Integrand size = 13, antiderivative size = 151 \[ \int x^m \left (a+b x^3\right )^8 \, dx=\frac {a^8 x^{1+m}}{1+m}+\frac {8 a^7 b x^{4+m}}{4+m}+\frac {28 a^6 b^2 x^{7+m}}{7+m}+\frac {56 a^5 b^3 x^{10+m}}{10+m}+\frac {70 a^4 b^4 x^{13+m}}{13+m}+\frac {56 a^3 b^5 x^{16+m}}{16+m}+\frac {28 a^2 b^6 x^{19+m}}{19+m}+\frac {8 a b^7 x^{22+m}}{22+m}+\frac {b^8 x^{25+m}}{25+m} \]
a^8*x^(1+m)/(1+m)+8*a^7*b*x^(4+m)/(4+m)+28*a^6*b^2*x^(7+m)/(7+m)+56*a^5*b^ 3*x^(10+m)/(10+m)+70*a^4*b^4*x^(13+m)/(13+m)+56*a^3*b^5*x^(16+m)/(16+m)+28 *a^2*b^6*x^(19+m)/(19+m)+8*a*b^7*x^(22+m)/(22+m)+b^8*x^(25+m)/(25+m)
Time = 0.38 (sec) , antiderivative size = 136, normalized size of antiderivative = 0.90 \[ \int x^m \left (a+b x^3\right )^8 \, dx=x^{1+m} \left (\frac {a^8}{1+m}+\frac {8 a^7 b x^3}{4+m}+\frac {28 a^6 b^2 x^6}{7+m}+\frac {56 a^5 b^3 x^9}{10+m}+\frac {70 a^4 b^4 x^{12}}{13+m}+\frac {56 a^3 b^5 x^{15}}{16+m}+\frac {28 a^2 b^6 x^{18}}{19+m}+\frac {8 a b^7 x^{21}}{22+m}+\frac {b^8 x^{24}}{25+m}\right ) \]
x^(1 + m)*(a^8/(1 + m) + (8*a^7*b*x^3)/(4 + m) + (28*a^6*b^2*x^6)/(7 + m) + (56*a^5*b^3*x^9)/(10 + m) + (70*a^4*b^4*x^12)/(13 + m) + (56*a^3*b^5*x^1 5)/(16 + m) + (28*a^2*b^6*x^18)/(19 + m) + (8*a*b^7*x^21)/(22 + m) + (b^8* x^24)/(25 + m))
Time = 0.30 (sec) , antiderivative size = 151, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {802, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int x^m \left (a+b x^3\right )^8 \, dx\) |
\(\Big \downarrow \) 802 |
\(\displaystyle \int \left (a^8 x^m+8 a^7 b x^{m+3}+28 a^6 b^2 x^{m+6}+56 a^5 b^3 x^{m+9}+70 a^4 b^4 x^{m+12}+56 a^3 b^5 x^{m+15}+28 a^2 b^6 x^{m+18}+8 a b^7 x^{m+21}+b^8 x^{m+24}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {a^8 x^{m+1}}{m+1}+\frac {8 a^7 b x^{m+4}}{m+4}+\frac {28 a^6 b^2 x^{m+7}}{m+7}+\frac {56 a^5 b^3 x^{m+10}}{m+10}+\frac {70 a^4 b^4 x^{m+13}}{m+13}+\frac {56 a^3 b^5 x^{m+16}}{m+16}+\frac {28 a^2 b^6 x^{m+19}}{m+19}+\frac {8 a b^7 x^{m+22}}{m+22}+\frac {b^8 x^{m+25}}{m+25}\) |
(a^8*x^(1 + m))/(1 + m) + (8*a^7*b*x^(4 + m))/(4 + m) + (28*a^6*b^2*x^(7 + m))/(7 + m) + (56*a^5*b^3*x^(10 + m))/(10 + m) + (70*a^4*b^4*x^(13 + m))/ (13 + m) + (56*a^3*b^5*x^(16 + m))/(16 + m) + (28*a^2*b^6*x^(19 + m))/(19 + m) + (8*a*b^7*x^(22 + m))/(22 + m) + (b^8*x^(25 + m))/(25 + m)
3.6.83.3.1 Defintions of rubi rules used
Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_.), x_Symbol] :> Int[Exp andIntegrand[(c*x)^m*(a + b*x^n)^p, x], x] /; FreeQ[{a, b, c, m, n}, x] && IGtQ[p, 0]
Leaf count of result is larger than twice the leaf count of optimal. \(1021\) vs. \(2(151)=302\).
