Integrand size = 101, antiderivative size = 21 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2+e^4+\frac {2 x^2}{(16+\log (2))^4}}{\log (x)} \]
Time = 0.31 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.62 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {e^4 (16+\log (2))^4+2 \left (x^2+(16+\log (2))^4\right )}{(16+\log (2))^4 \log (x)} \]
Integrate[(-131072 - 65536*E^4 - 2*x^2 + (-32768 - 16384*E^4)*Log[2] + (-3 072 - 1536*E^4)*Log[2]^2 + (-128 - 64*E^4)*Log[2]^3 + (-2 - E^4)*Log[2]^4 + 4*x^2*Log[x])/((65536*x + 16384*x*Log[2] + 1536*x*Log[2]^2 + 64*x*Log[2] ^3 + x*Log[2]^4)*Log[x]^2),x]
Time = 0.49 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.67, number of steps used = 8, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {6, 6, 6, 6, 27, 25, 7293, 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.
| \(\displaystyle \int \frac {-2 x^2+4 x^2 \log (x)-65536 e^4-131072+\left (-2-e^4\right ) \log ^4(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-32768-16384 e^4\right ) \log (2)}{\left (65536 x+x \log ^4(2)+64 x \log ^3(2)+1536 x \log ^2(2)+16384 x \log (2)\right ) \log ^2(x)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-2 x^2+4 x^2 \log (x)-65536 e^4-131072+\left (-2-e^4\right ) \log ^4(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-32768-16384 e^4\right ) \log (2)}{\left (x \log ^4(2)+64 x \log ^3(2)+1536 x \log ^2(2)+x (65536+16384 \log (2))\right ) \log ^2(x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-2 x^2+4 x^2 \log (x)-65536 e^4-131072+\left (-2-e^4\right ) \log ^4(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-32768-16384 e^4\right ) \log (2)}{\left (x \log ^4(2)+x \left (64 \log ^3(2)+1536 \log ^2(2)\right )+x (65536+16384 \log (2))\right ) \log ^2(x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-2 x^2+4 x^2 \log (x)-65536 e^4-131072+\left (-2-e^4\right ) \log ^4(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-32768-16384 e^4\right ) \log (2)}{\left (x \left (65536+\log ^4(2)+16384 \log (2)\right )+x \left (64 \log ^3(2)+1536 \log ^2(2)\right )\right ) \log ^2(x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-2 x^2+4 x^2 \log (x)-65536 e^4-131072+\left (-2-e^4\right ) \log ^4(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-32768-16384 e^4\right ) \log (2)}{x \left (65536+\log ^4(2)+64 \log ^3(2)+1536 \log ^2(2)+16384 \log (2)\right ) \log ^2(x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {-4 \log (x) x^2+2 x^2+\left (2+e^4\right ) (16+\log (2))^4}{x \log ^2(x)}dx}{(16+\log (2))^4}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {-4 \log (x) x^2+2 x^2+\left (2+e^4\right ) (16+\log (2))^4}{x \log ^2(x)}dx}{(16+\log (2))^4}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (\frac {2 x^2+e^4 \log ^4(2)+2 \log ^4(2)+64 e^4 \log ^3(2)+128 \log ^3(2)+1536 e^4 \log ^2(2)+3072 \log ^2(2)+16384 e^4 \log (2)+32768 \log (2)+65536 e^4+131072}{x \log ^2(x)}-\frac {4 x}{\log (x)}\right )dx}{(16+\log (2))^4}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {-\frac {2 x^2}{\log (x)}-\frac {\left (2+e^4\right ) (16+\log (2))^4}{\log (x)}}{(16+\log (2))^4}\) |
Int[(-131072 - 65536*E^4 - 2*x^2 + (-32768 - 16384*E^4)*Log[2] + (-3072 - 1536*E^4)*Log[2]^2 + (-128 - 64*E^4)*Log[2]^3 + (-2 - E^4)*Log[2]^4 + 4*x^ 2*Log[x])/((65536*x + 16384*x*Log[2] + 1536*x*Log[2]^2 + 64*x*Log[2]^3 + x *Log[2]^4)*Log[x]^2),x]
3.2.6.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
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. \(65\) vs. \(2(20)=40\).
