^9+28 x^{10}\right ) \log (x)}{x^8}-\frac {\left (-4-x+x^2\right )^7 \left (28-x+9 x^2\right ) \log ^2(x)}{x^8}\right ) \, dx\\ &=-\left (2 \int \frac {\left (-4-x+x^2\right )^3 \left (20480+19456 x-6656 x^2-6272 x^3+180 x^4-1599 x^5+409 x^6+958 x^7-184 x^8-116 x^9+28 x^{10}\right ) \log (x)}{x^8} \, dx\right )+\int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}}{x^8} \, dx-\int \frac {\left (-4-x+x^2\right )^7 \left (28-x+9 x^2\right ) \log ^2(x)}{x^8} \, dx\\ &=-\left (2 \int \left (-45721 \log (x)-\frac {1310720 \log (x)}{x^8}-\frac {2228224 \log (x)}{x^7}+\frac {229376 \log (x)}{x^6}+\frac {1892352 \log (x)}{x^5}+\frac {313088 \log (x)}{x^4}-\frac {521728 \log (x)}{x^3}-\frac {65184 \log (x)}{x^2}-\frac {38496 \log (x)}{x}+67730 x \log (x)+20482 x^2 \log (x)-21200 x^3 \log (x)-2469 x^4 \log (x)+3198 x^5 \log (x)-88 x^6 \log (x)-200 x^7 \log (x)+28 x^8 \log (x)\right ) \, dx\right )+\int \left (171568+\frac {3735552}{x^8}+\frac {6291456}{x^7}-\frac {638976}{x^6}-\frac {5160960}{x^5}-\frac {815616}{x^4}+\frac {1257472}{x^3}+\frac {97216}{x^2}+\frac {232352}{x}-233522 x-67735 x^2+68780 x^3+7886 x^4-10118 x^5+276 x^6+624 x^7-87 x^8\right ) \, dx-\int \left (-11423 \log ^2(x)-\frac {458752 \log ^2(x)}{x^8}-\frac {786432 \log ^2(x)}{x^7}+\frac {81920 \log ^2(x)}{x^6}+\frac {688128 \log ^2(x)}{x^5}+\frac {118272 \log ^2(x)}{x^4}-\frac {207872 \log ^2(x)}{x^3}-\frac {32704 \log ^2(x)}{x^2}+19248 x \log ^2(x)+6132 x^2 \log ^2(x)-6496 x^3 \log ^2(x)-770 x^4 \log ^2(x)+1008 x^5 \log ^2(x)-28 x^6 \log ^2(x)-64 x^7 \log ^2(x)+9 x^8 \log ^2(x)\right ) \, dx\\ &=-\frac {3735552}{7 x^7}-\frac {1048576}{x^6}+\frac {638976}{5 x^5}+\frac {1290240}{x^4}+\frac {271872}{x^3}-\frac {628736}{x^2}-\frac {97216}{x}+171568 x-116761 x^2-\frac {67735 x^3}{3}+17195 x^4+\frac {7886 x^5}{5}-\frac {5059 x^6}{3}+\frac {276 x^7}{7}+78 x^8-\frac {29 x^9}{3}+232352 \log (x)-9 \int x^8 \log ^2(x) \, dx+28 \int x^6 \log ^2(x) \, dx-56 \int x^8 \log (x) \, dx+64 \int x^7 \log ^2(x) \, dx+176 \int x^6 \log (x) \, dx+400 \int x^7 \log (x) \, dx+770 \int x^4 \log ^2(x) \, dx-1008 \int x^5 \log ^2(x) \, dx+4938 \int x^4 \log (x) \, dx-6132 \int x^2 \log ^2(x) \, dx-6396 \int x^5 \log (x) \, dx+6496 \int x^3 \log ^2(x) \, dx+11423 \int \log ^2(x) \, dx-19248 \int x \log ^2(x) \, dx+32704 \int \frac {\log ^2(x)}{x^2} \, dx-40964 \int x^2 \log (x) \, dx+42400 \int x^3 \log (x) \, dx+76992 \int \frac {\log (x)}{x} \, dx-81920 \int \frac {\log ^2(x)}{x^6} \, dx+91442 \int \log (x) \, dx-118272 \int \frac {\log ^2(x)}{x^4} \, dx+130368 \int \frac {\log (x)}{x^2} \, dx-135460 \int x \log (x) \, dx+207872 \int \frac {\log ^2(x)}{x^3} \, dx-458752 \int \frac {\log (x)}{x^6} \, dx+458752 \int \frac {\log ^2(x)}{x^8} \, dx-626176 \int \frac {\log (x)}{x^4} \, dx-688128 \int \frac {\log ^2(x)}{x^5} \, dx+786432 \int \frac {\log ^2(x)}{x^7} \, dx+1043456 \int \frac {\log (x)}{x^3} \, dx+2621440 \int \frac {\log (x)}{x^8} \, dx-3784704 \int \frac {\log (x)}{x^5} \, dx+4456448 \int \frac {\log (x)}{x^7} \, dx\\ &=-\frac {28770304}{49 x^7}-\frac {10551296}{9 x^6}+\frac {3653632}{25 x^5}+\frac {1526784}{x^4}+\frac {3073024}{9 x^3}-\frac {889600}{x^2}-\frac {227584}{x}+80126 x-82896 x^2-\frac {162241 x^3}{9}+14545 x^4+\frac {34492 x^5}{25}-\frac {4526 x^6}{3}+\frac {1756 x^7}{49}+\frac {287 x^8}{4}-\frac {727 x^9}{81}+232352 \log (x)-\frac {2621440 \log (x)}{7 x^7}-\frac {2228224 \log (x)}{3 x^6}+\frac {458752 \log (x)}{5 x^5}+\frac {946176 \log (x)}{x^4}+\frac {626176 \log (x)}{3 x^3}-\frac {521728 \log (x)}{x^2}-\frac {130368 \log (x)}{x}+91442 x \log (x)-67730 x^2 \log (x)-\frac {40964}{3} x^3 \log (x)+10600 x^4 \log (x)+\frac {4938}{5} x^5 \log (x)-1066 x^6 \log (x)+\frac {176}{7} x^7 \log (x)+50 x^8 \log (x)-\frac {56}{9} x^9 \log (x)+38496 \log ^2(x)-\frac {65536 \log ^2(x)}{x^7}-\frac {131072 \log ^2(x)}{x^6}+\frac {16384 \log ^2(x)}{x^5}+\frac {172032 \log ^2(x)}{x^4}+\frac {39424 \log ^2(x)}{x^3}-\frac {103936 \log ^2(x)}{x^2}-\frac {32704 \log ^2(x)}{x}+11423 x \log ^2(x)-9624 x^2 \log ^2(x)-2044 x^3 \log ^2(x)+1624 x^4 \log ^2(x)+154 x^5 \log ^2(x)-168 x^6 \log ^2(x)+4 x^7 \log ^2(x)+8 x^8 \log ^2(x)-x^9 \log ^2(x)+2 \int x^8 \log (x) \, dx-8 \int x^6 \log (x) \, dx-16 \int x^7 \log (x) \, dx-308 \int x^4 \log (x) \, dx+336 \int x^5 \log (x) \, dx-3248 \int x^3 \log (x) \, dx+4088 \int x^2 \log (x) \, dx+19248 \int x \log (x) \, dx-22846 \int \log (x) \, dx-32768 \int \frac {\log (x)}{x^6} \, dx+65408 \int \frac {\log (x)}{x^2} \, dx-78848 \int \frac {\log (x)}{x^4} \, dx+131072 \int \frac {\log (x)}{x^8} \, dx+207872 \int \frac {\log (x)}{x^3} \, dx+262144 \int \frac {\log (x)}{x^7} \, dx-344064 \int \frac {\log (x)}{x^5} \, dx\\ &=-\frac {589824}{x^7}-\frac {1179648}{x^6}+\frac {147456}{x^5}+\frac {1548288}{x^4}+\frac {350208}{x^3}-\frac {941568}{x^2}-\frac {292992}{x}+102972 x-87708 x^2-18481 x^3+14748 x^4+1392 x^5-1518 x^6+36 x^7+72 x^8-9 x^9+232352 \log (x)-\frac {393216 \log (x)}{x^7}-\frac {786432 \log (x)}{x^6}+\frac {98304 \log (x)}{x^5}+\frac {1032192 \log (x)}{x^4}+\frac {235008 \log (x)}{x^3}-\frac {625664 \log (x)}{x^2}-\frac {195776 \log (x)}{x}+68596 x \log (x)-58106 x^2 \log (x)-12292 x^3 \log (x)+9788 x^4 \log (x)+926 x^5 \log (x)-1010 x^6 \log (x)+24 x^7 \log (x)+48 x^8 \log (x)-6 x^9 \log (x)+38496 \log ^2(x)-\frac {65536 \log ^2(x)}{x^7}-\frac {131072 \log ^2(x)}{x^6}+\frac {16384 \log ^2(x)}{x^5}+\frac {172032 \log ^2(x)}{x^4}+\frac {39424 \log ^2(x)}{x^3}-\frac {103936 \log ^2(x)}{x^2}-\frac {32704 \log ^2(x)}{x}+11423 x \log ^2(x)-9624 x^2 \log ^2(x)-2044 x^3 \log ^2(x)+1624 x^4 \log ^2(x)+154 x^5 \log ^2(x)-168 x^6 \log ^2(x)+4 x^7 \log ^2(x)+8 x^8 \log ^2(x)-x^9 \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.12, size = 149, normalized size = 5.32 \begin {gather*} -\frac {589824+1179648 x-147456 x^2-1548288 x^3-350208 x^4+941568 x^5+292992 x^6-102972 x^8+87708 x^9+18481 x^{10}-14748 x^{11}-1392 x^{12}+1518 x^{13}-36 x^{14}-72 x^{15}+9 x^{16}+2 \left (4+x-x^2\right )^4 \left (768+768 x-480 x^2-528 x^3+150 x^4+133 x^5-30 x^6-12 x^7+3 x^8\right ) \log (x)+\left (4+x-x^2\right )^8 \log ^2(x)}{x^7} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3735552 + 6291456*x - 638976*x^2 - 5160960*x^3 - 815616*x^4 + 1257472*x^5 + 97216*x^6 + 232352*x^7
+ 171568*x^8 - 233522*x^9 - 67735*x^10 + 68780*x^11 + 7886*x^12 - 10118*x^13 + 276*x^14 + 624*x^15 - 87*x^16 +
(2621440 + 4456448*x - 458752*x^2 - 3784704*x^3 - 626176*x^4 + 1043456*x^5 + 130368*x^6 + 76992*x^7 + 91442*x
^8 - 135460*x^9 - 40964*x^10 + 42400*x^11 + 4938*x^12 - 6396*x^13 + 176*x^14 + 400*x^15 - 56*x^16)*Log[x] + (4
58752 + 786432*x - 81920*x^2 - 688128*x^3 - 118272*x^4 + 207872*x^5 + 32704*x^6 + 11423*x^8 - 19248*x^9 - 6132
*x^10 + 6496*x^11 + 770*x^12 - 1008*x^13 + 28*x^14 + 64*x^15 - 9*x^16)*Log[x]^2)/x^8,x]