Time = 5.81 (sec) , antiderivative size = 1022, normalized size of antiderivative = 6.77
method | result | size |
risch | \(\text {Expression too large to display}\) | \(1022\) |
gosper | \(\text {Expression too large to display}\) | \(1023\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1270\) |
x*(b^8*m^8*x^24+92*b^8*m^7*x^24+3514*b^8*m^6*x^24+8*a*b^7*m^8*x^21+72128*b ^8*m^5*x^24+760*a*b^7*m^7*x^21+859369*b^8*m^4*x^24+29792*a*b^7*m^6*x^21+59 74388*b^8*m^3*x^24+28*a^2*b^6*m^8*x^18+624400*a*b^7*m^5*x^21+22963996*b^8* m^2*x^24+2744*a^2*b^6*m^7*x^18+7563752*a*b^7*m^4*x^21+42124592*b^8*m*x^24+ 110656*a^2*b^6*m^6*x^18+53266360*a*b^7*m^3*x^21+24344320*b^8*x^24+56*a^3*b ^5*m^8*x^15+2376920*a^2*b^6*m^5*x^18+206729648*a*b^7*m^2*x^21+5656*a^3*b^5 *m^7*x^15+29390452*a^2*b^6*m^4*x^18+381743680*a*b^7*m*x^21+235088*a^3*b^5* m^6*x^15+210422576*a^2*b^6*m^3*x^18+221312000*a*b^7*x^21+70*a^4*b^4*m^8*x^ 12+5197360*a^3*b^5*m^5*x^15+827034544*a^2*b^6*m^2*x^18+7280*a^4*b^4*m^7*x^ 12+65946104*a^3*b^5*m^4*x^15+1540629440*a^2*b^6*m*x^18+312340*a^4*b^4*m^6* x^12+482544664*a^3*b^5*m^3*x^15+896896000*a^2*b^6*x^18+56*a^5*b^3*m^8*x^9+ 7138040*a^4*b^4*m^5*x^12+1929412352*a^3*b^5*m^2*x^15+5992*a^5*b^3*m^7*x^9+ 93585310*a^4*b^4*m^4*x^12+3637973920*a^3*b^5*m*x^15+265664*a^5*b^3*m^6*x^9 +705493880*a^4*b^4*m^3*x^12+2130128000*a^3*b^5*x^15+28*a^6*b^2*m^8*x^6+630 2128*a^5*b^3*m^5*x^9+2891238280*a^4*b^4*m^2*x^12+3080*a^6*b^2*m^7*x^6+8608 2584*a^5*b^3*m^4*x^9+5549616800*a^4*b^4*m*x^12+141232*a^6*b^2*m^6*x^6+6768 56488*a^5*b^3*m^3*x^9+3277120000*a^4*b^4*x^12+8*a^7*b*m^8*x^3+3490760*a^6* b^2*m^5*x^6+2881562096*a^5*b^3*m^2*x^9+904*a^7*b*m^7*x^3+50116612*a^6*b^2* m^4*x^6+5692950592*a^5*b^3*m*x^9+42896*a^7*b*m^6*x^3+418024880*a^6*b^2*m^3 *x^6+3408204800*a^5*b^3*x^9+a^8*m^8+1108240*a^7*b*m^5*x^3+1898889328*a^...
Leaf count of result is larger than twice the leaf count of optimal. 847 vs. \(2 (151) = 302\).
