Integrand size = 74, antiderivative size = 28 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=e^4+\frac {43046721 x^{16}}{\left (-\frac {x}{4}+\log \left (4 x \left (\frac {3}{x}+x\right )\right )\right )^{16}} \] Output:
43046721/(ln(4*(x+3/x)*x)-1/4*x)^16*x^16+exp(4)
Time = 5.04 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=\frac {184884258895036416 x^{16}}{\left (-x+4 \log \left (4 \left (3+x^2\right )\right )\right )^{16}} \] Input:
Integrate[(184884258895036416*x^16*(-128*x^2 + (192 + 64*x^2)*Log[12 + 4*x ^2]))/((-x + 4*Log[12 + 4*x^2])^16*(-3*x^2 - x^4 + (12*x + 4*x^3)*Log[12 + 4*x^2])),x]
Output:
(184884258895036416*x^16)/(-x + 4*Log[4*(3 + x^2)])^16
Time = 1.97 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.68, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {27, 27, 7292, 7238}
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.
| \(\displaystyle \int \frac {184884258895036416 x^{16} \left (\left (64 x^2+192\right ) \log \left (4 x^2+12\right )-128 x^2\right )}{\left (4 \log \left (4 x^2+12\right )-x\right )^{16} \left (-x^4-3 x^2+\left (4 x^3+12 x\right ) \log \left (4 x^2+12\right )\right )} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 184884258895036416 \int \frac {64 x^{16} \left (2 x^2-\left (x^2+3\right ) \log \left (4 x^2+12\right )\right )}{\left (x-4 \log \left (4 x^2+12\right )\right )^{16} \left (x^4+3 x^2-4 \left (x^3+3 x\right ) \log \left (4 x^2+12\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 11832592569282330624 \int \frac {x^{16} \left (2 x^2-\left (x^2+3\right ) \log \left (4 x^2+12\right )\right )}{\left (x-4 \log \left (4 x^2+12\right )\right )^{16} \left (x^4+3 x^2-4 \left (x^3+3 x\right ) \log \left (4 x^2+12\right )\right )}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle 11832592569282330624 \int \frac {x^{15} \left (2 x^2-\left (x^2+3\right ) \log \left (4 x^2+12\right )\right )}{\left (x^2+3\right ) \left (x-4 \log \left (4 \left (x^2+3\right )\right )\right ) \left (x-4 \log \left (4 x^2+12\right )\right )^{16}}dx\) |
| \(\Big \downarrow \) 7238 |
| \(\displaystyle \frac {184884258895036416 x^{16}}{\left (x-4 \log \left (4 \left (x^2+3\right )\right )\right )^{16}}\) |
Input:
Int[(184884258895036416*x^16*(-128*x^2 + (192 + 64*x^2)*Log[12 + 4*x^2]))/ ((-x + 4*Log[12 + 4*x^2])^16*(-3*x^2 - x^4 + (12*x + 4*x^3)*Log[12 + 4*x^2 ])),x]
Output:
(184884258895036416*x^16)/(x - 4*Log[4*(3 + x^2)])^16
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*(y_)^(m_.)*(z_)^(n_.), x_Symbol] :> With[{q = DerivativeDivides[y* z, u*z^(n - m), x]}, Simp[q*y^(m + 1)*(z^(m + 1)/(m + 1)), x] /; !FalseQ[q ]] /; FreeQ[{m, n}, x] && NeQ[m, -1]
Time = 0.69 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.71
| method | result | size |
| risch | \(\frac {184884258895036416 x^{16}}{{\left (-4 \ln \left (4 x^{2}+12\right )+x \right )}^{16}}\) | \(20\) |
| parallelrisch | \(\frac {184884258895036416 x^{16}}{{\left (-4 \ln \left (4 x^{2}+12\right )+x \right )}^{16}}\) | \(20\) |
Input:
int(184884258895036416*((64*x^2+192)*ln(4*x^2+12)-128*x^2)*x^16/(4*ln(4*x^ 2+12)-x)^16/((4*x^3+12*x)*ln(4*x^2+12)-x^4-3*x^2),x,method=_RETURNVERBOSE)
Output:
184884258895036416*x^16/(-4*ln(4*x^2+12)+x)^16
Leaf count of result is larger than twice the leaf count of optimal. 244 vs. \(2 (25) = 50\).
