Integrand size = 275, antiderivative size = 31 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=\frac {\left (-3+e^{x/4}\right ) (2+x+\log (3))^2}{\left (4+e^5+\frac {e^5}{x^2}\right )^2} \] Output:
(exp(1/4*x)-3)*(ln(3)+2+x)^2/(4+exp(5)+exp(5)/x^2)^2
Leaf count is larger than twice the leaf count of optimal. \(265\) vs. \(2(31)=62\).
Time = 0.20 (sec) , antiderivative size = 265, normalized size of antiderivative = 8.55 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=\frac {192 e^{5+\frac {x}{4}} x^4 (2+x+\log (3))^2+48 e^{10+\frac {x}{4}} x^4 (2+x+\log (3))^2+4 e^{15+\frac {x}{4}} x^4 (2+x+\log (3))^2+256 e^{x/4} x^4 (2+x+\log (3))^2-768 x^5 (4+x+\log (9))-3 e^{15} \left (8 x^4+4 x^6-\log ^2(9)-2 (4+\log (6561))+x^5 (16+\log (6561))-x^2 (\log (9) \log (81)+2 (8+\log (43046721)))\right )-48 e^5 x^2 \left (8 x^2+12 x^4-\log (9) \log (81)-2 (16+\log (43046721))+x^3 (48+\log (282429536481))\right )-12 e^{10} \left (16 x^4+12 x^6-\log ^2(9)-2 (8+\log (6561))+x^5 (48+\log (282429536481))-x^2 (48+\log (9) \log (6561)+2 \log (1853020188851841))\right )}{4 \left (4+e^5\right )^3 \left (4 x^2+e^5 \left (1+x^2\right )\right )^2} \] Input:
Integrate[(-192*x^6 - 96*x^7 + E^5*(-192*x^3 - 240*x^4 - 72*x^5 - 48*x^6 - 24*x^7) + (-96*x^6 + E^5*(-192*x^3 - 120*x^4 - 24*x^6))*Log[3] - 48*E^5*x ^3*Log[3]^2 + E^(x/4)*(80*x^6 + 48*x^7 + 4*x^8 + E^5*(64*x^3 + 84*x^4 + 28 *x^5 + 21*x^6 + 12*x^7 + x^8) + (48*x^6 + 8*x^7 + E^5*(64*x^3 + 44*x^4 + 2 *x^5 + 12*x^6 + 2*x^7))*Log[3] + (4*x^6 + E^5*(16*x^3 + x^4 + x^6))*Log[3] ^2))/(256*x^6 + E^15*(4 + 12*x^2 + 12*x^4 + 4*x^6) + E^10*(48*x^2 + 96*x^4 + 48*x^6) + E^5*(192*x^4 + 192*x^6)),x]
Output:
(192*E^(5 + x/4)*x^4*(2 + x + Log[3])^2 + 48*E^(10 + x/4)*x^4*(2 + x + Log [3])^2 + 4*E^(15 + x/4)*x^4*(2 + x + Log[3])^2 + 256*E^(x/4)*x^4*(2 + x + Log[3])^2 - 768*x^5*(4 + x + Log[9]) - 3*E^15*(8*x^4 + 4*x^6 - Log[9]^2 - 2*(4 + Log[6561]) + x^5*(16 + Log[6561]) - x^2*(Log[9]*Log[81] + 2*(8 + Lo g[43046721]))) - 48*E^5*x^2*(8*x^2 + 12*x^4 - Log[9]*Log[81] - 2*(16 + Log [43046721]) + x^3*(48 + Log[282429536481])) - 12*E^10*(16*x^4 + 12*x^6 - L og[9]^2 - 2*(8 + Log[6561]) + x^5*(48 + Log[282429536481]) - x^2*(48 + Log [9]*Log[6561] + 2*Log[1853020188851841])))/(4*(4 + E^5)^3*(4*x^2 + E^5*(1 + x^2))^2)
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.