[Out]

-((589824 + 1179648*x - 147456*x^2 - 1548288*x^3 - 350208*x^4 + 941568*x^5 + 292992*x^6 - 102972*x^8 + 87708*x
^9 + 18481*x^10 - 14748*x^11 - 1392*x^12 + 1518*x^13 - 36*x^14 - 72*x^15 + 9*x^16 + 2*(4 + x - x^2)^4*(768 + 7
68*x - 480*x^2 - 528*x^3 + 150*x^4 + 133*x^5 - 30*x^6 - 12*x^7 + 3*x^8)*Log[x] + (4 + x - x^2)^8*Log[x]^2)/x^7
)

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fricas [B]  time = 0.76, size = 247, normalized size = 8.82 \begin {gather*} -\frac {9 \, x^{16} - 72 \, x^{15} - 36 \, x^{14} + 1518 \, x^{13} - 1392 \, x^{12} - 14748 \, x^{11} + 18481 \, x^{10} + 87708 \, x^{9} - 102972 \, x^{8} + 292992 \, x^{6} + 941568 \, x^{5} - 350208 \, x^{4} - 1548288 \, x^{3} + {\left (x^{16} - 8 \, x^{15} - 4 \, x^{14} + 168 \, x^{13} - 154 \, x^{12} - 1624 \, x^{11} + 2044 \, x^{10} + 9624 \, x^{9} - 11423 \, x^{8} - 38496 \, x^{7} + 32704 \, x^{6} + 103936 \, x^{5} - 39424 \, x^{4} - 172032 \, x^{3} - 16384 \, x^{2} + 131072 \, x + 65536\right )} \log \relax (x)^{2} - 147456 \, x^{2} + 2 \, {\left (3 \, x^{16} - 24 \, x^{15} - 12 \, x^{14} + 505 \, x^{13} - 463 \, x^{12} - 4894 \, x^{11} + 6146 \, x^{10} + 29053 \, x^{9} - 34298 \, x^{8} - 116176 \, x^{7} + 97888 \, x^{6} + 312832 \, x^{5} - 117504 \, x^{4} - 516096 \, x^{3} - 49152 \, x^{2} + 393216 \, x + 196608\right )} \log \relax (x) + 1179648 \, x + 589824}{x^{7}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10-19248*x^9+11423*x^8+32704*x^6+20787
2*x^5-118272*x^4-688128*x^3-81920*x^2+786432*x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^1
2+42400*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^5-626176*x^4-3784704*x^3-458752*x^
2+4456448*x+2621440)*log(x)-87*x^16+624*x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+17
1568*x^8+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+6291456*x+3735552)/x^8,x, algorith
m="fricas")