Time = 0.07 (sec) , antiderivative size = 244, normalized size of antiderivative = 8.71 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=\frac {184884258895036416 \, x^{16}}{x^{16} - 64 \, x^{15} \log \left (4 \, x^{2} + 12\right ) + 1920 \, x^{14} \log \left (4 \, x^{2} + 12\right )^{2} - 35840 \, x^{13} \log \left (4 \, x^{2} + 12\right )^{3} + 465920 \, x^{12} \log \left (4 \, x^{2} + 12\right )^{4} - 4472832 \, x^{11} \log \left (4 \, x^{2} + 12\right )^{5} + 32800768 \, x^{10} \log \left (4 \, x^{2} + 12\right )^{6} - 187432960 \, x^{9} \log \left (4 \, x^{2} + 12\right )^{7} + 843448320 \, x^{8} \log \left (4 \, x^{2} + 12\right )^{8} - 2998927360 \, x^{7} \log \left (4 \, x^{2} + 12\right )^{9} + 8396996608 \, x^{6} \log \left (4 \, x^{2} + 12\right )^{10} - 18320719872 \, x^{5} \log \left (4 \, x^{2} + 12\right )^{11} + 30534533120 \, x^{4} \log \left (4 \, x^{2} + 12\right )^{12} - 37580963840 \, x^{3} \log \left (4 \, x^{2} + 12\right )^{13} + 32212254720 \, x^{2} \log \left (4 \, x^{2} + 12\right )^{14} - 17179869184 \, x \log \left (4 \, x^{2} + 12\right )^{15} + 4294967296 \, \log \left (4 \, x^{2} + 12\right )^{16}} \] Input:
integrate(184884258895036416*((64*x^2+192)*log(4*x^2+12)-128*x^2)*x^16/(4* log(4*x^2+12)-x)^16/((4*x^3+12*x)*log(4*x^2+12)-x^4-3*x^2),x, algorithm="f ricas")
Output:
184884258895036416*x^16/(x^16 - 64*x^15*log(4*x^2 + 12) + 1920*x^14*log(4* x^2 + 12)^2 - 35840*x^13*log(4*x^2 + 12)^3 + 465920*x^12*log(4*x^2 + 12)^4 - 4472832*x^11*log(4*x^2 + 12)^5 + 32800768*x^10*log(4*x^2 + 12)^6 - 1874 32960*x^9*log(4*x^2 + 12)^7 + 843448320*x^8*log(4*x^2 + 12)^8 - 2998927360 *x^7*log(4*x^2 + 12)^9 + 8396996608*x^6*log(4*x^2 + 12)^10 - 18320719872*x ^5*log(4*x^2 + 12)^11 + 30534533120*x^4*log(4*x^2 + 12)^12 - 37580963840*x ^3*log(4*x^2 + 12)^13 + 32212254720*x^2*log(4*x^2 + 12)^14 - 17179869184*x *log(4*x^2 + 12)^15 + 4294967296*log(4*x^2 + 12)^16)
Leaf count of result is larger than twice the leaf count of optimal. 245 vs. \(2 (22) = 44\).