| \(\displaystyle \int \frac {-96 x^7-192 x^6-48 e^5 x^3 \log ^2(3)+\left (e^5 \left (-24 x^6-120 x^4-192 x^3\right )-96 x^6\right ) \log (3)+e^5 \left (-24 x^7-48 x^6-72 x^5-240 x^4-192 x^3\right )+e^{x/4} \left (4 x^8+48 x^7+80 x^6+\left (4 x^6+e^5 \left (x^6+x^4+16 x^3\right )\right ) \log ^2(3)+\left (8 x^7+48 x^6+e^5 \left (2 x^7+12 x^6+2 x^5+44 x^4+64 x^3\right )\right ) \log (3)+e^5 \left (x^8+12 x^7+21 x^6+28 x^5+84 x^4+64 x^3\right )\right )}{256 x^6+e^5 \left (192 x^6+192 x^4\right )+e^{15} \left (4 x^6+12 x^4+12 x^2+4\right )+e^{10} \left (48 x^6+96 x^4+48 x^2\right )} \, dx\) |
| \(\Big \downarrow \) 2070 |
| \(\displaystyle \int \frac {-96 x^7-192 x^6-48 e^5 x^3 \log ^2(3)+\left (e^5 \left (-24 x^6-120 x^4-192 x^3\right )-96 x^6\right ) \log (3)+e^5 \left (-24 x^7-48 x^6-72 x^5-240 x^4-192 x^3\right )+e^{x/4} \left (4 x^8+48 x^7+80 x^6+\left (4 x^6+e^5 \left (x^6+x^4+16 x^3\right )\right ) \log ^2(3)+\left (8 x^7+48 x^6+e^5 \left (2 x^7+12 x^6+2 x^5+44 x^4+64 x^3\right )\right ) \log (3)+e^5 \left (x^8+12 x^7+21 x^6+28 x^5+84 x^4+64 x^3\right )\right )}{\left (2^{2/3} \left (4+e^5\right ) x^2+2^{2/3} e^5\right )^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (x+2+\log (3)) \left (-96 x^3+4 e^{x/4} x^3 (x+10+\log (3))-24 e^5 \left (x^3+3 x+4+\log (9)\right )+e^{\frac {x}{4}+5} \left (x^4+x^3 (10+\log (3))+x^2+x (26+\log (3))+16 (2+\log (3))\right )\right )}{4 \left (\left (4+e^5\right ) x^2+e^5\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{4} \int -\frac {x^3 (x+\log (3)+2) \left (-4 e^{x/4} (x+\log (3)+10) x^3+96 x^3-e^{\frac {x}{4}+5} \left (x^4+(10+\log (3)) x^3+x^2+(26+\log (3)) x+16 (2+\log (3))\right )+24 e^5 \left (x^3+3 x+\log (9)+4\right )\right )}{\left (\left (4+e^5\right ) x^2+e^5\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{4} \int \frac {x^3 (x+\log (3)+2) \left (-4 e^{x/4} (x+\log (3)+10) x^3+96 x^3-e^{\frac {x}{4}+5} \left (x^4+(10+\log (3)) x^3+x^2+(26+\log (3)) x+16 (2+\log (3))\right )+24 e^5 \left (x^3+3 x+\log (9)+4\right )\right )}{\left (\left (4+e^5\right ) x^2+e^5\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{4} \int \left (\frac {e^{x/4} (x+\log (3)+2) \left (-\left (\left (4+e^5\right ) x^4\right )-\left (4+e^5\right ) (10+\log (3)) x^3-e^5 x^2-e^5 (26+\log (3)) x-16 e^5 (2+\log (3))\right ) x^3}{\left (\left (4+e^5\right ) x^2+e^5\right )^3}+\frac {24 (x+\log (3)+2) \left (\left (4+e^5\right ) x^3+3 e^5 x+e^5 (4+\log (9))\right ) x^3}{\left (\left (4+e^5\right ) x^2+e^5\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{4} \left (-\frac {12 (x+\log (3)+2)^2 x^4}{\left (\left (4+e^5\right ) x^2+e^5\right )^2}+\frac {4 e^{x/4} x^2}{\left (4+e^5\right )^2}+\frac {8 e^{x/4} (6+\log (3)) x}{\left (4+e^5\right )^2}-\frac {32 e^{x/4} x}{\left (4+e^5\right )^2}-\frac {16 \left (4 (2+\log (3))^2+e^5 \left (3+\log ^2(3)+\log (81)\right )\right ) \int \frac {e^{\frac {x}{4}+10} x}{\left (\left (4+e^5\right ) x^2+e^5\right )^3}dx}{\left (4+e^5\right )^2}+\frac {2 \left (32 (2+\log (3))^2+e^5 \left (22+33 \log (3)+8 \log ^2(3)\right )\right ) \int \frac {e^{\frac {x}{4}+5} x}{\left (\left (4+e^5\right ) x^2+e^5\right )^2}dx}{\left (4+e^5\right )^2}-\frac {e^{\frac {5}{2}+\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (-\frac {i e^{5/2}-\sqrt {4+e^5} x}{4 \sqrt {4+e^5}}\right ) \left (4 e^{5/2} \sqrt {4+e^5} (2+\log (3))+i \left (96+32 \log (3)-8 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )\right )\right )}{2 \left (4+e^5\right )^{7/2}}+\frac {4 e^{x/4} \left (e^5 \left (18+12 \log (3)+\log ^2(3)\right )+4 \left (20+12 \log (3)+\log ^2(3)\right )\right )}{\left (4+e^5\right )^3}-\frac {i e^{\frac {5}{2}-\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (\frac {\sqrt {4+e^5} x+i e^{5/2}}{4 \sqrt {4+e^5}}\right ) \left (4 \left (108+52 \log (3)-\log ^2(3)\right )+e^5 \left (109+52 \log (3)-\log ^2(3)\right )\right )}{4 \left (4+e^5\right )^{7/2}}+\frac {i e^{\frac {5}{2}+\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (-\frac {i e^{5/2} \sqrt {4+e^5}-\left (4+e^5\right ) x}{4 \left (4+e^5\right )}\right ) \left (4 \left (108+52 \log (3)-\log ^2(3)\right )+e^5 \left (109+52 \log (3)-\log ^2(3)\right )\right )}{4 \left (4+e^5\right )^{7/2}}+\frac {e^{5-\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (\frac {\sqrt {4+e^5} x+i e^{5/2}}{4 \sqrt {4+e^5}}\right ) \left (432+208 \log (3)-4 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )\right )}{16 \left (4+e^5\right )^4}+\frac {e^{5+\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (-\frac {i e^{5/2} \sqrt {4+e^5}-\left (4+e^5\right ) x}{4 \left (4+e^5\right )}\right ) \left (432+208 \log (3)-4 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )\right )}{16 \left (4+e^5\right )^4}-\frac {e^{\frac {x}{4}+5} \left (432+208 \log (3)-4 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )\right )}{4 \left (4+e^5\right )^{7/2} \left (\sqrt {4+e^5} x+i e^{5/2}\right )}+\frac {e^{\frac {x}{4}+5} \left (432+208 \log (3)-4 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )\right )}{4 \left (4+e^5\right )^3 \left (i e^{5/2} \sqrt {4+e^5}-\left (4+e^5\right ) x\right )}-\frac {e^{\frac {5}{2}-\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (\frac {\sqrt {4+e^5} x+i e^{5/2}}{4 \sqrt {4+e^5}}\right ) \left (4 e^{5/2} \sqrt {4+e^5} (2+\log (3))-i e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )-8 i \left (12+4 \log (3)-\log ^2(3)\right )\right )}{2 \left (4+e^5\right )^{7/2}}-\frac {32 e^{x/4} (6+\log (3))}{\left (4+e^5\right )^2}-\frac {6 i e^{\frac {5}{2}+\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (-\frac {i e^{5/2}-\sqrt {4+e^5} x}{4 \sqrt {4+e^5}}\right ) (2+\log (3))}{\left (4+e^5\right )^{5/2}}+\frac {i e^{\frac {15}{2}+\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (-\frac {i e^{5/2}-\sqrt {4+e^5} x}{4 \sqrt {4+e^5}}\right ) (2+\log (3))}{8 \left (4+e^5\right )^{7/2}}+\frac {6 i e^{\frac {5}{2}-\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (\frac {\sqrt {4+e^5} x+i e^{5/2}}{4 \sqrt {4+e^5}}\right ) (2+\log (3))}{\left (4+e^5\right )^{5/2}}-\frac {3 e^{5-\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (\frac {\sqrt {4+e^5} x+i e^{5/2}}{4 \sqrt {4+e^5}}\right ) (2+\log (3))}{2 \left (4+e^5\right )^3}-\frac {i e^{\frac {15}{2}-\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (\frac {\sqrt {4+e^5} x+i e^{5/2}}{4 \sqrt {4+e^5}}\right ) (2+\log (3))}{8 \left (4+e^5\right )^{7/2}}-\frac {3 e^{5+\frac {i e^{5/2}}{4 \sqrt {4+e^5}}} \operatorname {ExpIntegralEi}\left (-\frac {i e^{5/2} \sqrt {4+e^5}-\left (4+e^5\right ) x}{4 \left (4+e^5\right )}\right ) (2+\log (3))}{2 \left (4+e^5\right )^3}+\frac {i e^{\frac {x}{4}+\frac {15}{2}} (2+\log (3))}{2 \left (4+e^5\right )^3 \left (i e^{5/2}-\sqrt {4+e^5} x\right )}+\frac {6 e^{\frac {x}{4}+5} (2+\log (3))}{\left (4+e^5\right )^{5/2} \left (\sqrt {4+e^5} x+i e^{5/2}\right )}-\frac {6 e^{\frac {x}{4}+5} (2+\log (3))}{\left (4+e^5\right )^2 \left (i e^{5/2} \sqrt {4+e^5}-\left (4+e^5\right ) x\right )}+\frac {i e^{\frac {x}{4}+\frac {15}{2}} (2+\log (3))}{2 \sqrt {4+e^5} \left (\left (4+e^5\right )^3 x+i \left (e \left (4+e^5\right )\right )^{5/2}\right )}-\frac {2 i e^{\frac {x}{4}+\frac {15}{2}} (2+\log (3))}{\left (4+e^5\right )^{5/2} \left (i e^{5/2}-\sqrt {4+e^5} x\right )^2}+\frac {2 i e^{\frac {x}{4}+\frac {15}{2}} (2+\log (3))}{\left (4+e^5\right )^{5/2} \left (\sqrt {4+e^5} x+i e^{5/2}\right )^2}+\frac {128 e^{x/4}}{\left (4+e^5\right )^2}\right )\) |
Input:
Int[(-192*x^6 - 96*x^7 + E^5*(-192*x^3 - 240*x^4 - 72*x^5 - 48*x^6 - 24*x^ 7) + (-96*x^6 + E^5*(-192*x^3 - 120*x^4 - 24*x^6))*Log[3] - 48*E^5*x^3*Log [3]^2 + E^(x/4)*(80*x^6 + 48*x^7 + 4*x^8 + E^5*(64*x^3 + 84*x^4 + 28*x^5 + 21*x^6 + 12*x^7 + x^8) + (48*x^6 + 8*x^7 + E^5*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7))*Log[3] + (4*x^6 + E^5*(16*x^3 + x^4 + x^6))*Log[3]^2))/( 256*x^6 + E^15*(4 + 12*x^2 + 12*x^4 + 4*x^6) + E^10*(48*x^2 + 96*x^4 + 48* x^6) + E^5*(192*x^4 + 192*x^6)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(89\) vs. \(2(26)=52\).