Time = 0.19 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.14
| method | result | size |
| norman | \(\frac {\frac {2 x^{2}}{16+\ln \left (2\right )}+8192+{\mathrm e}^{4} \ln \left (2\right )^{3}+48 \,{\mathrm e}^{4} \ln \left (2\right )^{2}+2 \ln \left (2\right )^{3}+768 \,{\mathrm e}^{4} \ln \left (2\right )+96 \ln \left (2\right )^{2}+4096 \,{\mathrm e}^{4}+1536 \ln \left (2\right )}{\left (16+\ln \left (2\right )\right )^{3} \ln \left (x \right )}\) | \(66\) |
| risch | \(\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}+64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}+2 \ln \left (2\right )^{4}+1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}+128 \ln \left (2\right )^{3}+16384 \,{\mathrm e}^{4} \ln \left (2\right )+3072 \ln \left (2\right )^{2}+2 x^{2}+65536 \,{\mathrm e}^{4}+32768 \ln \left (2\right )+131072}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}\) | \(92\) |
| parallelrisch | \(\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}+64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}+2 \ln \left (2\right )^{4}+1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}+128 \ln \left (2\right )^{3}+16384 \,{\mathrm e}^{4} \ln \left (2\right )+3072 \ln \left (2\right )^{2}+2 x^{2}+65536 \,{\mathrm e}^{4}+32768 \ln \left (2\right )+131072}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}\) | \(92\) |
| parts | \(-\frac {4 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}-\frac {-\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}}{\ln \left (x \right )}-\frac {64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}}{\ln \left (x \right )}-\frac {2 \ln \left (2\right )^{4}}{\ln \left (x \right )}-\frac {1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}}{\ln \left (x \right )}-\frac {128 \ln \left (2\right )^{3}}{\ln \left (x \right )}-\frac {16384 \,{\mathrm e}^{4} \ln \left (2\right )}{\ln \left (x \right )}-\frac {3072 \ln \left (2\right )^{2}}{\ln \left (x \right )}-\frac {2 x^{2}}{\ln \left (x \right )}-4 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )-\frac {65536 \,{\mathrm e}^{4}}{\ln \left (x \right )}-\frac {32768 \ln \left (2\right )}{\ln \left (x \right )}-\frac {131072}{\ln \left (x \right )}}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}\) | \(176\) |
| default | \(\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {2 \ln \left (2\right )^{4}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}-\frac {4 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}+\frac {1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {128 \ln \left (2\right )^{3}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {16384 \,{\mathrm e}^{4} \ln \left (2\right )}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {3072 \ln \left (2\right )^{2}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}-\frac {2 \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}+\frac {65536 \,{\mathrm e}^{4}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {32768 \ln \left (2\right )}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {131072}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}\) | \(415\) |
int((4*x^2*ln(x)+(-exp(4)-2)*ln(2)^4+(-64*exp(4)-128)*ln(2)^3+(-1536*exp(4 )-3072)*ln(2)^2+(-16384*exp(4)-32768)*ln(2)-65536*exp(4)-2*x^2-131072)/(x* ln(2)^4+64*x*ln(2)^3+1536*x*ln(2)^2+16384*x*ln(2)+65536*x)/ln(x)^2,x,metho d=_RETURNVERBOSE)
(2/(16+ln(2))*x^2+8192+exp(4)*ln(2)^3+48*exp(4)*ln(2)^2+2*ln(2)^3+768*exp( 4)*ln(2)+96*ln(2)^2+4096*exp(4)+1536*ln(2))/(16+ln(2))^3/ln(x)
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (20) = 40\).