Time = 0.62 (sec) , antiderivative size = 245, normalized size of antiderivative = 8.75 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=\frac {184884258895036416 x^{16}}{x^{16} - 64 x^{15} \log {\left (4 x^{2} + 12 \right )} + 1920 x^{14} \log {\left (4 x^{2} + 12 \right )}^{2} - 35840 x^{13} \log {\left (4 x^{2} + 12 \right )}^{3} + 465920 x^{12} \log {\left (4 x^{2} + 12 \right )}^{4} - 4472832 x^{11} \log {\left (4 x^{2} + 12 \right )}^{5} + 32800768 x^{10} \log {\left (4 x^{2} + 12 \right )}^{6} - 187432960 x^{9} \log {\left (4 x^{2} + 12 \right )}^{7} + 843448320 x^{8} \log {\left (4 x^{2} + 12 \right )}^{8} - 2998927360 x^{7} \log {\left (4 x^{2} + 12 \right )}^{9} + 8396996608 x^{6} \log {\left (4 x^{2} + 12 \right )}^{10} - 18320719872 x^{5} \log {\left (4 x^{2} + 12 \right )}^{11} + 30534533120 x^{4} \log {\left (4 x^{2} + 12 \right )}^{12} - 37580963840 x^{3} \log {\left (4 x^{2} + 12 \right )}^{13} + 32212254720 x^{2} \log {\left (4 x^{2} + 12 \right )}^{14} - 17179869184 x \log {\left (4 x^{2} + 12 \right )}^{15} + 4294967296 \log {\left (4 x^{2} + 12 \right )}^{16}} \] Input:
integrate(184884258895036416*((64*x**2+192)*ln(4*x**2+12)-128*x**2)*x**16/ (4*ln(4*x**2+12)-x)**16/((4*x**3+12*x)*ln(4*x**2+12)-x**4-3*x**2),x)
Output:
184884258895036416*x**16/(x**16 - 64*x**15*log(4*x**2 + 12) + 1920*x**14*l og(4*x**2 + 12)**2 - 35840*x**13*log(4*x**2 + 12)**3 + 465920*x**12*log(4* x**2 + 12)**4 - 4472832*x**11*log(4*x**2 + 12)**5 + 32800768*x**10*log(4*x **2 + 12)**6 - 187432960*x**9*log(4*x**2 + 12)**7 + 843448320*x**8*log(4*x **2 + 12)**8 - 2998927360*x**7*log(4*x**2 + 12)**9 + 8396996608*x**6*log(4 *x**2 + 12)**10 - 18320719872*x**5*log(4*x**2 + 12)**11 + 30534533120*x**4 *log(4*x**2 + 12)**12 - 37580963840*x**3*log(4*x**2 + 12)**13 + 3221225472 0*x**2*log(4*x**2 + 12)**14 - 17179869184*x*log(4*x**2 + 12)**15 + 4294967 296*log(4*x**2 + 12)**16)
Leaf count of result is larger than twice the leaf count of optimal. 1341 vs. \(2 (25) = 50\).
Time = 7.00 (sec) , antiderivative size = 1341, normalized size of antiderivative = 47.89 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=\text {Too large to display} \] Input:
integrate(184884258895036416*((64*x^2+192)*log(4*x^2+12)-128*x^2)*x^16/(4* log(4*x^2+12)-x)^16/((4*x^3+12*x)*log(4*x^2+12)-x^4-3*x^2),x, algorithm="m axima")
Output:
184884258895036416*x^16/(x^16 - 128*x^15*log(2) + 7680*x^14*log(2)^2 - 286 720*x^13*log(2)^3 + 7454720*x^12*log(2)^4 - 143130624*x^11*log(2)^5 + 2099 249152*x^10*log(2)^6 - 23991418880*x^9*log(2)^7 + 215922769920*x^8*log(2)^ 8 - 1535450808320*x^7*log(2)^9 + 8598524526592*x^6*log(2)^10 - 37520834297 856*x^5*log(2)^11 + 125069447659520*x^4*log(2)^12 - 307863255777280*x^3*lo g(2)^13 + 527765581332480*x^2*log(2)^14 - 562949953421312*x*log(2)^15 + 28 1474976710656*log(2)^16 - 17179869184*(x - 8*log(2))*log(x^2 + 3)^15 + 429 4967296*log(x^2 + 3)^16 + 32212254720*(x^2 - 16*x*log(2) + 64*log(2)^2)*lo g(x^2 + 3)^14 - 37580963840*(x^3 - 24*x^2*log(2) + 192*x*log(2)^2 - 512*lo g(2)^3)*log(x^2 + 3)^13 + 30534533120*(x^4 - 32*x^3*log(2) + 384*x^2*log(2 )^2 - 2048*x*log(2)^3 + 4096*log(2)^4)*log(x^2 + 3)^12 - 18320719872*(x^5 - 40*x^4*log(2) + 640*x^3*log(2)^2 - 5120*x^2*log(2)^3 + 20480*x*log(2)^4 - 32768*log(2)^5)*log(x^2 + 3)^11 + 8396996608*(x^6 - 48*x^5*log(2) + 960* x^4*log(2)^2 - 10240*x^3*log(2)^3 + 61440*x^2*log(2)^4 - 196608*x*log(2)^5 + 262144*log(2)^6)*log(x^2 + 3)^10 - 2998927360*(x^7 - 56*x^6*log(2) + 13 44*x^5*log(2)^2 - 17920*x^4*log(2)^3 + 143360*x^3*log(2)^4 - 688128*x^2*lo g(2)^5 + 1835008*x*log(2)^6 - 2097152*log(2)^7)*log(x^2 + 3)^9 + 843448320 *(x^8 - 64*x^7*log(2) + 1792*x^6*log(2)^2 - 28672*x^5*log(2)^3 + 286720*x^ 4*log(2)^4 - 1835008*x^3*log(2)^5 + 7340032*x^2*log(2)^6 - 16777216*x*log( 2)^7 + 16777216*log(2)^8)*log(x^2 + 3)^8 - 187432960*(x^9 - 72*x^8*log(...