Time = 8.46 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.90
| method | result | size |
| norman | \(\frac {\left (-6 \ln \left (3\right )-12\right ) x^{5}+\left (-3 \ln \left (3\right )^{2}-12 \ln \left (3\right )-12\right ) x^{4}+{\mathrm e}^{\frac {x}{4}} x^{6}+\left (2 \ln \left (3\right )+4\right ) x^{5} {\mathrm e}^{\frac {x}{4}}+\left (\ln \left (3\right )^{2}+4 \ln \left (3\right )+4\right ) x^{4} {\mathrm e}^{\frac {x}{4}}-3 x^{6}}{\left (x^{2} {\mathrm e}^{5}+4 x^{2}+{\mathrm e}^{5}\right )^{2}}\) | \(90\) |
| parallelrisch | \(\frac {\left (4 \,{\mathrm e}^{10} \ln \left (3\right )^{2} {\mathrm e}^{\frac {x}{4}} x^{4}+8 \,{\mathrm e}^{10} \ln \left (3\right ) {\mathrm e}^{\frac {x}{4}} x^{5}+4 \,{\mathrm e}^{10} {\mathrm e}^{\frac {x}{4}} x^{6}-12 \,{\mathrm e}^{10} \ln \left (3\right )^{2} x^{4}-24 \,{\mathrm e}^{10} \ln \left (3\right ) x^{5}+16 \,{\mathrm e}^{10} \ln \left (3\right ) {\mathrm e}^{\frac {x}{4}} x^{4}-12 x^{6} {\mathrm e}^{10}+16 \,{\mathrm e}^{10} {\mathrm e}^{\frac {x}{4}} x^{5}-48 \,{\mathrm e}^{10} \ln \left (3\right ) x^{4}-48 \,{\mathrm e}^{10} x^{5}+16 \,{\mathrm e}^{10} {\mathrm e}^{\frac {x}{4}} x^{4}-48 \,{\mathrm e}^{10} x^{4}\right ) {\mathrm e}^{-10}}{4 \,{\mathrm e}^{10} x^{4}+32 x^{4} {\mathrm e}^{5}+8 x^{2} {\mathrm e}^{10}+64 x^{4}+32 x^{2} {\mathrm e}^{5}+4 \,{\mathrm e}^{10}}\) | \(199\) |
| risch | \(-\frac {6 \ln \left (3\right ) x}{{\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16}-\frac {3 x^{2}}{{\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16}-\frac {12 x}{{\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16}+\frac {12 \,{\mathrm e}^{5} \left ({\mathrm e}^{5} \ln \left (3\right )+2 \,{\mathrm e}^{5}+4 \ln \left (3\right )+8\right ) x^{3}+3 \left (2 \,{\mathrm e}^{5} \ln \left (3\right )^{2}+8 \,{\mathrm e}^{5} \ln \left (3\right )+8 \ln \left (3\right )^{2}+5 \,{\mathrm e}^{5}+32 \ln \left (3\right )+32\right ) {\mathrm e}^{5} x^{2}+\left (6 \,{\mathrm e}^{10} \ln \left (3\right )+12 \,{\mathrm e}^{10}\right ) x +\frac {3 \,{\mathrm e}^{10} \left ({\mathrm e}^{5} \ln \left (3\right )^{2}+4 \,{\mathrm e}^{5} \ln \left (3\right )+4 \ln \left (3\right )^{2}+2 \,{\mathrm e}^{5}+16 \ln \left (3\right )+16\right )}{4+{\mathrm e}^{5}}}{\left ({\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16\right ) \left ({\mathrm e}^{10} x^{4}+8 x^{4} {\mathrm e}^{5}+2 x^{2} {\mathrm e}^{10}+16 x^{4}+8 x^{2} {\mathrm e}^{5}+{\mathrm e}^{10}\right )}+\frac {\left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}+4 \ln \left (3\right )+4 x +4\right ) x^{4} {\mathrm e}^{\frac {x}{4}}}{\left (x^{2} {\mathrm e}^{5}+4 x^{2}+{\mathrm e}^{5}\right )^{2}}\) | \(250\) |
| parts | \(\text {Expression too large to display}\) | \(11384\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(12925\) |
| default | \(\text {Expression too large to display}\) | \(12925\) |
Input:
int(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*ln(3)^2+((2*x^7+12*x^6+2*x^5+44*x^4+ 64*x^3)*exp(5)+8*x^7+48*x^6)*ln(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^4+64*x^3 )*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*ln(3)^2+((-24*x^6-1 20*x^4-192*x^3)*exp(5)-96*x^6)*ln(3)+(-24*x^7-48*x^6-72*x^5-240*x^4-192*x^ 3)*exp(5)-96*x^7-192*x^6)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48*x^6+96*x^4 +48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x,method=_RETURNVERBOS E)
Output:
((-6*ln(3)-12)*x^5+(-3*ln(3)^2-12*ln(3)-12)*x^4+exp(1/4*x)*x^6+(2*ln(3)+4) *x^5*exp(1/4*x)+(ln(3)^2+4*ln(3)+4)*x^4*exp(1/4*x)-3*x^6)/(x^2*exp(5)+4*x^ 2+exp(5))^2
Leaf count of result is larger than twice the leaf count of optimal. 420 vs. \(2 (26) = 52\).