[Out]

-(9*x^16 - 72*x^15 - 36*x^14 + 1518*x^13 - 1392*x^12 - 14748*x^11 + 18481*x^10 + 87708*x^9 - 102972*x^8 + 2929
92*x^6 + 941568*x^5 - 350208*x^4 - 1548288*x^3 + (x^16 - 8*x^15 - 4*x^14 + 168*x^13 - 154*x^12 - 1624*x^11 + 2
044*x^10 + 9624*x^9 - 11423*x^8 - 38496*x^7 + 32704*x^6 + 103936*x^5 - 39424*x^4 - 172032*x^3 - 16384*x^2 + 13
1072*x + 65536)*log(x)^2 - 147456*x^2 + 2*(3*x^16 - 24*x^15 - 12*x^14 + 505*x^13 - 463*x^12 - 4894*x^11 + 6146
*x^10 + 29053*x^9 - 34298*x^8 - 116176*x^7 + 97888*x^6 + 312832*x^5 - 117504*x^4 - 516096*x^3 - 49152*x^2 + 39
3216*x + 196608)*log(x) + 1179648*x + 589824)/x^7

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {87 \, x^{16} - 624 \, x^{15} - 276 \, x^{14} + 10118 \, x^{13} - 7886 \, x^{12} - 68780 \, x^{11} + 67735 \, x^{10} + 233522 \, x^{9} - 171568 \, x^{8} - 232352 \, x^{7} - 97216 \, x^{6} - 1257472 \, x^{5} + 815616 \, x^{4} + 5160960 \, x^{3} + {\left (9 \, x^{16} - 64 \, x^{15} - 28 \, x^{14} + 1008 \, x^{13} - 770 \, x^{12} - 6496 \, x^{11} + 6132 \, x^{10} + 19248 \, x^{9} - 11423 \, x^{8} - 32704 \, x^{6} - 207872 \, x^{5} + 118272 \, x^{4} + 688128 \, x^{3} + 81920 \, x^{2} - 786432 \, x - 458752\right )} \log \relax (x)^{2} + 638976 \, x^{2} + 2 \, {\left (28 \, x^{16} - 200 \, x^{15} - 88 \, x^{14} + 3198 \, x^{13} - 2469 \, x^{12} - 21200 \, x^{11} + 20482 \, x^{10} + 67730 \, x^{9} - 45721 \, x^{8} - 38496 \, x^{7} - 65184 \, x^{6} - 521728 \, x^{5} + 313088 \, x^{4} + 1892352 \, x^{3} + 229376 \, x^{2} - 2228224 \, x - 1310720\right )} \log \relax (x) - 6291456 \, x - 3735552}{x^{8}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10-19248*x^9+11423*x^8+32704*x^6+20787
2*x^5-118272*x^4-688128*x^3-81920*x^2+786432*x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^1
2+42400*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^5-626176*x^4-3784704*x^3-458752*x^
2+4456448*x+2621440)*log(x)-87*x^16+624*x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+17
1568*x^8+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+6291456*x+3735552)/x^8,x, algorith
m="giac")

[Out]

integrate(-(87*x^16 - 624*x^15 - 276*x^14 + 10118*x^13 - 7886*x^12 - 68780*x^11 + 67735*x^10 + 233522*x^9 - 17
1568*x^8 - 232352*x^7 - 97216*x^6 - 1257472*x^5 + 815616*x^4 + 5160960*x^3 + (9*x^16 - 64*x^15 - 28*x^14 + 100
8*x^13 - 770*x^12 - 6496*x^11 + 6132*x^10 + 19248*x^9 - 11423*x^8 - 32704*x^6 - 207872*x^5 + 118272*x^4 + 6881
28*x^3 + 81920*x^2 - 786432*x - 458752)*log(x)^2 + 638976*x^2 + 2*(28*x^16 - 200*x^15 - 88*x^14 + 3198*x^13 -
2469*x^12 - 21200*x^11 + 20482*x^10 + 67730*x^9 - 45721*x^8 - 38496*x^7 - 65184*x^6 - 521728*x^5 + 313088*x^4
+ 1892352*x^3 + 229376*x^2 - 2228224*x - 1310720)*log(x) - 6291456*x - 3735552)/x^8, x)