Time = 0.32 (sec) , antiderivative size = 847, normalized size of antiderivative = 5.61 \[ \int x^m \left (a+b x^3\right )^8 \, dx=\frac {{\left ({\left (b^{8} m^{8} + 92 \, b^{8} m^{7} + 3514 \, b^{8} m^{6} + 72128 \, b^{8} m^{5} + 859369 \, b^{8} m^{4} + 5974388 \, b^{8} m^{3} + 22963996 \, b^{8} m^{2} + 42124592 \, b^{8} m + 24344320 \, b^{8}\right )} x^{25} + 8 \, {\left (a b^{7} m^{8} + 95 \, a b^{7} m^{7} + 3724 \, a b^{7} m^{6} + 78050 \, a b^{7} m^{5} + 945469 \, a b^{7} m^{4} + 6658295 \, a b^{7} m^{3} + 25841206 \, a b^{7} m^{2} + 47717960 \, a b^{7} m + 27664000 \, a b^{7}\right )} x^{22} + 28 \, {\left (a^{2} b^{6} m^{8} + 98 \, a^{2} b^{6} m^{7} + 3952 \, a^{2} b^{6} m^{6} + 84890 \, a^{2} b^{6} m^{5} + 1049659 \, a^{2} b^{6} m^{4} + 7515092 \, a^{2} b^{6} m^{3} + 29536948 \, a^{2} b^{6} m^{2} + 55022480 \, a^{2} b^{6} m + 32032000 \, a^{2} b^{6}\right )} x^{19} + 56 \, {\left (a^{3} b^{5} m^{8} + 101 \, a^{3} b^{5} m^{7} + 4198 \, a^{3} b^{5} m^{6} + 92810 \, a^{3} b^{5} m^{5} + 1177609 \, a^{3} b^{5} m^{4} + 8616869 \, a^{3} b^{5} m^{3} + 34453792 \, a^{3} b^{5} m^{2} + 64963820 \, a^{3} b^{5} m + 38038000 \, a^{3} b^{5}\right )} x^{16} + 70 \, {\left (a^{4} b^{4} m^{8} + 104 \, a^{4} b^{4} m^{7} + 4462 \, a^{4} b^{4} m^{6} + 101972 \, a^{4} b^{4} m^{5} + 1336933 \, a^{4} b^{4} m^{4} + 10078484 \, a^{4} b^{4} m^{3} + 41303404 \, a^{4} b^{4} m^{2} + 79280240 \, a^{4} b^{4} m + 46816000 \, a^{4} b^{4}\right )} x^{13} + 56 \, {\left (a^{5} b^{3} m^{8} + 107 \, a^{5} b^{3} m^{7} + 4744 \, a^{5} b^{3} m^{6} + 112538 \, a^{5} b^{3} m^{5} + 1537189 \, a^{5} b^{3} m^{4} + 12086723 \, a^{5} b^{3} m^{3} + 51456466 \, a^{5} b^{3} m^{2} + 101659832 \, a^{5} b^{3} m + 60860800 \, a^{5} b^{3}\right )} x^{10} + 28 \, {\left (a^{6} b^{2} m^{8} + 110 \, a^{6} b^{2} m^{7} + 5044 \, a^{6} b^{2} m^{6} + 124670 \, a^{6} b^{2} m^{5} + 1789879 \, a^{6} b^{2} m^{4} + 14929460 \, a^{6} b^{2} m^{3} + 67817476 \, a^{6} b^{2} m^{2} + 141502160 \, a^{6} b^{2} m + 86944000 \, a^{6} b^{2}\right )} x^{7} + 8 \, {\left (a^{7} b m^{8} + 113 \, a^{7} b m^{7} + 5362 \, a^{7} b m^{6} + 138530 \, a^{7} b m^{5} + 2108449 \, a^{7} b m^{4} + 19024817 \, a^{7} b m^{3} + 96224428 \, a^{7} b m^{2} + 231326780 \, a^{7} b m + 152152000 \, a^{7} b\right )} x^{4} + {\left (a^{8} m^{8} + 116 \, a^{8} m^{7} + 5698 \, a^{8} m^{6} + 154280 \, a^{8} m^{5} + 2508289 \, a^{8} m^{4} + 24950324 \, a^{8} m^{3} + 147373372 \, a^{8} m^{2} + 468851120 \, a^{8} m + 608608000 \, a^{8}\right )} x\right )} x^{m}}{m^{9} + 117 \, m^{8} + 5814 \, m^{7} + 159978 \, m^{6} + 2662569 \, m^{5} + 27458613 \, m^{4} + 172323696 \, m^{3} + 616224492 \, m^{2} + 1077459120 \, m + 608608000} \]
((b^8*m^8 + 92*b^8*m^7 + 3514*b^8*m^6 + 72128*b^8*m^5 + 859369*b^8*m^4 + 5 974388*b^8*m^3 + 22963996*b^8*m^2 + 42124592*b^8*m + 24344320*b^8)*x^25 + 8*(a*b^7*m^8 + 95*a*b^7*m^7 + 3724*a*b^7*m^6 + 78050*a*b^7*m^5 + 945469*a* b^7*m^4 + 6658295*a*b^7*m^3 + 25841206*a*b^7*m^2 + 47717960*a*b^7*m + 2766 4000*a*b^7)*x^22 + 28*(a^2*b^6*m^8 + 98*a^2*b^6*m^7 + 3952*a^2*b^6*m^6 + 8 4890*a^2*b^6*m^5 + 1049659*a^2*b^6*m^4 + 7515092*a^2*b^6*m^3 + 29536948*a^ 2*b^6*m^2 + 55022480*a^2*b^6*m + 32032000*a^2*b^6)*x^19 + 56*(a^3*b^5*m^8 + 101*a^3*b^5*m^7 + 4198*a^3*b^5*m^6 + 92810*a^3*b^5*m^5 + 1177609*a^3*b^5 *m^4 + 8616869*a^3*b^5*m^3 + 34453792*a^3*b^5*m^2 + 64963820*a^3*b^5*m + 3 8038000*a^3*b^5)*x^16 + 70*(a^4*b^4*m^8 + 104*a^4*b^4*m^7 + 4462*a^4*b^4*m ^6 + 101972*a^4*b^4*m^5 + 1336933*a^4*b^4*m^4 + 10078484*a^4*b^4*m^3 + 413 03404*a^4*b^4*m^2 + 79280240*a^4*b^4*m + 46816000*a^4*b^4)*x^13 + 56*(a^5* b^3*m^8 + 107*a^5*b^3*m^7 + 4744*a^5*b^3*m^6 + 112538*a^5*b^3*m^5 + 153718 9*a^5*b^3*m^4 + 12086723*a^5*b^3*m^3 + 51456466*a^5*b^3*m^2 + 101659832*a^ 5*b^3*m + 60860800*a^5*b^3)*x^10 + 28*(a^6*b^2*m^8 + 110*a^6*b^2*m^7 + 504 4*a^6*b^2*m^6 + 124670*a^6*b^2*m^5 + 1789879*a^6*b^2*m^4 + 14929460*a^6*b^ 2*m^3 + 67817476*a^6*b^2*m^2 + 141502160*a^6*b^2*m + 86944000*a^6*b^2)*x^7 + 8*(a^7*b*m^8 + 113*a^7*b*m^7 + 5362*a^7*b*m^6 + 138530*a^7*b*m^5 + 2108 449*a^7*b*m^4 + 19024817*a^7*b*m^3 + 96224428*a^7*b*m^2 + 231326780*a^7*b* m + 152152000*a^7*b)*x^4 + (a^8*m^8 + 116*a^8*m^7 + 5698*a^8*m^6 + 1542...
Leaf count of result is larger than twice the leaf count of optimal. 5902 vs. \(2 (138) = 276\).