Leaf count of result is larger than twice the leaf count of optimal. 739 vs. \(2 (25) = 50\).
Time = 0.29 (sec) , antiderivative size = 739, normalized size of antiderivative = 26.39 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx =\text {Too large to display} \] Input:
integrate(184884258895036416*((64*x^2+192)*log(4*x^2+12)-128*x^2)*x^16/(4* log(4*x^2+12)-x)^16/((4*x^3+12*x)*log(4*x^2+12)-x^4-3*x^2),x, algorithm="g iac")
Output:
184884258895036416*(x^18 - 8*x^17 + 3*x^16)/(x^18 - 64*x^17*log(4*x^2 + 12 ) + 1920*x^16*log(4*x^2 + 12)^2 - 35840*x^15*log(4*x^2 + 12)^3 + 465920*x^ 14*log(4*x^2 + 12)^4 - 4472832*x^13*log(4*x^2 + 12)^5 + 32800768*x^12*log( 4*x^2 + 12)^6 - 187432960*x^11*log(4*x^2 + 12)^7 + 843448320*x^10*log(4*x^ 2 + 12)^8 - 2998927360*x^9*log(4*x^2 + 12)^9 + 8396996608*x^8*log(4*x^2 + 12)^10 - 18320719872*x^7*log(4*x^2 + 12)^11 + 30534533120*x^6*log(4*x^2 + 12)^12 - 37580963840*x^5*log(4*x^2 + 12)^13 + 32212254720*x^4*log(4*x^2 + 12)^14 - 17179869184*x^3*log(4*x^2 + 12)^15 + 4294967296*x^2*log(4*x^2 + 1 2)^16 - 8*x^17 + 512*x^16*log(4*x^2 + 12) - 15360*x^15*log(4*x^2 + 12)^2 + 286720*x^14*log(4*x^2 + 12)^3 - 3727360*x^13*log(4*x^2 + 12)^4 + 35782656 *x^12*log(4*x^2 + 12)^5 - 262406144*x^11*log(4*x^2 + 12)^6 + 1499463680*x^ 10*log(4*x^2 + 12)^7 - 6747586560*x^9*log(4*x^2 + 12)^8 + 23991418880*x^8* log(4*x^2 + 12)^9 - 67175972864*x^7*log(4*x^2 + 12)^10 + 146565758976*x^6* log(4*x^2 + 12)^11 - 244276264960*x^5*log(4*x^2 + 12)^12 + 300647710720*x^ 4*log(4*x^2 + 12)^13 - 257698037760*x^3*log(4*x^2 + 12)^14 + 137438953472* x^2*log(4*x^2 + 12)^15 - 34359738368*x*log(4*x^2 + 12)^16 + 3*x^16 - 192*x ^15*log(4*x^2 + 12) + 5760*x^14*log(4*x^2 + 12)^2 - 107520*x^13*log(4*x^2 + 12)^3 + 1397760*x^12*log(4*x^2 + 12)^4 - 13418496*x^11*log(4*x^2 + 12)^5 + 98402304*x^10*log(4*x^2 + 12)^6 - 562298880*x^9*log(4*x^2 + 12)^7 + 253 0344960*x^8*log(4*x^2 + 12)^8 - 8996782080*x^7*log(4*x^2 + 12)^9 + 2519...