Time = 0.11 (sec) , antiderivative size = 420, normalized size of antiderivative = 13.55 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=-\frac {192 \, x^{6} + 768 \, x^{5} - 3 \, {\left (32 \, x^{2} e^{5} + {\left (2 \, x^{2} + 1\right )} e^{15} + 4 \, {\left (4 \, x^{2} + 1\right )} e^{10}\right )} \log \left (3\right )^{2} + 3 \, {\left (x^{6} + 4 \, x^{5} + 2 \, x^{4} - 4 \, x^{2} - 2\right )} e^{15} + 12 \, {\left (3 \, x^{6} + 12 \, x^{5} + 4 \, x^{4} - 12 \, x^{2} - 4\right )} e^{10} + 48 \, {\left (3 \, x^{6} + 12 \, x^{5} + 2 \, x^{4} - 8 \, x^{2}\right )} e^{5} - {\left (64 \, x^{6} + 256 \, x^{5} + 256 \, x^{4} + {\left (x^{4} e^{15} + 12 \, x^{4} e^{10} + 48 \, x^{4} e^{5} + 64 \, x^{4}\right )} \log \left (3\right )^{2} + {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{15} + 12 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{10} + 48 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{5} + 2 \, {\left (64 \, x^{5} + 128 \, x^{4} + {\left (x^{5} + 2 \, x^{4}\right )} e^{15} + 12 \, {\left (x^{5} + 2 \, x^{4}\right )} e^{10} + 48 \, {\left (x^{5} + 2 \, x^{4}\right )} e^{5}\right )} \log \left (3\right )\right )} e^{\left (\frac {1}{4} \, x\right )} + 6 \, {\left (64 \, x^{5} + {\left (x^{5} - 4 \, x^{2} - 2\right )} e^{15} + 4 \, {\left (3 \, x^{5} - 8 \, x^{2} - 2\right )} e^{10} + 16 \, {\left (3 \, x^{5} - 4 \, x^{2}\right )} e^{5}\right )} \log \left (3\right )}{1024 \, x^{4} + {\left (x^{4} + 2 \, x^{2} + 1\right )} e^{25} + 4 \, {\left (5 \, x^{4} + 8 \, x^{2} + 3\right )} e^{20} + 16 \, {\left (10 \, x^{4} + 12 \, x^{2} + 3\right )} e^{15} + 64 \, {\left (10 \, x^{4} + 8 \, x^{2} + 1\right )} e^{10} + 256 \, {\left (5 \, x^{4} + 2 \, x^{2}\right )} e^{5}} \] Input:
integrate(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+ 44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^ 4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+(( -24*x^6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240* x^4-192*x^3)*exp(5)-96*x^7-192*x^6)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48* x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x, algorithm ="fricas")
Output:
-(192*x^6 + 768*x^5 - 3*(32*x^2*e^5 + (2*x^2 + 1)*e^15 + 4*(4*x^2 + 1)*e^1 0)*log(3)^2 + 3*(x^6 + 4*x^5 + 2*x^4 - 4*x^2 - 2)*e^15 + 12*(3*x^6 + 12*x^ 5 + 4*x^4 - 12*x^2 - 4)*e^10 + 48*(3*x^6 + 12*x^5 + 2*x^4 - 8*x^2)*e^5 - ( 64*x^6 + 256*x^5 + 256*x^4 + (x^4*e^15 + 12*x^4*e^10 + 48*x^4*e^5 + 64*x^4 )*log(3)^2 + (x^6 + 4*x^5 + 4*x^4)*e^15 + 12*(x^6 + 4*x^5 + 4*x^4)*e^10 + 48*(x^6 + 4*x^5 + 4*x^4)*e^5 + 2*(64*x^5 + 128*x^4 + (x^5 + 2*x^4)*e^15 + 12*(x^5 + 2*x^4)*e^10 + 48*(x^5 + 2*x^4)*e^5)*log(3))*e^(1/4*x) + 6*(64*x^ 5 + (x^5 - 4*x^2 - 2)*e^15 + 4*(3*x^5 - 8*x^2 - 2)*e^10 + 16*(3*x^5 - 4*x^ 2)*e^5)*log(3))/(1024*x^4 + (x^4 + 2*x^2 + 1)*e^25 + 4*(5*x^4 + 8*x^2 + 3) *e^20 + 16*(10*x^4 + 12*x^2 + 3)*e^15 + 64*(10*x^4 + 8*x^2 + 1)*e^10 + 256 *(5*x^4 + 2*x^2)*e^5)
Leaf count of result is larger than twice the leaf count of optimal. 405 vs. \(2 (27) = 54\).