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maple [B]  time = 0.04, size = 257, normalized size = 9.18

method	result	size
risch	\(-\frac {\left (x^{16}-8 x^{15}-4 x^{14}+168 x^{13}-154 x^{12}-1624 x^{11}+2044 x^{10}+9624 x^{9}-11423 x^{8}-38496 x^{7}+32704 x^{6}+103936 x^{5}-39424 x^{4}-172032 x^{3}-16384 x^{2}+131072 x +65536\right ) \ln \relax (x )^{2}}{x^{7}}-\frac {2 \left (3 x^{16}-24 x^{15}-12 x^{14}+505 x^{13}-463 x^{12}-4894 x^{11}+6146 x^{10}+29053 x^{9}-34298 x^{8}+97888 x^{6}+312832 x^{5}-117504 x^{4}-516096 x^{3}-49152 x^{2}+393216 x +196608\right ) \ln \relax (x )}{x^{7}}+\frac {-9 x^{16}+72 x^{15}+36 x^{14}-1518 x^{13}+1392 x^{12}+14748 x^{11}-18481 x^{10}-87708 x^{9}+232352 x^{7} \ln \relax (x )+102972 x^{8}-292992 x^{6}-941568 x^{5}+350208 x^{4}+1548288 x^{3}+147456 x^{2}-1179648 x -589824}{x^{7}}\)	\(257\)
default	\(102972 x -x^{9} \ln \relax (x )^{2}-58106 x^{2} \ln \relax (x )+4 x^{7} \ln \relax (x )^{2}-6 x^{9} \ln \relax (x )+\frac {1548288}{x^{4}}+\frac {147456}{x^{5}}-9624 x^{2} \ln \relax (x )^{2}-\frac {195776 \ln \relax (x )}{x}-9 x^{9}+36 x^{7}+72 x^{8}+232352 \ln \relax (x )+38496 \ln \relax (x )^{2}+14748 x^{4}-18481 x^{3}-87708 x^{2}-1518 x^{6}+1392 x^{5}-12292 x^{3} \ln \relax (x )+8 x^{8} \ln \relax (x )^{2}-168 x^{6} \ln \relax (x )^{2}-1010 x^{6} \ln \relax (x )+24 x^{7} \ln \relax (x )-\frac {625664 \ln \relax (x )}{x^{2}}-\frac {32704 \ln \relax (x )^{2}}{x}+926 x^{5} \ln \relax (x )+1624 x^{4} \ln \relax (x )^{2}-\frac {1179648}{x^{6}}+48 x^{8} \ln \relax (x )+9788 x^{4} \ln \relax (x )+11423 x \ln \relax (x )^{2}+68596 x \ln \relax (x )-\frac {941568}{x^{2}}-\frac {292992}{x}+\frac {39424 \ln \relax (x )^{2}}{x^{3}}+\frac {172032 \ln \relax (x )^{2}}{x^{4}}+\frac {1032192 \ln \relax (x )}{x^{4}}+154 x^{5} \ln \relax (x )^{2}-\frac {103936 \ln \relax (x )^{2}}{x^{2}}+\frac {350208}{x^{3}}-2044 x^{3} \ln \relax (x )^{2}+\frac {235008 \ln \relax (x )}{x^{3}}-\frac {589824}{x^{7}}+\frac {16384 \ln \relax (x )^{2}}{x^{5}}-\frac {786432 \ln \relax (x )}{x^{6}}-\frac {131072 \ln \relax (x )^{2}}{x^{6}}+\frac {98304 \ln \relax (x )}{x^{5}}-\frac {65536 \ln \relax (x )^{2}}{x^{7}}-\frac {393216 \ln \relax (x )}{x^{7}}\)	\(342\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10-19248*x^9+11423*x^8+32704*x^6+207872*x^5-
118272*x^4-688128*x^3-81920*x^2+786432*x+458752)*ln(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^12+42400
*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^5-626176*x^4-3784704*x^3-458752*x^2+44564
48*x+2621440)*ln(x)-87*x^16+624*x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+171568*x^8
+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+6291456*x+3735552)/x^8,x,method=_RETURNVER
BOSE)

[Out]