Time = 2.47 (sec) , antiderivative size = 5902, normalized size of antiderivative = 39.09 \[ \int x^m \left (a+b x^3\right )^8 \, dx=\text {Too large to display} \]
Piecewise((-a**8/(24*x**24) - 8*a**7*b/(21*x**21) - 14*a**6*b**2/(9*x**18) - 56*a**5*b**3/(15*x**15) - 35*a**4*b**4/(6*x**12) - 56*a**3*b**5/(9*x**9 ) - 14*a**2*b**6/(3*x**6) - 8*a*b**7/(3*x**3) + b**8*log(x), Eq(m, -25)), (-a**8/(21*x**21) - 4*a**7*b/(9*x**18) - 28*a**6*b**2/(15*x**15) - 14*a**5 *b**3/(3*x**12) - 70*a**4*b**4/(9*x**9) - 28*a**3*b**5/(3*x**6) - 28*a**2* b**6/(3*x**3) + 8*a*b**7*log(x) + b**8*x**3/3, Eq(m, -22)), (-a**8/(18*x** 18) - 8*a**7*b/(15*x**15) - 7*a**6*b**2/(3*x**12) - 56*a**5*b**3/(9*x**9) - 35*a**4*b**4/(3*x**6) - 56*a**3*b**5/(3*x**3) + 28*a**2*b**6*log(x) + 8* a*b**7*x**3/3 + b**8*x**6/6, Eq(m, -19)), (-a**8/(15*x**15) - 2*a**7*b/(3* x**12) - 28*a**6*b**2/(9*x**9) - 28*a**5*b**3/(3*x**6) - 70*a**4*b**4/(3*x **3) + 56*a**3*b**5*log(x) + 28*a**2*b**6*x**3/3 + 4*a*b**7*x**6/3 + b**8* x**9/9, Eq(m, -16)), (-a**8/(12*x**12) - 8*a**7*b/(9*x**9) - 14*a**6*b**2/ (3*x**6) - 56*a**5*b**3/(3*x**3) + 70*a**4*b**4*log(x) + 56*a**3*b**5*x**3 /3 + 14*a**2*b**6*x**6/3 + 8*a*b**7*x**9/9 + b**8*x**12/12, Eq(m, -13)), ( -a**8/(9*x**9) - 4*a**7*b/(3*x**6) - 28*a**6*b**2/(3*x**3) + 56*a**5*b**3* log(x) + 70*a**4*b**4*x**3/3 + 28*a**3*b**5*x**6/3 + 28*a**2*b**6*x**9/9 + 2*a*b**7*x**12/3 + b**8*x**15/15, Eq(m, -10)), (-a**8/(6*x**6) - 8*a**7*b /(3*x**3) + 28*a**6*b**2*log(x) + 56*a**5*b**3*x**3/3 + 35*a**4*b**4*x**6/ 3 + 56*a**3*b**5*x**9/9 + 7*a**2*b**6*x**12/3 + 8*a*b**7*x**15/15 + b**8*x **18/18, Eq(m, -7)), (-a**8/(3*x**3) + 8*a**7*b*log(x) + 28*a**6*b**2*x...
Time = 0.22 (sec) , antiderivative size = 151, normalized size of antiderivative = 1.00 \[ \int x^m \left (a+b x^3\right )^8 \, dx=\frac {b^{8} x^{m + 25}}{m + 25} + \frac {8 \, a b^{7} x^{m + 22}}{m + 22} + \frac {28 \, a^{2} b^{6} x^{m + 19}}{m + 19} + \frac {56 \, a^{3} b^{5} x^{m + 16}}{m + 16} + \frac {70 \, a^{4} b^{4} x^{m + 13}}{m + 13} + \frac {56 \, a^{5} b^{3} x^{m + 10}}{m + 10} + \frac {28 \, a^{6} b^{2} x^{m + 7}}{m + 7} + \frac {8 \, a^{7} b x^{m + 4}}{m + 4} + \frac {a^{8} x^{m + 1}}{m + 1} \]
b^8*x^(m + 25)/(m + 25) + 8*a*b^7*x^(m + 22)/(m + 22) + 28*a^2*b^6*x^(m + 19)/(m + 19) + 56*a^3*b^5*x^(m + 16)/(m + 16) + 70*a^4*b^4*x^(m + 13)/(m + 13) + 56*a^5*b^3*x^(m + 10)/(m + 10) + 28*a^6*b^2*x^(m + 7)/(m + 7) + 8*a ^7*b*x^(m + 4)/(m + 4) + a^8*x^(m + 1)/(m + 1)
Leaf count of result is larger than twice the leaf count of optimal. 1269 vs. \(2 (151) = 302\).