Time = 92.57 (sec) , antiderivative size = 405, normalized size of antiderivative = 13.06 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=- \frac {3 x^{2}}{16 + 8 e^{5} + e^{10}} - x \left (\frac {6 \log {\left (3 \right )}}{16 + 8 e^{5} + e^{10}} + \frac {12}{16 + 8 e^{5} + e^{10}}\right ) - \frac {x^{3} \left (- 24 e^{15} - 12 e^{15} \log {\left (3 \right )} - 192 e^{10} - 96 e^{10} \log {\left (3 \right )} - 384 e^{5} - 192 e^{5} \log {\left (3 \right )}\right ) + x^{2} \left (- 24 e^{15} \log {\left (3 \right )} - 15 e^{15} - 6 e^{15} \log {\left (3 \right )}^{2} - 192 e^{10} \log {\left (3 \right )} - 156 e^{10} - 48 e^{10} \log {\left (3 \right )}^{2} - 384 e^{5} \log {\left (3 \right )} - 384 e^{5} - 96 e^{5} \log {\left (3 \right )}^{2}\right ) + x \left (- 12 e^{15} - 6 e^{15} \log {\left (3 \right )} - 48 e^{10} - 24 e^{10} \log {\left (3 \right )}\right ) - 12 e^{15} \log {\left (3 \right )} - 6 e^{15} - 3 e^{15} \log {\left (3 \right )}^{2} - 48 e^{10} \log {\left (3 \right )} - 48 e^{10} - 12 e^{10} \log {\left (3 \right )}^{2}}{x^{4} \cdot \left (1024 + 1280 e^{5} + 640 e^{10} + 160 e^{15} + 20 e^{20} + e^{25}\right ) + x^{2} \cdot \left (512 e^{5} + 512 e^{10} + 192 e^{15} + 32 e^{20} + 2 e^{25}\right ) + 64 e^{10} + 48 e^{15} + 12 e^{20} + e^{25}} + \frac {\left (x^{6} + 2 x^{5} \log {\left (3 \right )} + 4 x^{5} + x^{4} \log {\left (3 \right )}^{2} + 4 x^{4} + 4 x^{4} \log {\left (3 \right )}\right ) e^{\frac {x}{4}}}{16 x^{4} + 8 x^{4} e^{5} + x^{4} e^{10} + 8 x^{2} e^{5} + 2 x^{2} e^{10} + e^{10}} \] Input:
integrate(((((x**6+x**4+16*x**3)*exp(5)+4*x**6)*ln(3)**2+((2*x**7+12*x**6+ 2*x**5+44*x**4+64*x**3)*exp(5)+8*x**7+48*x**6)*ln(3)+(x**8+12*x**7+21*x**6 +28*x**5+84*x**4+64*x**3)*exp(5)+4*x**8+48*x**7+80*x**6)*exp(1/4*x)-48*x** 3*exp(5)*ln(3)**2+((-24*x**6-120*x**4-192*x**3)*exp(5)-96*x**6)*ln(3)+(-24 *x**7-48*x**6-72*x**5-240*x**4-192*x**3)*exp(5)-96*x**7-192*x**6)/((4*x**6 +12*x**4+12*x**2+4)*exp(5)**3+(48*x**6+96*x**4+48*x**2)*exp(5)**2+(192*x** 6+192*x**4)*exp(5)+256*x**6),x)
Output:
-3*x**2/(16 + 8*exp(5) + exp(10)) - x*(6*log(3)/(16 + 8*exp(5) + exp(10)) + 12/(16 + 8*exp(5) + exp(10))) - (x**3*(-24*exp(15) - 12*exp(15)*log(3) - 192*exp(10) - 96*exp(10)*log(3) - 384*exp(5) - 192*exp(5)*log(3)) + x**2* (-24*exp(15)*log(3) - 15*exp(15) - 6*exp(15)*log(3)**2 - 192*exp(10)*log(3 ) - 156*exp(10) - 48*exp(10)*log(3)**2 - 384*exp(5)*log(3) - 384*exp(5) - 96*exp(5)*log(3)**2) + x*(-12*exp(15) - 6*exp(15)*log(3) - 48*exp(10) - 24 *exp(10)*log(3)) - 12*exp(15)*log(3) - 6*exp(15) - 3*exp(15)*log(3)**2 - 4 8*exp(10)*log(3) - 48*exp(10) - 12*exp(10)*log(3)**2)/(x**4*(1024 + 1280*e xp(5) + 640*exp(10) + 160*exp(15) + 20*exp(20) + exp(25)) + x**2*(512*exp( 5) + 512*exp(10) + 192*exp(15) + 32*exp(20) + 2*exp(25)) + 64*exp(10) + 48 *exp(15) + 12*exp(20) + exp(25)) + (x**6 + 2*x**5*log(3) + 4*x**5 + x**4*l og(3)**2 + 4*x**4 + 4*x**4*log(3))*exp(x/4)/(16*x**4 + 8*x**4*exp(5) + x** 4*exp(10) + 8*x**2*exp(5) + 2*x**2*exp(10) + exp(10))
Leaf count of result is larger than twice the leaf count of optimal. 1473 vs. \(2 (26) = 52\).