-(x^16-8*x^15-4*x^14+168*x^13-154*x^12-1624*x^11+2044*x^10+9624*x^9-11423*x^8-38496*x^7+32704*x^6+103936*x^5-3
9424*x^4-172032*x^3-16384*x^2+131072*x+65536)/x^7*ln(x)^2-2*(3*x^16-24*x^15-12*x^14+505*x^13-463*x^12-4894*x^1
1+6146*x^10+29053*x^9-34298*x^8+97888*x^6+312832*x^5-117504*x^4-516096*x^3-49152*x^2+393216*x+196608)/x^7*ln(x
)+(-9*x^16+72*x^15+36*x^14-1518*x^13+1392*x^12+14748*x^11-18481*x^10-87708*x^9+232352*x^7*ln(x)+102972*x^8-292
992*x^6-941568*x^5+350208*x^4+1548288*x^3+147456*x^2-1179648*x-589824)/x^7

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maxima [B]  time = 0.49, size = 465, normalized size = 16.61 \begin {gather*} -\frac {1}{81} \, {\left (81 \, \log \relax (x)^{2} - 18 \, \log \relax (x) + 2\right )} x^{9} - \frac {56}{9} \, x^{9} \log \relax (x) + \frac {1}{4} \, {\left (32 \, \log \relax (x)^{2} - 8 \, \log \relax (x) + 1\right )} x^{8} - \frac {727}{81} \, x^{9} + 50 \, x^{8} \log \relax (x) + \frac {4}{49} \, {\left (49 \, \log \relax (x)^{2} - 14 \, \log \relax (x) + 2\right )} x^{7} + \frac {287}{4} \, x^{8} + \frac {176}{7} \, x^{7} \log \relax (x) - \frac {28}{3} \, {\left (18 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 1\right )} x^{6} + \frac {1756}{49} \, x^{7} - 1066 \, x^{6} \log \relax (x) + \frac {154}{25} \, {\left (25 \, \log \relax (x)^{2} - 10 \, \log \relax (x) + 2\right )} x^{5} - \frac {4526}{3} \, x^{6} + \frac {4938}{5} \, x^{5} \log \relax (x) + 203 \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} + \frac {34492}{25} \, x^{5} + 10600 \, x^{4} \log \relax (x) - \frac {2044}{9} \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} + 14545 \, x^{4} - \frac {40964}{3} \, x^{3} \log \relax (x) - 4812 \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} - \frac {162241}{9} \, x^{3} - 67730 \, x^{2} \log \relax (x) + 11423 \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x - 82896 \, x^{2} + 91442 \, x \log \relax (x) + 38496 \, \log \relax (x)^{2} + 80126 \, x - \frac {32704 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 2\right )}}{x} - \frac {130368 \, \log \relax (x)}{x} - \frac {51968 \, {\left (2 \, \log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )}}{x^{2}} - \frac {227584}{x} - \frac {521728 \, \log \relax (x)}{x^{2}} + \frac {39424 \, {\left (9 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 2\right )}}{9 \, x^{3}} - \frac {889600}{x^{2}} + \frac {626176 \, \log \relax (x)}{3 \, x^{3}} + \frac {21504 \, {\left (8 \, \log \relax (x)^{2} + 4 \, \log \relax (x) + 1\right )}}{x^{4}} + \frac {3073024}{9 \, x^{3}} + \frac {946176 \, \log \relax (x)}{x^{4}} + \frac {16384 \, {\left (25 \, \log \relax (x)^{2} + 10 \, \log \relax (x) + 2\right )}}{25 \, x^{5}} + \frac {1526784}{x^{4}} + \frac {458752 \, \log \relax (x)}{5 \, x^{5}} - \frac {65536 \, {\left (18 \, \log \relax (x)^{2} + 6 \, \log \relax (x) + 1\right )}}{9 \, x^{6}} + \frac {3653632}{25 \, x^{5}} - \frac {2228224 \, \log \relax (x)}{3 \, x^{6}} - \frac {65536 \, {\left (49 \, \log \relax (x)^{2} + 14 \, \log \relax (x) + 2\right )}}{49 \, x^{7}} - \frac {10551296}{9 \, x^{6}} - \frac {2621440 \, \log \relax (x)}{7 \, x^{7}} - \frac {28770304}{49 \, x^{7}} + 232352 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10-19248*x^9+11423*x^8+32704*x^6+20787
2*x^5-118272*x^4-688128*x^3-81920*x^2+786432*x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^1
2+42400*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^5-626176*x^4-3784704*x^3-458752*x^
2+4456448*x+2621440)*log(x)-87*x^16+624*x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+17
1568*x^8+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+6291456*x+3735552)/x^8,x, algorith
m="maxima")

[Out]

