Integrand size = 412, antiderivative size = 23 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\frac {1}{\left (x^2-\left (3-\frac {-4+x}{x+\log (49)}\right )^2\right )^2} \] Output:
1/(x^2-(3-(-4+x)/(x+2*ln(7)))^2)^2
Leaf count is larger than twice the leaf count of optimal. \(535\) vs. \(2(23)=46\).
Time = 0.90 (sec) , antiderivative size = 535, normalized size of antiderivative = 23.26 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\frac {\left (x^4+2 x^3 \log (49)-4 x (4+3 \log (49))-(4+3 \log (49))^2+x^2 \left (-4+\log ^2(49)\right )\right ) \left (-2640 \log ^9(49)+108 \log ^{10}(49)+27 \log ^{11}(49)-8 \log ^8(49) (3103+15 \log (2401))-12288 (-300+41 \log (2401))-4 \log ^7(49) (1870+129 \log (2401))+64 \log ^5(49) (91161+505 \log (2401))-1536 \log (49) (-11176+701 \log (2401))+4 \log ^6(49) (228864+971 \log (2401))+32 \log ^4(49) (560004+1675 \log (2401))-448 \log ^2(49) (-71392+1723 \log (2401))-64 \log ^3(49) (-492390+2521 \log (2401))\right )+(4+3 \log (49))^2 \left (-240-256 \log (49)-56 \log ^2(49)+\log ^4(49)\right ) \left (2 x^3 \left (-164 \log ^4(49)+4 \log ^5(49)+3 \log ^6(49)+8 \log (49) (-124+\log (2401))+16 \log (2401)-4 \log ^2(49) (440+\log (2401))-2 \log ^3(49) (492+\log (2401))\right )+x^2 \left (-818 \log ^5(49)+20 \log ^6(49)+15 \log ^7(49)-128 (30+\log (2401))-80 \log (49) (84+\log (2401))-12 \log ^3(49) (782+\log (2401))-5 \log ^4(49) (984+\log (2401))-4 \log ^2(49) (2152+\log (2401))\right )+(4+3 \log (49)) \left (-652 \log ^4(49)-49 \log ^6(49)+\log ^8(49)+\log ^5(49) (-232+\log (2401))-32 (120+\log (2401))-2 \log ^3(49) (1640+19 \log (2401))-8 \log ^2(49) (1100+23 \log (2401))-8 \log (49) (1224+25 \log (2401))\right )+2 x \left (-4340 \log ^4(49)-320 \log ^6(49)+8 \log ^7(49)+6 \log ^8(49)+\log ^5(49) (-1936+\log (2401))-96 (80+3 \log (2401))-24 \log ^2(49) (718+15 \log (2401))-2 \log ^3(49) (4248+31 \log (2401))-8 \log (49) (2392+73 \log (2401))\right )\right )}{(4+3 \log (49))^3 \left (240+256 \log (49)+56 \log ^2(49)-\log ^4(49)\right )^2 \left (x^4+2 x^3 \log (49)-4 x (4+3 \log (49))-(4+3 \log (49))^2+x^2 \left (-4+\log ^2(49)\right )\right )^2} \] Input:
