Integrand size = 128, antiderivative size = 19 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625 x^{16} \left (3+\log \left (\frac {x^2}{4}\right )\right )^8}{4722366482869645213696} \]
Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625 x^{16} \left (3+\log \left (\frac {x^2}{4}\right )\right )^8}{4722366482869645213696} \]
Integrate[(57460436295776367187500*x^15 + 148439460430755615234375*x^15*Lo g[x^2/4] + 167592939196014404296875*x^15*Log[x^2/4]^2 + 108004338592987060 546875*x^15*Log[x^2/4]^3 + 43450021273040771484375*x^15*Log[x^2/4]^4 + 111 72862613067626953125*x^15*Log[x^2/4]^5 + 1793175481109619140625*x^15*Log[x ^2/4]^6 + 164210208892822265625*x^15*Log[x^2/4]^7 + 6568408355712890625*x^ 15*Log[x^2/4]^8)/295147905179352825856,x]
Leaf count is larger than twice the leaf count of optimal. \(146\) vs. \(2(19)=38\).
Time = 0.57 (sec) , antiderivative size = 146, normalized size of antiderivative = 7.68, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {27, 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.
| \(\displaystyle \int \frac {57460436295776367187500 x^{15}+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \left (6568408355712890625 \log ^8\left (\frac {x^2}{4}\right ) x^{15}+164210208892822265625 \log ^7\left (\frac {x^2}{4}\right ) x^{15}+1793175481109619140625 \log ^6\left (\frac {x^2}{4}\right ) x^{15}+11172862613067626953125 \log ^5\left (\frac {x^2}{4}\right ) x^{15}+43450021273040771484375 \log ^4\left (\frac {x^2}{4}\right ) x^{15}+108004338592987060546875 \log ^3\left (\frac {x^2}{4}\right ) x^{15}+167592939196014404296875 \log ^2\left (\frac {x^2}{4}\right ) x^{15}+148439460430755615234375 \log \left (\frac {x^2}{4}\right ) x^{15}+57460436295776367187500 x^{15}\right )dx}{295147905179352825856}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\frac {43095327221832275390625 x^{16}}{16}+\frac {6568408355712890625}{16} x^{16} \log ^8\left (\frac {x^2}{4}\right )+\frac {19705225067138671875}{2} x^{16} \log ^7\left (\frac {x^2}{4}\right )+\frac {413809726409912109375}{4} x^{16} \log ^6\left (\frac {x^2}{4}\right )+\frac {1241429179229736328125}{2} x^{16} \log ^5\left (\frac {x^2}{4}\right )+\frac {18621437688446044921875}{8} x^{16} \log ^4\left (\frac {x^2}{4}\right )+\frac {11172862613067626953125}{2} x^{16} \log ^3\left (\frac {x^2}{4}\right )+\frac {33518587839202880859375}{4} x^{16} \log ^2\left (\frac {x^2}{4}\right )+\frac {14365109073944091796875}{2} x^{16} \log \left (\frac {x^2}{4}\right )}{295147905179352825856}\) |
Int[(57460436295776367187500*x^15 + 148439460430755615234375*x^15*Log[x^2/ 4] + 167592939196014404296875*x^15*Log[x^2/4]^2 + 108004338592987060546875 *x^15*Log[x^2/4]^3 + 43450021273040771484375*x^15*Log[x^2/4]^4 + 111728626 13067626953125*x^15*Log[x^2/4]^5 + 1793175481109619140625*x^15*Log[x^2/4]^ 6 + 164210208892822265625*x^15*Log[x^2/4]^7 + 6568408355712890625*x^15*Log [x^2/4]^8)/295147905179352825856,x]
((43095327221832275390625*x^16)/16 + (14365109073944091796875*x^16*Log[x^2 /4])/2 + (33518587839202880859375*x^16*Log[x^2/4]^2)/4 + (1117286261306762 6953125*x^16*Log[x^2/4]^3)/2 + (18621437688446044921875*x^16*Log[x^2/4]^4) /8 + (1241429179229736328125*x^16*Log[x^2/4]^5)/2 + (413809726409912109375 *x^16*Log[x^2/4]^6)/4 + (19705225067138671875*x^16*Log[x^2/4]^7)/2 + (6568 408355712890625*x^16*Log[x^2/4]^8)/16)/295147905179352825856
3.2.70.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(108\) vs. \(2(15)=30\).