-1/81*(81*log(x)^2 - 18*log(x) + 2)*x^9 - 56/9*x^9*log(x) + 1/4*(32*log(x)^2 - 8*log(x) + 1)*x^8 - 727/81*x^9
+ 50*x^8*log(x) + 4/49*(49*log(x)^2 - 14*log(x) + 2)*x^7 + 287/4*x^8 + 176/7*x^7*log(x) - 28/3*(18*log(x)^2 -
6*log(x) + 1)*x^6 + 1756/49*x^7 - 1066*x^6*log(x) + 154/25*(25*log(x)^2 - 10*log(x) + 2)*x^5 - 4526/3*x^6 + 49
38/5*x^5*log(x) + 203*(8*log(x)^2 - 4*log(x) + 1)*x^4 + 34492/25*x^5 + 10600*x^4*log(x) - 2044/9*(9*log(x)^2 -
6*log(x) + 2)*x^3 + 14545*x^4 - 40964/3*x^3*log(x) - 4812*(2*log(x)^2 - 2*log(x) + 1)*x^2 - 162241/9*x^3 - 67
730*x^2*log(x) + 11423*(log(x)^2 - 2*log(x) + 2)*x - 82896*x^2 + 91442*x*log(x) + 38496*log(x)^2 + 80126*x - 3
2704*(log(x)^2 + 2*log(x) + 2)/x - 130368*log(x)/x - 51968*(2*log(x)^2 + 2*log(x) + 1)/x^2 - 227584/x - 521728
*log(x)/x^2 + 39424/9*(9*log(x)^2 + 6*log(x) + 2)/x^3 - 889600/x^2 + 626176/3*log(x)/x^3 + 21504*(8*log(x)^2 +
4*log(x) + 1)/x^4 + 3073024/9/x^3 + 946176*log(x)/x^4 + 16384/25*(25*log(x)^2 + 10*log(x) + 2)/x^5 + 1526784/
x^4 + 458752/5*log(x)/x^5 - 65536/9*(18*log(x)^2 + 6*log(x) + 1)/x^6 + 3653632/25/x^5 - 2228224/3*log(x)/x^6 -
65536/49*(49*log(x)^2 + 14*log(x) + 2)/x^7 - 10551296/9/x^6 - 2621440/7*log(x)/x^7 - 28770304/49/x^7 + 232352
*log(x)

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mupad [B]  time = 1.56, size = 255, normalized size = 9.11 \begin {gather*} 102972\,x+\frac {15119344\,\ln \relax (x)}{35}-{\ln \relax (x)}^2\,\left (\frac {x^{16}-8\,x^{15}-4\,x^{14}+168\,x^{13}-154\,x^{12}-1624\,x^{11}+2044\,x^{10}+9624\,x^9-11423\,x^8+32704\,x^6+103936\,x^5-39424\,x^4-172032\,x^3-16384\,x^2+131072\,x+65536}{x^7}-38496\right )-\frac {292992\,x^6+941568\,x^5-350208\,x^4-1548288\,x^3-147456\,x^2+1179648\,x+589824}{x^7}-87708\,x^2-18481\,x^3+14748\,x^4+1392\,x^5-1518\,x^6+36\,x^7+72\,x^8-9\,x^9-\frac {\ln \relax (x)\,\left (6\,x^{16}-48\,x^{15}-24\,x^{14}+1010\,x^{13}-926\,x^{12}-9788\,x^{11}+12292\,x^{10}+58106\,x^9-68596\,x^8+\frac {6987024\,x^7}{35}+195776\,x^6+625664\,x^5-235008\,x^4-1032192\,x^3-98304\,x^2+786432\,x+393216\right )}{x^7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6291456*x + log(x)*(4456448*x - 458752*x^2 - 3784704*x^3 - 626176*x^4 + 1043456*x^5 + 130368*x^6 + 76992*
x^7 + 91442*x^8 - 135460*x^9 - 40964*x^10 + 42400*x^11 + 4938*x^12 - 6396*x^13 + 176*x^14 + 400*x^15 - 56*x^16
+ 2621440) - 638976*x^2 - 5160960*x^3 - 815616*x^4 + 1257472*x^5 + 97216*x^6 + 232352*x^7 + 171568*x^8 - 2335
22*x^9 - 67735*x^10 + 68780*x^11 + 7886*x^12 - 10118*x^13 + 276*x^14 + 624*x^15 - 87*x^16 + log(x)^2*(786432*x
- 81920*x^2 - 688128*x^3 - 118272*x^4 + 207872*x^5 + 32704*x^6 + 11423*x^8 - 19248*x^9 - 6132*x^10 + 6496*x^1
1 + 770*x^12 - 1008*x^13 + 28*x^14 + 64*x^15 - 9*x^16 + 458752) + 3735552)/x^8,x)

[Out]