Integrate[(-64*x^3 - 32*x^4 - 4*x^7 + (-192*x^2 - 160*x^3 - 8*x^4 - 24*x^6 )*Log[49] + (-192*x - 288*x^2 - 36*x^3 - 60*x^5)*Log[49]^2 + (-64 - 224*x - 60*x^2 - 80*x^4)*Log[49]^3 + (-64 - 44*x - 60*x^3)*Log[49]^4 + (-12 - 24 *x^2)*Log[49]^5 - 4*x*Log[49]^6)/(-4096 - 12288*x - 15360*x^2 - 10240*x^3 - 3072*x^4 + 768*x^5 + 1088*x^6 + 384*x^7 - 48*x^9 - 12*x^10 + x^12 + (-18 432 - 46080*x - 46080*x^2 - 21504*x^3 - 384*x^4 + 5184*x^5 + 2496*x^6 + 19 2*x^7 - 264*x^8 - 84*x^9 + 6*x^11)*Log[49] + (-34560 - 69120*x - 51072*x^2 - 11136*x^3 + 8496*x^4 + 6432*x^5 + 984*x^6 - 576*x^7 - 243*x^8 + 15*x^10 )*Log[49]^2 + (-34560 - 51840*x - 23616*x^2 + 4320*x^3 + 8208*x^4 + 2040*x ^5 - 624*x^6 - 372*x^7 + 20*x^9)*Log[49]^3 + (-19440 - 19440*x - 2268*x^2 + 5184*x^3 + 2139*x^4 - 336*x^5 - 318*x^6 + 15*x^8)*Log[49]^4 + (-5832 - 2 916*x + 1296*x^2 + 1134*x^3 - 72*x^4 - 144*x^5 + 6*x^7)*Log[49]^5 + (-729 + 243*x^2 - 27*x^4 + x^6)*Log[49]^6),x]
Output:
((x^4 + 2*x^3*Log[49] - 4*x*(4 + 3*Log[49]) - (4 + 3*Log[49])^2 + x^2*(-4 + Log[49]^2))*(-2640*Log[49]^9 + 108*Log[49]^10 + 27*Log[49]^11 - 8*Log[49 ]^8*(3103 + 15*Log[2401]) - 12288*(-300 + 41*Log[2401]) - 4*Log[49]^7*(187 0 + 129*Log[2401]) + 64*Log[49]^5*(91161 + 505*Log[2401]) - 1536*Log[49]*( -11176 + 701*Log[2401]) + 4*Log[49]^6*(228864 + 971*Log[2401]) + 32*Log[49 ]^4*(560004 + 1675*Log[2401]) - 448*Log[49]^2*(-71392 + 1723*Log[2401]) - 64*Log[49]^3*(-492390 + 2521*Log[2401])) + (4 + 3*Log[49])^2*(-240 - 256*L og[49] - 56*Log[49]^2 + Log[49]^4)*(2*x^3*(-164*Log[49]^4 + 4*Log[49]^5 + 3*Log[49]^6 + 8*Log[49]*(-124 + Log[2401]) + 16*Log[2401] - 4*Log[49]^2*(4 40 + Log[2401]) - 2*Log[49]^3*(492 + Log[2401])) + x^2*(-818*Log[49]^5 + 2 0*Log[49]^6 + 15*Log[49]^7 - 128*(30 + Log[2401]) - 80*Log[49]*(84 + Log[2 401]) - 12*Log[49]^3*(782 + Log[2401]) - 5*Log[49]^4*(984 + Log[2401]) - 4 *Log[49]^2*(2152 + Log[2401])) + (4 + 3*Log[49])*(-652*Log[49]^4 - 49*Log[ 49]^6 + Log[49]^8 + Log[49]^5*(-232 + Log[2401]) - 32*(120 + Log[2401]) - 2*Log[49]^3*(1640 + 19*Log[2401]) - 8*Log[49]^2*(1100 + 23*Log[2401]) - 8* Log[49]*(1224 + 25*Log[2401])) + 2*x*(-4340*Log[49]^4 - 320*Log[49]^6 + 8* Log[49]^7 + 6*Log[49]^8 + Log[49]^5*(-1936 + Log[2401]) - 96*(80 + 3*Log[2 401]) - 24*Log[49]^2*(718 + 15*Log[2401]) - 2*Log[49]^3*(4248 + 31*Log[240 1]) - 8*Log[49]*(2392 + 73*Log[2401]))))/((4 + 3*Log[49])^3*(240 + 256*Log [49] + 56*Log[49]^2 - Log[49]^4)^2*(x^4 + 2*x^3*Log[49] - 4*x*(4 + 3*Lo...
Leaf count is larger than twice the leaf count of optimal. \(893\) vs. \(2(23)=46\).
Time = 3.06 (sec) , antiderivative size = 893, normalized size of antiderivative = 38.83, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {2462, 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.