Time = 0.31 (sec) , antiderivative size = 1269, normalized size of antiderivative = 8.40 \[ \int x^m \left (a+b x^3\right )^8 \, dx=\text {Too large to display} \]
(b^8*m^8*x^25*x^m + 92*b^8*m^7*x^25*x^m + 3514*b^8*m^6*x^25*x^m + 8*a*b^7* m^8*x^22*x^m + 72128*b^8*m^5*x^25*x^m + 760*a*b^7*m^7*x^22*x^m + 859369*b^ 8*m^4*x^25*x^m + 29792*a*b^7*m^6*x^22*x^m + 5974388*b^8*m^3*x^25*x^m + 28* a^2*b^6*m^8*x^19*x^m + 624400*a*b^7*m^5*x^22*x^m + 22963996*b^8*m^2*x^25*x ^m + 2744*a^2*b^6*m^7*x^19*x^m + 7563752*a*b^7*m^4*x^22*x^m + 42124592*b^8 *m*x^25*x^m + 110656*a^2*b^6*m^6*x^19*x^m + 53266360*a*b^7*m^3*x^22*x^m + 24344320*b^8*x^25*x^m + 56*a^3*b^5*m^8*x^16*x^m + 2376920*a^2*b^6*m^5*x^19 *x^m + 206729648*a*b^7*m^2*x^22*x^m + 5656*a^3*b^5*m^7*x^16*x^m + 29390452 *a^2*b^6*m^4*x^19*x^m + 381743680*a*b^7*m*x^22*x^m + 235088*a^3*b^5*m^6*x^ 16*x^m + 210422576*a^2*b^6*m^3*x^19*x^m + 221312000*a*b^7*x^22*x^m + 70*a^ 4*b^4*m^8*x^13*x^m + 5197360*a^3*b^5*m^5*x^16*x^m + 827034544*a^2*b^6*m^2* x^19*x^m + 7280*a^4*b^4*m^7*x^13*x^m + 65946104*a^3*b^5*m^4*x^16*x^m + 154 0629440*a^2*b^6*m*x^19*x^m + 312340*a^4*b^4*m^6*x^13*x^m + 482544664*a^3*b ^5*m^3*x^16*x^m + 896896000*a^2*b^6*x^19*x^m + 56*a^5*b^3*m^8*x^10*x^m + 7 138040*a^4*b^4*m^5*x^13*x^m + 1929412352*a^3*b^5*m^2*x^16*x^m + 5992*a^5*b ^3*m^7*x^10*x^m + 93585310*a^4*b^4*m^4*x^13*x^m + 3637973920*a^3*b^5*m*x^1 6*x^m + 265664*a^5*b^3*m^6*x^10*x^m + 705493880*a^4*b^4*m^3*x^13*x^m + 213 0128000*a^3*b^5*x^16*x^m + 28*a^6*b^2*m^8*x^7*x^m + 6302128*a^5*b^3*m^5*x^ 10*x^m + 2891238280*a^4*b^4*m^2*x^13*x^m + 3080*a^6*b^2*m^7*x^7*x^m + 8608 2584*a^5*b^3*m^4*x^10*x^m + 5549616800*a^4*b^4*m*x^13*x^m + 141232*a^6*...