Time = 0.26 (sec) , antiderivative size = 1473, normalized size of antiderivative = 47.52 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=\text {Too large to display} \] Input:
integrate(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+ 44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^ 4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+(( -24*x^6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240* x^4-192*x^3)*exp(5)-96*x^7-192*x^6)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48* x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x, algorithm ="maxima")
Output:
3/4*(15*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(5/2)/((e^15 + 12*e^10 + 48*e^5 + 64)*sqrt(e^5 + 4)) - (9*x^3*(e^10 + 4*e^5) + 7*x*e^10)/(x^4*(e^25 + 20* e^20 + 160*e^15 + 640*e^10 + 1280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20 + 96 *e^15 + 256*e^10 + 256*e^5) + e^25 + 12*e^20 + 48*e^15 + 64*e^10) - 8*x/(e ^15 + 12*e^10 + 48*e^5 + 64))*e^5*log(3) - 15/4*(3*arctan(x*sqrt(e^5 + 4)* e^(-5/2))*e^(-5/2)/((e^10 + 8*e^5 + 16)*sqrt(e^5 + 4)) - (5*x^3*(e^5 + 4) + 3*x*e^5)/(x^4*(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e^20 + 8*e^15 + 16*e^10))*e^5*log(3) + 3*(2 *x^2*(e^5 + 4) + e^5)*e^5*log(3)^2/(x^4*(e^20 + 16*e^15 + 96*e^10 + 256*e^ 5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e^20 + 8*e^15 + 16* e^10) - 3/2*(2*x^2/(e^15 + 12*e^10 + 48*e^5 + 64) - 6*e^5*log(x^2*(e^5 + 4 ) + e^5)/(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) - (6*x^2*(e^15 + 4*e^1 0) + 5*e^15)/(x^4*(e^30 + 24*e^25 + 240*e^20 + 1280*e^15 + 3840*e^10 + 614 4*e^5 + 4096) + 2*x^2*(e^30 + 20*e^25 + 160*e^20 + 640*e^15 + 1280*e^10 + 1024*e^5) + e^30 + 16*e^25 + 96*e^20 + 256*e^15 + 256*e^10))*e^5 + 3/2*(15 *arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(5/2)/((e^15 + 12*e^10 + 48*e^5 + 64)* sqrt(e^5 + 4)) - (9*x^3*(e^10 + 4*e^5) + 7*x*e^10)/(x^4*(e^25 + 20*e^20 + 160*e^15 + 640*e^10 + 1280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20 + 96*e^15 + 256*e^10 + 256*e^5) + e^25 + 12*e^20 + 48*e^15 + 64*e^10) - 8*x/(e^15 + 1 2*e^10 + 48*e^5 + 64))*e^5 - 15/2*(3*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e...
Leaf count of result is larger than twice the leaf count of optimal. 2810 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 2810, normalized size of antiderivative = 90.65 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=\text {Too large to display} \] Input:
integrate(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+ 44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^ 4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+(( -24*x^6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240* x^4-192*x^3)*exp(5)-96*x^7-192*x^6)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48* x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x, algorithm ="giac")
Output:
-(3*x^6*e^45 + 108*x^6*e^40 + 1728*x^6*e^35 + 16128*x^6*e^30 + 96768*x^6*e ^25 + 387072*x^6*e^20 + 1032192*x^6*e^15 + 1769472*x^6*e^10 + 1769472*x^6* e^5 - 262144*x^6*e^(1/4*x) - x^6*e^(1/4*x + 45) - 36*x^6*e^(1/4*x + 40) - 576*x^6*e^(1/4*x + 35) - 5376*x^6*e^(1/4*x + 30) - 32256*x^6*e^(1/4*x + 25 ) - 129024*x^6*e^(1/4*x + 20) - 344064*x^6*e^(1/4*x + 15) - 589824*x^6*e^( 1/4*x + 10) - 589824*x^6*e^(1/4*x + 5) + 6*x^5*e^45*log(3) + 216*x^5*e^40* log(3) + 3456*x^5*e^35*log(3) + 32256*x^5*e^30*log(3) + 193536*x^5*e^25*lo g(3) + 774144*x^5*e^20*log(3) + 2064384*x^5*e^15*log(3) + 3538944*x^5*e^10 *log(3) + 3538944*x^5*e^5*log(3) - 524288*x^5*e^(1/4*x)*log(3) - 2*x^5*e^( 1/4*x + 45)*log(3) - 72*x^5*e^(1/4*x + 40)*log(3) - 1152*x^5*e^(1/4*x + 35 )*log(3) - 10752*x^5*e^(1/4*x + 30)*log(3) - 64512*x^5*e^(1/4*x + 25)*log( 3) - 258048*x^5*e^(1/4*x + 20)*log(3) - 688128*x^5*e^(1/4*x + 15)*log(3) - 1179648*x^5*e^(1/4*x + 10)*log(3) - 1179648*x^5*e^(1/4*x + 5)*log(3) - 26 2144*x^4*e^(1/4*x)*log(3)^2 - x^4*e^(1/4*x + 45)*log(3)^2 - 36*x^4*e^(1/4* x + 40)*log(3)^2 - 576*x^4*e^(1/4*x + 35)*log(3)^2 - 5376*x^4*e^(1/4*x + 3 0)*log(3)^2 - 32256*x^4*e^(1/4*x + 25)*log(3)^2 - 129024*x^4*e^(1/4*x + 20 )*log(3)^2 - 344064*x^4*e^(1/4*x + 15)*log(3)^2 - 589824*x^4*e^(1/4*x + 10 )*log(3)^2 - 589824*x^4*e^(1/4*x + 5)*log(3)^2 + 786432*x^6 + 12*x^5*e^45 + 432*x^5*e^40 + 6912*x^5*e^35 + 64512*x^5*e^30 + 387072*x^5*e^25 + 154828 8*x^5*e^20 + 4128768*x^5*e^15 + 7077888*x^5*e^10 + 7077888*x^5*e^5 - 10...