Time = 0.11 (sec) , antiderivative size = 109, normalized size of antiderivative = 5.74
| method | result | size |
| risch | \(\frac {6568408355712890625 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{8}}{4722366482869645213696}+\frac {19705225067138671875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{7}}{590295810358705651712}+\frac {413809726409912109375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{6}}{1180591620717411303424}+\frac {1241429179229736328125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{5}}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{4}}{2361183241434822606848}+\frac {11172862613067626953125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{3}}{590295810358705651712}+\frac {33518587839202880859375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{2}}{1180591620717411303424}+\frac {14365109073944091796875 x^{16} \ln \left (\frac {x^{2}}{4}\right )}{590295810358705651712}+\frac {43095327221832275390625 x^{16}}{4722366482869645213696}\) | \(109\) |
| parallelrisch | \(\frac {6568408355712890625 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{8}}{4722366482869645213696}+\frac {19705225067138671875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{7}}{590295810358705651712}+\frac {413809726409912109375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{6}}{1180591620717411303424}+\frac {1241429179229736328125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{5}}{590295810358705651712}+\frac {18621437688446044921875 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{4}}{2361183241434822606848}+\frac {11172862613067626953125 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{3}}{590295810358705651712}+\frac {33518587839202880859375 x^{16} \ln \left (\frac {x^{2}}{4}\right )^{2}}{1180591620717411303424}+\frac {14365109073944091796875 x^{16} \ln \left (\frac {x^{2}}{4}\right )}{590295810358705651712}+\frac {43095327221832275390625 x^{16}}{4722366482869645213696}\) | \(109\) |
int(6568408355712890625/295147905179352825856*x^15*ln(1/4*x^2)^8+164210208 892822265625/295147905179352825856*x^15*ln(1/4*x^2)^7+17931754811096191406 25/295147905179352825856*x^15*ln(1/4*x^2)^6+11172862613067626953125/295147 905179352825856*x^15*ln(1/4*x^2)^5+43450021273040771484375/295147905179352 825856*x^15*ln(1/4*x^2)^4+108004338592987060546875/295147905179352825856*x ^15*ln(1/4*x^2)^3+167592939196014404296875/295147905179352825856*x^15*ln(1 /4*x^2)^2+148439460430755615234375/295147905179352825856*x^15*ln(1/4*x^2)+ 14365109073944091796875/73786976294838206464*x^15,x,method=_RETURNVERBOSE)
6568408355712890625/4722366482869645213696*x^16*ln(1/4*x^2)^8+197052250671 38671875/590295810358705651712*x^16*ln(1/4*x^2)^7+413809726409912109375/11 80591620717411303424*x^16*ln(1/4*x^2)^6+1241429179229736328125/59029581035 8705651712*x^16*ln(1/4*x^2)^5+18621437688446044921875/23611832414348226068 48*x^16*ln(1/4*x^2)^4+11172862613067626953125/590295810358705651712*x^16*l n(1/4*x^2)^3+33518587839202880859375/1180591620717411303424*x^16*ln(1/4*x^ 2)^2+14365109073944091796875/590295810358705651712*x^16*ln(1/4*x^2)+430953 27221832275390625/4722366482869645213696*x^16
Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (15) = 30\).