Time = 0.29 (sec) , antiderivative size = 77, normalized size of antiderivative = 3.67 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {{\left (e^{4} + 2\right )} \log \left (2\right )^{4} + 64 \, {\left (e^{4} + 2\right )} \log \left (2\right )^{3} + 1536 \, {\left (e^{4} + 2\right )} \log \left (2\right )^{2} + 2 \, x^{2} + 16384 \, {\left (e^{4} + 2\right )} \log \left (2\right ) + 65536 \, e^{4} + 131072}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} \]
integrate((4*x^2*log(x)+(-exp(4)-2)*log(2)^4+(-64*exp(4)-128)*log(2)^3+(-1 536*exp(4)-3072)*log(2)^2+(-16384*exp(4)-32768)*log(2)-65536*exp(4)-2*x^2- 131072)/(x*log(2)^4+64*x*log(2)^3+1536*x*log(2)^2+16384*x*log(2)+65536*x)/ log(x)^2,x, algorithm=\
((e^4 + 2)*log(2)^4 + 64*(e^4 + 2)*log(2)^3 + 1536*(e^4 + 2)*log(2)^2 + 2* x^2 + 16384*(e^4 + 2)*log(2) + 65536*e^4 + 131072)/((log(2)^4 + 64*log(2)^ 3 + 1536*log(2)^2 + 16384*log(2) + 65536)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (19) = 38\).
Time = 0.07 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.86 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2 x^{2} + 2 \log {\left (2 \right )}^{4} + e^{4} \log {\left (2 \right )}^{4} + 128 \log {\left (2 \right )}^{3} + 64 e^{4} \log {\left (2 \right )}^{3} + 3072 \log {\left (2 \right )}^{2} + 32768 \log {\left (2 \right )} + 1536 e^{4} \log {\left (2 \right )}^{2} + 131072 + 16384 e^{4} \log {\left (2 \right )} + 65536 e^{4}}{\left (\log {\left (2 \right )}^{4} + 64 \log {\left (2 \right )}^{3} + 1536 \log {\left (2 \right )}^{2} + 16384 \log {\left (2 \right )} + 65536\right ) \log {\left (x \right )}} \]
integrate((4*x**2*ln(x)+(-exp(4)-2)*ln(2)**4+(-64*exp(4)-128)*ln(2)**3+(-1 536*exp(4)-3072)*ln(2)**2+(-16384*exp(4)-32768)*ln(2)-65536*exp(4)-2*x**2- 131072)/(x*ln(2)**4+64*x*ln(2)**3+1536*x*ln(2)**2+16384*x*ln(2)+65536*x)/l n(x)**2,x)
(2*x**2 + 2*log(2)**4 + exp(4)*log(2)**4 + 128*log(2)**3 + 64*exp(4)*log(2 )**3 + 3072*log(2)**2 + 32768*log(2) + 1536*exp(4)*log(2)**2 + 131072 + 16 384*exp(4)*log(2) + 65536*exp(4))/((log(2)**4 + 64*log(2)**3 + 1536*log(2) **2 + 16384*log(2) + 65536)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 371 vs. \(2 (20) = 40\).