Timed out. \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=-\int \frac {\ln \left (3\right )\,\left ({\mathrm {e}}^5\,\left (24\,x^6+120\,x^4+192\,x^3\right )+96\,x^6\right )+{\mathrm {e}}^5\,\left (24\,x^7+48\,x^6+72\,x^5+240\,x^4+192\,x^3\right )-{\mathrm {e}}^{x/4}\,\left ({\mathrm {e}}^5\,\left (x^8+12\,x^7+21\,x^6+28\,x^5+84\,x^4+64\,x^3\right )+{\ln \left (3\right )}^2\,\left ({\mathrm {e}}^5\,\left (x^6+x^4+16\,x^3\right )+4\,x^6\right )+\ln \left (3\right )\,\left ({\mathrm {e}}^5\,\left (2\,x^7+12\,x^6+2\,x^5+44\,x^4+64\,x^3\right )+48\,x^6+8\,x^7\right )+80\,x^6+48\,x^7+4\,x^8\right )+192\,x^6+96\,x^7+48\,x^3\,{\mathrm {e}}^5\,{\ln \left (3\right )}^2}{{\mathrm {e}}^5\,\left (192\,x^6+192\,x^4\right )+{\mathrm {e}}^{15}\,\left (4\,x^6+12\,x^4+12\,x^2+4\right )+{\mathrm {e}}^{10}\,\left (48\,x^6+96\,x^4+48\,x^2\right )+256\,x^6} \,d x \] Input:
int(-(log(3)*(exp(5)*(192*x^3 + 120*x^4 + 24*x^6) + 96*x^6) + exp(5)*(192* x^3 + 240*x^4 + 72*x^5 + 48*x^6 + 24*x^7) - exp(x/4)*(exp(5)*(64*x^3 + 84* x^4 + 28*x^5 + 21*x^6 + 12*x^7 + x^8) + log(3)^2*(exp(5)*(16*x^3 + x^4 + x ^6) + 4*x^6) + log(3)*(exp(5)*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7) + 48*x^6 + 8*x^7) + 80*x^6 + 48*x^7 + 4*x^8) + 192*x^6 + 96*x^7 + 48*x^3*ex p(5)*log(3)^2)/(exp(5)*(192*x^4 + 192*x^6) + exp(15)*(12*x^2 + 12*x^4 + 4* x^6 + 4) + exp(10)*(48*x^2 + 96*x^4 + 48*x^6) + 256*x^6),x)
Output:
-int((log(3)*(exp(5)*(192*x^3 + 120*x^4 + 24*x^6) + 96*x^6) + exp(5)*(192* x^3 + 240*x^4 + 72*x^5 + 48*x^6 + 24*x^7) - exp(x/4)*(exp(5)*(64*x^3 + 84* x^4 + 28*x^5 + 21*x^6 + 12*x^7 + x^8) + log(3)^2*(exp(5)*(16*x^3 + x^4 + x ^6) + 4*x^6) + log(3)*(exp(5)*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7) + 48*x^6 + 8*x^7) + 80*x^6 + 48*x^7 + 4*x^8) + 192*x^6 + 96*x^7 + 48*x^3*ex p(5)*log(3)^2)/(exp(5)*(192*x^4 + 192*x^6) + exp(15)*(12*x^2 + 12*x^4 + 4* x^6 + 4) + exp(10)*(48*x^2 + 96*x^4 + 48*x^6) + 256*x^6), x)
Time = 0.17 (sec) , antiderivative size = 124, normalized size of antiderivative = 4.00 \[ \int \frac {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx=\frac {x^{4} \left (e^{\frac {x}{4}} \mathrm {log}\left (3\right )^{2}+2 e^{\frac {x}{4}} \mathrm {log}\left (3\right ) x +4 e^{\frac {x}{4}} \mathrm {log}\left (3\right )+e^{\frac {x}{4}} x^{2}+4 e^{\frac {x}{4}} x +4 e^{\frac {x}{4}}-3 \mathrm {log}\left (3\right )^{2}-6 \,\mathrm {log}\left (3\right ) x -12 \,\mathrm {log}\left (3\right )-3 x^{2}-12 x -12\right )}{e^{10} x^{4}+2 e^{10} x^{2}+e^{10}+8 e^{5} x^{4}+8 e^{5} x^{2}+16 x^{4}} \] Input:
int(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+44*x^4 +64*x^3)*exp(5)+8*x^7+48*x^6)*log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^4+64*x ^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+((-24*x^ 6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240*x^4-19 2*x^3)*exp(5)-96*x^7-192*x^6)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48*x^6+96 *x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x)
Output:
(x**4*(e**(x/4)*log(3)**2 + 2*e**(x/4)*log(3)*x + 4*e**(x/4)*log(3) + e**( x/4)*x**2 + 4*e**(x/4)*x + 4*e**(x/4) - 3*log(3)**2 - 6*log(3)*x - 12*log( 3) - 3*x**2 - 12*x - 12))/(e**10*x**4 + 2*e**10*x**2 + e**10 + 8*e**5*x**4 + 8*e**5*x**2 + 16*x**4)