Time = 0.25 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625}{4722366482869645213696} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{8} + \frac {19705225067138671875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{7} + \frac {413809726409912109375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{6} + \frac {1241429179229736328125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{5} + \frac {18621437688446044921875}{2361183241434822606848} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{4} + \frac {11172862613067626953125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{3} + \frac {33518587839202880859375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{2} + \frac {14365109073944091796875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right ) + \frac {43095327221832275390625}{4722366482869645213696} \, x^{16} \]
integrate(6568408355712890625/295147905179352825856*x^15*log(1/4*x^2)^8+16 4210208892822265625/295147905179352825856*x^15*log(1/4*x^2)^7+179317548110 9619140625/295147905179352825856*x^15*log(1/4*x^2)^6+111728626130676269531 25/295147905179352825856*x^15*log(1/4*x^2)^5+43450021273040771484375/29514 7905179352825856*x^15*log(1/4*x^2)^4+108004338592987060546875/295147905179 352825856*x^15*log(1/4*x^2)^3+167592939196014404296875/2951479051793528258 56*x^15*log(1/4*x^2)^2+148439460430755615234375/295147905179352825856*x^15 *log(1/4*x^2)+14365109073944091796875/73786976294838206464*x^15,x, algorit hm=\
6568408355712890625/4722366482869645213696*x^16*log(1/4*x^2)^8 + 197052250 67138671875/590295810358705651712*x^16*log(1/4*x^2)^7 + 413809726409912109 375/1180591620717411303424*x^16*log(1/4*x^2)^6 + 1241429179229736328125/59 0295810358705651712*x^16*log(1/4*x^2)^5 + 18621437688446044921875/23611832 41434822606848*x^16*log(1/4*x^2)^4 + 11172862613067626953125/5902958103587 05651712*x^16*log(1/4*x^2)^3 + 33518587839202880859375/1180591620717411303 424*x^16*log(1/4*x^2)^2 + 14365109073944091796875/590295810358705651712*x^ 16*log(1/4*x^2) + 43095327221832275390625/4722366482869645213696*x^16
Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (15) = 30\).
Time = 0.18 (sec) , antiderivative size = 126, normalized size of antiderivative = 6.63 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{8}}{4722366482869645213696} + \frac {19705225067138671875 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{7}}{590295810358705651712} + \frac {413809726409912109375 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{6}}{1180591620717411303424} + \frac {1241429179229736328125 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{5}}{590295810358705651712} + \frac {18621437688446044921875 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{4}}{2361183241434822606848} + \frac {11172862613067626953125 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{3}}{590295810358705651712} + \frac {33518587839202880859375 x^{16} \log {\left (\frac {x^{2}}{4} \right )}^{2}}{1180591620717411303424} + \frac {14365109073944091796875 x^{16} \log {\left (\frac {x^{2}}{4} \right )}}{590295810358705651712} + \frac {43095327221832275390625 x^{16}}{4722366482869645213696} \]
integrate(6568408355712890625/295147905179352825856*x**15*ln(1/4*x**2)**8+ 164210208892822265625/295147905179352825856*x**15*ln(1/4*x**2)**7+17931754 81109619140625/295147905179352825856*x**15*ln(1/4*x**2)**6+111728626130676 26953125/295147905179352825856*x**15*ln(1/4*x**2)**5+434500212730407714843 75/295147905179352825856*x**15*ln(1/4*x**2)**4+108004338592987060546875/29 5147905179352825856*x**15*ln(1/4*x**2)**3+167592939196014404296875/2951479 05179352825856*x**15*ln(1/4*x**2)**2+148439460430755615234375/295147905179 352825856*x**15*ln(1/4*x**2)+14365109073944091796875/73786976294838206464* x**15,x)
6568408355712890625*x**16*log(x**2/4)**8/4722366482869645213696 + 19705225 067138671875*x**16*log(x**2/4)**7/590295810358705651712 + 4138097264099121 09375*x**16*log(x**2/4)**6/1180591620717411303424 + 1241429179229736328125 *x**16*log(x**2/4)**5/590295810358705651712 + 18621437688446044921875*x**1 6*log(x**2/4)**4/2361183241434822606848 + 11172862613067626953125*x**16*lo g(x**2/4)**3/590295810358705651712 + 33518587839202880859375*x**16*log(x** 2/4)**2/1180591620717411303424 + 14365109073944091796875*x**16*log(x**2/4) /590295810358705651712 + 43095327221832275390625*x**16/4722366482869645213 696
Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (15) = 30\).