Time = 0.33 (sec) , antiderivative size = 371, normalized size of antiderivative = 17.67 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx =\text {Too large to display} \]
integrate((4*x^2*log(x)+(-exp(4)-2)*log(2)^4+(-64*exp(4)-128)*log(2)^3+(-1 536*exp(4)-3072)*log(2)^2+(-16384*exp(4)-32768)*log(2)-65536*exp(4)-2*x^2- 131072)/(x*log(2)^4+64*x*log(2)^3+1536*x*log(2)^2+16384*x*log(2)+65536*x)/ log(x)^2,x, algorithm=\
e^4*log(2)^4/((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384*log(2) + 655 36)*log(x)) + 64*e^4*log(2)^3/((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 1 6384*log(2) + 65536)*log(x)) + 2*log(2)^4/((log(2)^4 + 64*log(2)^3 + 1536* log(2)^2 + 16384*log(2) + 65536)*log(x)) + 1536*e^4*log(2)^2/((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384*log(2) + 65536)*log(x)) + 128*log(2)^3 /((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384*log(2) + 65536)*log(x)) + 2*x^2/((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384*log(2) + 65536)*l og(x)) + 16384*e^4*log(2)/((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384 *log(2) + 65536)*log(x)) + 3072*log(2)^2/((log(2)^4 + 64*log(2)^3 + 1536*l og(2)^2 + 16384*log(2) + 65536)*log(x)) + 65536*e^4/((log(2)^4 + 64*log(2) ^3 + 1536*log(2)^2 + 16384*log(2) + 65536)*log(x)) + 32768*log(2)/((log(2) ^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384*log(2) + 65536)*log(x)) + 131072/ ((log(2)^4 + 64*log(2)^3 + 1536*log(2)^2 + 16384*log(2) + 65536)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (20) = 40\).
Time = 0.26 (sec) , antiderivative size = 99, normalized size of antiderivative = 4.71 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {e^{4} \log \left (2\right )^{4} + 64 \, e^{4} \log \left (2\right )^{3} + 2 \, \log \left (2\right )^{4} + 1536 \, e^{4} \log \left (2\right )^{2} + 128 \, \log \left (2\right )^{3} + 2 \, x^{2} + 16384 \, e^{4} \log \left (2\right ) + 3072 \, \log \left (2\right )^{2} + 65536 \, e^{4} + 32768 \, \log \left (2\right ) + 131072}{\log \left (2\right )^{4} \log \left (x\right ) + 64 \, \log \left (2\right )^{3} \log \left (x\right ) + 1536 \, \log \left (2\right )^{2} \log \left (x\right ) + 16384 \, \log \left (2\right ) \log \left (x\right ) + 65536 \, \log \left (x\right )} \]
integrate((4*x^2*log(x)+(-exp(4)-2)*log(2)^4+(-64*exp(4)-128)*log(2)^3+(-1 536*exp(4)-3072)*log(2)^2+(-16384*exp(4)-32768)*log(2)-65536*exp(4)-2*x^2- 131072)/(x*log(2)^4+64*x*log(2)^3+1536*x*log(2)^2+16384*x*log(2)+65536*x)/ log(x)^2,x, algorithm=\
(e^4*log(2)^4 + 64*e^4*log(2)^3 + 2*log(2)^4 + 1536*e^4*log(2)^2 + 128*log (2)^3 + 2*x^2 + 16384*e^4*log(2) + 3072*log(2)^2 + 65536*e^4 + 32768*log(2 ) + 131072)/(log(2)^4*log(x) + 64*log(2)^3*log(x) + 1536*log(2)^2*log(x) + 16384*log(2)*log(x) + 65536*log(x))
Time = 9.86 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.48 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2\,x^2+65536\,{\mathrm {e}}^4+32768\,\ln \left (2\right )+16384\,{\mathrm {e}}^4\,\ln \left (2\right )+1536\,{\mathrm {e}}^4\,{\ln \left (2\right )}^2+64\,{\mathrm {e}}^4\,{\ln \left (2\right )}^3+{\mathrm {e}}^4\,{\ln \left (2\right )}^4+3072\,{\ln \left (2\right )}^2+128\,{\ln \left (2\right )}^3+2\,{\ln \left (2\right )}^4+131072}{\ln \left (x\right )\,{\left (\ln \left (2\right )+16\right )}^4} \]
int(-(65536*exp(4) - 4*x^2*log(x) + log(2)^3*(64*exp(4) + 128) + log(2)^2* (1536*exp(4) + 3072) + 2*x^2 + log(2)*(16384*exp(4) + 32768) + log(2)^4*(e xp(4) + 2) + 131072)/(log(x)^2*(65536*x + 16384*x*log(2) + 1536*x*log(2)^2 + 64*x*log(2)^3 + x*log(2)^4)),x)