102972*x + (15119344*log(x))/35 - log(x)^2*((131072*x - 16384*x^2 - 172032*x^3 - 39424*x^4 + 103936*x^5 + 3270
4*x^6 - 11423*x^8 + 9624*x^9 + 2044*x^10 - 1624*x^11 - 154*x^12 + 168*x^13 - 4*x^14 - 8*x^15 + x^16 + 65536)/x
^7 - 38496) - (1179648*x - 147456*x^2 - 1548288*x^3 - 350208*x^4 + 941568*x^5 + 292992*x^6 + 589824)/x^7 - 877
08*x^2 - 18481*x^3 + 14748*x^4 + 1392*x^5 - 1518*x^6 + 36*x^7 + 72*x^8 - 9*x^9 - (log(x)*(786432*x - 98304*x^2
- 1032192*x^3 - 235008*x^4 + 625664*x^5 + 195776*x^6 + (6987024*x^7)/35 - 68596*x^8 + 58106*x^9 + 12292*x^10
- 9788*x^11 - 926*x^12 + 1010*x^13 - 24*x^14 - 48*x^15 + 6*x^16 + 393216))/x^7

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sympy [B]  time = 0.59, size = 253, normalized size = 9.04 \begin {gather*} - 9 x^{9} + 72 x^{8} + 36 x^{7} - 1518 x^{6} + 1392 x^{5} + 14748 x^{4} - 18481 x^{3} - 87708 x^{2} + 102972 x + 232352 \log {\relax (x )} - \frac {292992 x^{6} + 941568 x^{5} - 350208 x^{4} - 1548288 x^{3} - 147456 x^{2} + 1179648 x + 589824}{x^{7}} + \frac {\left (- 6 x^{16} + 48 x^{15} + 24 x^{14} - 1010 x^{13} + 926 x^{12} + 9788 x^{11} - 12292 x^{10} - 58106 x^{9} + 68596 x^{8} - 195776 x^{6} - 625664 x^{5} + 235008 x^{4} + 1032192 x^{3} + 98304 x^{2} - 786432 x - 393216\right ) \log {\relax (x )}}{x^{7}} + \frac {\left (- x^{16} + 8 x^{15} + 4 x^{14} - 168 x^{13} + 154 x^{12} + 1624 x^{11} - 2044 x^{10} - 9624 x^{9} + 11423 x^{8} + 38496 x^{7} - 32704 x^{6} - 103936 x^{5} + 39424 x^{4} + 172032 x^{3} + 16384 x^{2} - 131072 x - 65536\right ) \log {\relax (x )}^{2}}{x^{7}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*x**16+64*x**15+28*x**14-1008*x**13+770*x**12+6496*x**11-6132*x**10-19248*x**9+11423*x**8+32704*
x**6+207872*x**5-118272*x**4-688128*x**3-81920*x**2+786432*x+458752)*ln(x)**2+(-56*x**16+400*x**15+176*x**14-6
396*x**13+4938*x**12+42400*x**11-40964*x**10-135460*x**9+91442*x**8+76992*x**7+130368*x**6+1043456*x**5-626176
*x**4-3784704*x**3-458752*x**2+4456448*x+2621440)*ln(x)-87*x**16+624*x**15+276*x**14-10118*x**13+7886*x**12+68
780*x**11-67735*x**10-233522*x**9+171568*x**8+232352*x**7+97216*x**6+1257472*x**5-815616*x**4-5160960*x**3-638
976*x**2+6291456*x+3735552)/x**8,x)

[Out]

-9*x**9 + 72*x**8 + 36*x**7 - 1518*x**6 + 1392*x**5 + 14748*x**4 - 18481*x**3 - 87708*x**2 + 102972*x + 232352
*log(x) - (292992*x**6 + 941568*x**5 - 350208*x**4 - 1548288*x**3 - 147456*x**2 + 1179648*x + 589824)/x**7 + (
-6*x**16 + 48*x**15 + 24*x**14 - 1010*x**13 + 926*x**12 + 9788*x**11 - 12292*x**10 - 58106*x**9 + 68596*x**8 -
195776*x**6 - 625664*x**5 + 235008*x**4 + 1032192*x**3 + 98304*x**2 - 786432*x - 393216)*log(x)/x**7 + (-x**1
6 + 8*x**15 + 4*x**14 - 168*x**13 + 154*x**12 + 1624*x**11 - 2044*x**10 - 9624*x**9 + 11423*x**8 + 38496*x**7
- 32704*x**6 - 103936*x**5 + 39424*x**4 + 172032*x**3 + 16384*x**2 - 131072*x - 65536)*log(x)**2/x**7

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