Time = 0.19 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625}{4722366482869645213696} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{8} + \frac {19705225067138671875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{7} + \frac {413809726409912109375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{6} + \frac {1241429179229736328125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{5} + \frac {18621437688446044921875}{2361183241434822606848} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{4} + \frac {11172862613067626953125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{3} + \frac {33518587839202880859375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{2} + \frac {14365109073944091796875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right ) + \frac {43095327221832275390625}{4722366482869645213696} \, x^{16} \]
integrate(6568408355712890625/295147905179352825856*x^15*log(1/4*x^2)^8+16 4210208892822265625/295147905179352825856*x^15*log(1/4*x^2)^7+179317548110 9619140625/295147905179352825856*x^15*log(1/4*x^2)^6+111728626130676269531 25/295147905179352825856*x^15*log(1/4*x^2)^5+43450021273040771484375/29514 7905179352825856*x^15*log(1/4*x^2)^4+108004338592987060546875/295147905179 352825856*x^15*log(1/4*x^2)^3+167592939196014404296875/2951479051793528258 56*x^15*log(1/4*x^2)^2+148439460430755615234375/295147905179352825856*x^15 *log(1/4*x^2)+14365109073944091796875/73786976294838206464*x^15,x, algorit hm=\
6568408355712890625/4722366482869645213696*x^16*log(1/4*x^2)^8 + 197052250 67138671875/590295810358705651712*x^16*log(1/4*x^2)^7 + 413809726409912109 375/1180591620717411303424*x^16*log(1/4*x^2)^6 + 1241429179229736328125/59 0295810358705651712*x^16*log(1/4*x^2)^5 + 18621437688446044921875/23611832 41434822606848*x^16*log(1/4*x^2)^4 + 11172862613067626953125/5902958103587 05651712*x^16*log(1/4*x^2)^3 + 33518587839202880859375/1180591620717411303 424*x^16*log(1/4*x^2)^2 + 14365109073944091796875/590295810358705651712*x^ 16*log(1/4*x^2) + 43095327221832275390625/4722366482869645213696*x^16
Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (15) = 30\).
Time = 0.26 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625}{4722366482869645213696} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{8} + \frac {19705225067138671875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{7} + \frac {413809726409912109375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{6} + \frac {1241429179229736328125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{5} + \frac {18621437688446044921875}{2361183241434822606848} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{4} + \frac {11172862613067626953125}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{3} + \frac {33518587839202880859375}{1180591620717411303424} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right )^{2} + \frac {14365109073944091796875}{590295810358705651712} \, x^{16} \log \left (\frac {1}{4} \, x^{2}\right ) + \frac {43095327221832275390625}{4722366482869645213696} \, x^{16} \]
integrate(6568408355712890625/295147905179352825856*x^15*log(1/4*x^2)^8+16 4210208892822265625/295147905179352825856*x^15*log(1/4*x^2)^7+179317548110 9619140625/295147905179352825856*x^15*log(1/4*x^2)^6+111728626130676269531 25/295147905179352825856*x^15*log(1/4*x^2)^5+43450021273040771484375/29514 7905179352825856*x^15*log(1/4*x^2)^4+108004338592987060546875/295147905179 352825856*x^15*log(1/4*x^2)^3+167592939196014404296875/2951479051793528258 56*x^15*log(1/4*x^2)^2+148439460430755615234375/295147905179352825856*x^15 *log(1/4*x^2)+14365109073944091796875/73786976294838206464*x^15,x, algorit hm=\