Time = 6.87 (sec) , antiderivative size = 860, normalized size of antiderivative = 5.70 \[ \int x^m \left (a+b x^3\right )^8 \, dx=\frac {a^8\,x\,x^m\,\left (m^8+116\,m^7+5698\,m^6+154280\,m^5+2508289\,m^4+24950324\,m^3+147373372\,m^2+468851120\,m+608608000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {b^8\,x^m\,x^{25}\,\left (m^8+92\,m^7+3514\,m^6+72128\,m^5+859369\,m^4+5974388\,m^3+22963996\,m^2+42124592\,m+24344320\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {28\,a^2\,b^6\,x^m\,x^{19}\,\left (m^8+98\,m^7+3952\,m^6+84890\,m^5+1049659\,m^4+7515092\,m^3+29536948\,m^2+55022480\,m+32032000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {56\,a^3\,b^5\,x^m\,x^{16}\,\left (m^8+101\,m^7+4198\,m^6+92810\,m^5+1177609\,m^4+8616869\,m^3+34453792\,m^2+64963820\,m+38038000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {70\,a^4\,b^4\,x^m\,x^{13}\,\left (m^8+104\,m^7+4462\,m^6+101972\,m^5+1336933\,m^4+10078484\,m^3+41303404\,m^2+79280240\,m+46816000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {56\,a^5\,b^3\,x^m\,x^{10}\,\left (m^8+107\,m^7+4744\,m^6+112538\,m^5+1537189\,m^4+12086723\,m^3+51456466\,m^2+101659832\,m+60860800\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {28\,a^6\,b^2\,x^m\,x^7\,\left (m^8+110\,m^7+5044\,m^6+124670\,m^5+1789879\,m^4+14929460\,m^3+67817476\,m^2+141502160\,m+86944000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {8\,a\,b^7\,x^m\,x^{22}\,\left (m^8+95\,m^7+3724\,m^6+78050\,m^5+945469\,m^4+6658295\,m^3+25841206\,m^2+47717960\,m+27664000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000}+\frac {8\,a^7\,b\,x^m\,x^4\,\left (m^8+113\,m^7+5362\,m^6+138530\,m^5+2108449\,m^4+19024817\,m^3+96224428\,m^2+231326780\,m+152152000\right )}{m^9+117\,m^8+5814\,m^7+159978\,m^6+2662569\,m^5+27458613\,m^4+172323696\,m^3+616224492\,m^2+1077459120\,m+608608000} \]
(a^8*x*x^m*(468851120*m + 147373372*m^2 + 24950324*m^3 + 2508289*m^4 + 154 280*m^5 + 5698*m^6 + 116*m^7 + m^8 + 608608000))/(1077459120*m + 616224492 *m^2 + 172323696*m^3 + 27458613*m^4 + 2662569*m^5 + 159978*m^6 + 5814*m^7 + 117*m^8 + m^9 + 608608000) + (b^8*x^m*x^25*(42124592*m + 22963996*m^2 + 5974388*m^3 + 859369*m^4 + 72128*m^5 + 3514*m^6 + 92*m^7 + m^8 + 24344320) )/(1077459120*m + 616224492*m^2 + 172323696*m^3 + 27458613*m^4 + 2662569*m ^5 + 159978*m^6 + 5814*m^7 + 117*m^8 + m^9 + 608608000) + (28*a^2*b^6*x^m* x^19*(55022480*m + 29536948*m^2 + 7515092*m^3 + 1049659*m^4 + 84890*m^5 + 3952*m^6 + 98*m^7 + m^8 + 32032000))/(1077459120*m + 616224492*m^2 + 17232 3696*m^3 + 27458613*m^4 + 2662569*m^5 + 159978*m^6 + 5814*m^7 + 117*m^8 + m^9 + 608608000) + (56*a^3*b^5*x^m*x^16*(64963820*m + 34453792*m^2 + 86168 69*m^3 + 1177609*m^4 + 92810*m^5 + 4198*m^6 + 101*m^7 + m^8 + 38038000))/( 1077459120*m + 616224492*m^2 + 172323696*m^3 + 27458613*m^4 + 2662569*m^5 + 159978*m^6 + 5814*m^7 + 117*m^8 + m^9 + 608608000) + (70*a^4*b^4*x^m*x^1 3*(79280240*m + 41303404*m^2 + 10078484*m^3 + 1336933*m^4 + 101972*m^5 + 4 462*m^6 + 104*m^7 + m^8 + 46816000))/(1077459120*m + 616224492*m^2 + 17232 3696*m^3 + 27458613*m^4 + 2662569*m^5 + 159978*m^6 + 5814*m^7 + 117*m^8 + m^9 + 608608000) + (56*a^5*b^3*x^m*x^10*(101659832*m + 51456466*m^2 + 1208 6723*m^3 + 1537189*m^4 + 112538*m^5 + 4744*m^6 + 107*m^7 + m^8 + 60860800) )/(1077459120*m + 616224492*m^2 + 172323696*m^3 + 27458613*m^4 + 266256...