Time = 9.26 (sec) , antiderivative size = 8176, normalized size of antiderivative = 292.00 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=\text {Too large to display} \] Input:
int((184884258895036416*x^16*(128*x^2 - log(4*x^2 + 12)*(64*x^2 + 192)))/( (x - 4*log(4*x^2 + 12))^16*(3*x^2 - log(4*x^2 + 12)*(12*x + 4*x^3) + x^4)) ,x)
Output:
((253613523861504*(x^2 + 3)*(570856987916899892308900800*x^6 - 30841595137 789280098254000*x^4 - 187818288541614916107372450*x^5 - 902395816198297067 146500*x^3 + 2439747160072844559509672100*x^7 - 82957440274656743449889235 00*x^8 - 543812506969457624576052375*x^9 + 27661171264596385794915436800*x ^10 - 32016135378737035236167156700*x^11 + 1372161664319434099018607700*x^ 12 + 5746721477213530940132956950*x^13 + 22974313738968139869460339200*x^1 4 - 40821777747974883056387690700*x^15 + 95478874838397193700810553300*x^1 6 - 294673194421325099068314225600*x^17 + 692099850152361406824080812800*x ^18 - 1415216444774448003463750174200*x^19 + 27042898845330332788533057948 60*x^20 - 4696494682313934465967955313360*x^21 + 7374793890354571956503281 173120*x^22 - 10589317044162230360848825061280*x^23 + 13899052526495278135 263007111920*x^24 - 16626308531595710820653586573495*x^25 + 18155334364912 055148401151544320*x^26 - 18083932845576877756510514200440*x^27 + 16355777 910252757682964944436360*x^28 - 13370544085224559107216239909460*x^29 + 97 95021684183143165248345956096*x^30 - 6306071997921949003951883254680*x^31 + 3437358816930241296807623887272*x^32 - 1435248709647264957060765930168*x ^33 + 264462491110340650440600806400*x^34 + 262251968858219279836629973260 *x^35 - 390486430499815737214346593944*x^36 + 3328420079896577325442776569 58*x^37 - 221662472651738303306339317824*x^38 + 12476720342830906413343918 9476*x^39 - 61107633140795550812794862988*x^40 + 2593727496359299145631...
Time = 0.16 (sec) , antiderivative size = 471, normalized size of antiderivative = 16.82 \[ \int \frac {184884258895036416 x^{16} \left (-128 x^2+\left (192+64 x^2\right ) \log \left (12+4 x^2\right )\right )}{\left (-x+4 \log \left (12+4 x^2\right )\right )^{16} \left (-3 x^2-x^4+\left (12 x+4 x^3\right ) \log \left (12+4 x^2\right )\right )} \, dx=\frac {11832592569282330624 \,\mathrm {log}\left (4 x^{2}+12\right ) \left (-67108864 \mathrm {log}\left (4 x^{2}+12\right )^{15}+268435456 \mathrm {log}\left (4 x^{2}+12\right )^{14} x -503316480 \mathrm {log}\left (4 x^{2}+12\right )^{13} x^{2}+587202560 \mathrm {log}\left (4 x^{2}+12\right )^{12} x^{3}-477102080 \mathrm {log}\left (4 x^{2}+12\right )^{11} x^{4}+286261248 \mathrm {log}\left (4 x^{2}+12\right )^{10} x^{5}-131203072 \mathrm {log}\left (4 x^{2}+12\right )^{9} x^{6}+46858240 \mathrm {log}\left (4 x^{2}+12\right )^{8} x^{7}-13178880 \mathrm {log}\left (4 x^{2}+12\right )^{7} x^{8}+2928640 \mathrm {log}\left (4 x^{2}+12\right )^{6} x^{9}-512512 \mathrm {log}\left (4 x^{2}+12\right )^{5} x^{10}+69888 \mathrm {log}\left (4 x^{2}+12\right )^{4} x^{11}-7280 \mathrm {log}\left (4 x^{2}+12\right )^{3} x^{12}+560 \mathrm {log}\left (4 x^{2}+12\right )^{2} x^{13}-30 \,\mathrm {log}\left (4 x^{2}+12\right ) x^{14}+x^{15}\right )}{4294967296 \mathrm {log}\left (4 x^{2}+12\right )^{16}-17179869184 \mathrm {log}\left (4 x^{2}+12\right )^{15} x +32212254720 \mathrm {log}\left (4 x^{2}+12\right )^{14} x^{2}-37580963840 \mathrm {log}\left (4 x^{2}+12\right )^{13} x^{3}+30534533120 \mathrm {log}\left (4 x^{2}+12\right )^{12} x^{4}-18320719872 \mathrm {log}\left (4 x^{2}+12\right )^{11} x^{5}+8396996608 \mathrm {log}\left (4 x^{2}+12\right )^{10} x^{6}-2998927360 \mathrm {log}\left (4 x^{2}+12\right )^{9} x^{7}+843448320 \mathrm {log}\left (4 x^{2}+12\right )^{8} x^{8}-187432960 \mathrm {log}\left (4 x^{2}+12\right )^{7} x^{9}+32800768 \mathrm {log}\left (4 x^{2}+12\right )^{6} x^{10}-4472832 \mathrm {log}\left (4 x^{2}+12\right )^{5} x^{11}+465920 \mathrm {log}\left (4 x^{2}+12\right )^{4} x^{12}-35840 \mathrm {log}\left (4 x^{2}+12\right )^{3} x^{13}+1920 \mathrm {log}\left (4 x^{2}+12\right )^{2} x^{14}-64 \,\mathrm {log}\left (4 x^{2}+12\right ) x^{15}+x^{16}} \] Input:
int(184884258895036416*((64*x^2+192)*log(4*x^2+12)-128*x^2)*x^16/(4*log(4* x^2+12)-x)^16/((4*x^3+12*x)*log(4*x^2+12)-x^4-3*x^2),x)
Output:
(11832592569282330624*log(4*x**2 + 12)*( - 67108864*log(4*x**2 + 12)**15 + 268435456*log(4*x**2 + 12)**14*x - 503316480*log(4*x**2 + 12)**13*x**2 + 587202560*log(4*x**2 + 12)**12*x**3 - 477102080*log(4*x**2 + 12)**11*x**4 + 286261248*log(4*x**2 + 12)**10*x**5 - 131203072*log(4*x**2 + 12)**9*x**6 + 46858240*log(4*x**2 + 12)**8*x**7 - 13178880*log(4*x**2 + 12)**7*x**8 + 2928640*log(4*x**2 + 12)**6*x**9 - 512512*log(4*x**2 + 12)**5*x**10 + 698 88*log(4*x**2 + 12)**4*x**11 - 7280*log(4*x**2 + 12)**3*x**12 + 560*log(4* x**2 + 12)**2*x**13 - 30*log(4*x**2 + 12)*x**14 + x**15))/(4294967296*log( 4*x**2 + 12)**16 - 17179869184*log(4*x**2 + 12)**15*x + 32212254720*log(4* x**2 + 12)**14*x**2 - 37580963840*log(4*x**2 + 12)**13*x**3 + 30534533120* log(4*x**2 + 12)**12*x**4 - 18320719872*log(4*x**2 + 12)**11*x**5 + 839699 6608*log(4*x**2 + 12)**10*x**6 - 2998927360*log(4*x**2 + 12)**9*x**7 + 843 448320*log(4*x**2 + 12)**8*x**8 - 187432960*log(4*x**2 + 12)**7*x**9 + 328 00768*log(4*x**2 + 12)**6*x**10 - 4472832*log(4*x**2 + 12)**5*x**11 + 4659 20*log(4*x**2 + 12)**4*x**12 - 35840*log(4*x**2 + 12)**3*x**13 + 1920*log( 4*x**2 + 12)**2*x**14 - 64*log(4*x**2 + 12)*x**15 + x**16)