6568408355712890625/4722366482869645213696*x^16*log(1/4*x^2)^8 + 197052250 67138671875/590295810358705651712*x^16*log(1/4*x^2)^7 + 413809726409912109 375/1180591620717411303424*x^16*log(1/4*x^2)^6 + 1241429179229736328125/59 0295810358705651712*x^16*log(1/4*x^2)^5 + 18621437688446044921875/23611832 41434822606848*x^16*log(1/4*x^2)^4 + 11172862613067626953125/5902958103587 05651712*x^16*log(1/4*x^2)^3 + 33518587839202880859375/1180591620717411303 424*x^16*log(1/4*x^2)^2 + 14365109073944091796875/590295810358705651712*x^ 16*log(1/4*x^2) + 43095327221832275390625/4722366482869645213696*x^16
Time = 8.89 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.68 \[ \int \frac {57460436295776367187500 x^{15}+148439460430755615234375 x^{15} \log \left (\frac {x^2}{4}\right )+167592939196014404296875 x^{15} \log ^2\left (\frac {x^2}{4}\right )+108004338592987060546875 x^{15} \log ^3\left (\frac {x^2}{4}\right )+43450021273040771484375 x^{15} \log ^4\left (\frac {x^2}{4}\right )+11172862613067626953125 x^{15} \log ^5\left (\frac {x^2}{4}\right )+1793175481109619140625 x^{15} \log ^6\left (\frac {x^2}{4}\right )+164210208892822265625 x^{15} \log ^7\left (\frac {x^2}{4}\right )+6568408355712890625 x^{15} \log ^8\left (\frac {x^2}{4}\right )}{295147905179352825856} \, dx=\frac {6568408355712890625\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^8}{4722366482869645213696}+\frac {19705225067138671875\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^7}{590295810358705651712}+\frac {413809726409912109375\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^6}{1180591620717411303424}+\frac {1241429179229736328125\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^5}{590295810358705651712}+\frac {18621437688446044921875\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^4}{2361183241434822606848}+\frac {11172862613067626953125\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^3}{590295810358705651712}+\frac {33518587839202880859375\,x^{16}\,{\ln \left (\frac {x^2}{4}\right )}^2}{1180591620717411303424}+\frac {14365109073944091796875\,x^{16}\,\ln \left (\frac {x^2}{4}\right )}{590295810358705651712}+\frac {43095327221832275390625\,x^{16}}{4722366482869645213696} \]
int((167592939196014404296875*x^15*log(x^2/4)^2)/295147905179352825856 + ( 108004338592987060546875*x^15*log(x^2/4)^3)/295147905179352825856 + (43450 021273040771484375*x^15*log(x^2/4)^4)/295147905179352825856 + (11172862613 067626953125*x^15*log(x^2/4)^5)/295147905179352825856 + (17931754811096191 40625*x^15*log(x^2/4)^6)/295147905179352825856 + (164210208892822265625*x^ 15*log(x^2/4)^7)/295147905179352825856 + (6568408355712890625*x^15*log(x^2 /4)^8)/295147905179352825856 + (14365109073944091796875*x^15)/737869762948 38206464 + (148439460430755615234375*x^15*log(x^2/4))/29514790517935282585 6,x)
(33518587839202880859375*x^16*log(x^2/4)^2)/1180591620717411303424 + (1117 2862613067626953125*x^16*log(x^2/4)^3)/590295810358705651712 + (1862143768 8446044921875*x^16*log(x^2/4)^4)/2361183241434822606848 + (124142917922973 6328125*x^16*log(x^2/4)^5)/590295810358705651712 + (413809726409912109375* x^16*log(x^2/4)^6)/1180591620717411303424 + (19705225067138671875*x^16*log (x^2/4)^7)/590295810358705651712 + (6568408355712890625*x^16*log(x^2/4)^8) /4722366482869645213696 + (43095327221832275390625*x^16)/47223664828696452 13696 + (14365109073944091796875*x^16*log(x^2/4))/590295810358705651712