| \(\displaystyle \int \frac {-4 x^7-32 x^4-64 x^3+\left (-60 x^3-44 x-64\right ) \log ^4(49)+\left (-24 x^2-12\right ) \log ^5(49)+\left (-80 x^4-60 x^2-224 x-64\right ) \log ^3(49)+\left (-60 x^5-36 x^3-288 x^2-192 x\right ) \log ^2(49)+\left (-24 x^6-8 x^4-160 x^3-192 x^2\right ) \log (49)-4 x \log ^6(49)}{x^{12}-12 x^{10}-48 x^9+384 x^7+1088 x^6+768 x^5-3072 x^4-10240 x^3-15360 x^2+\left (x^6-27 x^4+243 x^2-729\right ) \log ^6(49)+\left (6 x^7-144 x^5-72 x^4+1134 x^3+1296 x^2-2916 x-5832\right ) \log ^5(49)+\left (15 x^8-318 x^6-336 x^5+2139 x^4+5184 x^3-2268 x^2-19440 x-19440\right ) \log ^4(49)+\left (20 x^9-372 x^7-624 x^6+2040 x^5+8208 x^4+4320 x^3-23616 x^2-51840 x-34560\right ) \log ^3(49)+\left (15 x^{10}-243 x^8-576 x^7+984 x^6+6432 x^5+8496 x^4-11136 x^3-51072 x^2-69120 x-34560\right ) \log ^2(49)+\left (6 x^{11}-84 x^9-264 x^8+192 x^7+2496 x^6+5184 x^5-384 x^4-21504 x^3-46080 x^2-46080 x-18432\right ) \log (49)-12288 x-4096} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {-8-\log ^3(49)-\log (2401)}{4 (4+3 \log (49))^3 \left (-x^2+x (2-\log (49))+4+3 \log (49)\right )}+\frac {-8-\log ^3(49)-\log (2401)}{4 (4+3 \log (49))^3 \left (x^2+x (2+\log (49))+4+3 \log (49)\right )}+\frac {x \left (16-\log ^4(49)-2 \log ^3(49)+4 \log ^2(49)+20 \log (49)\right )+64-\log ^5(49)-7 \log ^4(49)+29 \log ^3(49)+138 \log ^2(49)+168 \log (49)}{4 (4+3 \log (49))^3 \left (x^2+x (2+\log (49))+4+3 \log (49)\right )^2}+\frac {-\left (x \left (48-\log ^4(49)+2 \log ^3(49)+4 \log ^2(49)+28 \log (49)\right )\right )+128+\log ^5(49)-7 \log ^4(49)-37 \log ^3(49)-118 \log ^2(49)-40 \log (49)}{4 (4+3 \log (49))^3 \left (-x^2+x (2-\log (49))+4+3 \log (49)\right )^2}+\frac {-\left (x \left (32+\log ^4(49)-8 \log ^3(49)-6 \log ^2(49)+32 \log (49)\right )\right )-32-\log ^5(49)+9 \log ^4(49)+5 \log ^3(49)-66 \log ^2(49)-96 \log (49)}{2 (4+3 \log (49))^2 \left (x^2+x (2+\log (49))+4+3 \log (49)\right )^3}+\frac {x \left (32+\log ^4(49)+8 \log ^3(49)+26 \log ^2(49)+32 \log (49)\right )-32+\log ^5(49)+9 \log ^4(49)+35 \log ^3(49)+62 \log ^2(49)+64 \log (49)}{2 (4+3 \log (49))^2 \left (-x^2+x (2-\log (49))+4+3 \log (49)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {\left (8+\log ^3(49)+\log (2401)\right ) \arctan \left (\frac {2 x+\log (49)+2}{\sqrt {12+8 \log (49)-\log ^2(49)}}\right )}{2 (4+3 \log (49))^3 \sqrt {12+8 \log (49)-\log ^2(49)}}+\frac {\left (96+280 \log (49)+248 \log ^2(49)+58 \log ^3(49)-10 \log ^4(49)-\log ^5(49)\right ) \arctan \left (\frac {2 x+\log (49)+2}{\sqrt {12+8 \log (49)-\log ^2(49)}}\right )}{2 (4+3 \log (49))^3 \left (12+8 \log (49)-\log ^2(49)\right )^{3/2}}-\frac {3 \log (49) \left (8+4 \log (49)-\log ^2(49)\right ) \arctan \left (\frac {2 x+\log (49)+2}{\sqrt {12+8 \log (49)-\log ^2(49)}}\right )}{(4+3 \log (49))^2 \left (12+8 \log (49)-\log ^2(49)\right )^{3/2}}+\frac {-\log (49) \left (8+4 \log (49)-\log ^2(49)\right ) x+\log ^4(49)-5 \log ^3(49)-11 \log ^2(49)+8 \log (49)+16}{4 (4+3 \log (49))^2 \left (x^2+(2+\log (49)) x+3 \log (49)+4\right )^2}+\frac {\log (49) \left (8+4 \log (49)+\log ^2(49)\right ) x+\log ^4(49)+5 \log ^3(49)+13 \log ^2(49)+8 \log (49)+16}{4 (4+3 \log (49))^2 \left (-x^2+(2-\log (49)) x+3 \log (49)+4\right )^2}+\frac {\left (96+280 \log (49)+248 \log ^2(49)+58 \log ^3(49)-10 \log ^4(49)-\log ^5(49)\right ) x+\log (49) (4+\log (49)) \left (36+64 \log (49)+31 \log ^2(49)+\log ^3(49)-\log ^4(49)\right )}{4 (4+3 \log (49))^3 \left (12+8 \log (49)-\log ^2(49)\right ) \left (x^2+(2+\log (49)) x+3 \log (49)+4\right )}-\frac {-\left (\left (160-88 \log (49)-216 \log ^2(49)-74 \log ^3(49)-10 \log ^4(49)+\log ^5(49)\right ) x\right )-\log ^6(49)+3 \log ^5(49)+27 \log ^4(49)+84 \log ^3(49)+4 \log ^2(49)+304 \log (49)+640}{4 (4+3 \log (49))^3 \left (-x^2+(2-\log (49)) x+3 \log (49)+4\right ) \left (20+8 \log (49)+\log ^2(49)\right )}-\frac {3 \log (49) (2 x+\log (49)+2) \left (8+4 \log (49)-\log ^2(49)\right )}{4 (4+3 \log (49))^2 \left (12+8 \log (49)-\log ^2(49)\right ) \left (x^2+(2+\log (49)) x+3 \log (49)+4\right )}+\frac {\text {arctanh}\left (\frac {-2 x-\log (49)+2}{\sqrt {20+8 \log (49)+\log ^2(49)}}\right ) \left (8+\log ^3(49)+\log (2401)\right )}{2 (4+3 \log (49))^3 \sqrt {20+8 \log (49)+\log ^2(49)}}-\frac {\text {arctanh}\left (\frac {-2 x-\log (49)+2}{\sqrt {20+8 \log (49)+\log ^2(49)}}\right ) \left (160-88 \log (49)-216 \log ^2(49)-74 \log ^3(49)-10 \log ^4(49)+\log ^5(49)\right )}{2 (4+3 \log (49))^3 \left (20+8 \log (49)+\log ^2(49)\right )^{3/2}}-\frac {3 (-2 x-\log (49)+2) \log (49) \left (8+4 \log (49)+\log ^2(49)\right )}{4 (4+3 \log (49))^2 \left (-x^2+(2-\log (49)) x+3 \log (49)+4\right ) \left (20+8 \log (49)+\log ^2(49)\right )}-\frac {3 \text {arctanh}\left (\frac {-2 x-\log (49)+2}{\sqrt {20+8 \log (49)+\log ^2(49)}}\right ) \log (49) \left (8+4 \log (49)+\log ^2(49)\right )}{(4+3 \log (49))^2 \left (20+8 \log (49)+\log ^2(49)\right )^{3/2}}\) |
Input:
Int[(-64*x^3 - 32*x^4 - 4*x^7 + (-192*x^2 - 160*x^3 - 8*x^4 - 24*x^6)*Log[ 49] + (-192*x - 288*x^2 - 36*x^3 - 60*x^5)*Log[49]^2 + (-64 - 224*x - 60*x ^2 - 80*x^4)*Log[49]^3 + (-64 - 44*x - 60*x^3)*Log[49]^4 + (-12 - 24*x^2)* Log[49]^5 - 4*x*Log[49]^6)/(-4096 - 12288*x - 15360*x^2 - 10240*x^3 - 3072 *x^4 + 768*x^5 + 1088*x^6 + 384*x^7 - 48*x^9 - 12*x^10 + x^12 + (-18432 - 46080*x - 46080*x^2 - 21504*x^3 - 384*x^4 + 5184*x^5 + 2496*x^6 + 192*x^7 - 264*x^8 - 84*x^9 + 6*x^11)*Log[49] + (-34560 - 69120*x - 51072*x^2 - 111 36*x^3 + 8496*x^4 + 6432*x^5 + 984*x^6 - 576*x^7 - 243*x^8 + 15*x^10)*Log[ 49]^2 + (-34560 - 51840*x - 23616*x^2 + 4320*x^3 + 8208*x^4 + 2040*x^5 - 6 24*x^6 - 372*x^7 + 20*x^9)*Log[49]^3 + (-19440 - 19440*x - 2268*x^2 + 5184 *x^3 + 2139*x^4 - 336*x^5 - 318*x^6 + 15*x^8)*Log[49]^4 + (-5832 - 2916*x + 1296*x^2 + 1134*x^3 - 72*x^4 - 144*x^5 + 6*x^7)*Log[49]^5 + (-729 + 243* x^2 - 27*x^4 + x^6)*Log[49]^6),x]
Output:
(-3*ArcTan[(2 + 2*x + Log[49])/Sqrt[12 + 8*Log[49] - Log[49]^2]]*Log[49]*( 8 + 4*Log[49] - Log[49]^2))/((4 + 3*Log[49])^2*(12 + 8*Log[49] - Log[49]^2 )^(3/2)) - (3*ArcTanh[(2 - 2*x - Log[49])/Sqrt[20 + 8*Log[49] + Log[49]^2] ]*Log[49]*(8 + 4*Log[49] + Log[49]^2))/((4 + 3*Log[49])^2*(20 + 8*Log[49] + Log[49]^2)^(3/2)) - (3*(2 - 2*x - Log[49])*Log[49]*(8 + 4*Log[49] + Log[ 49]^2))/(4*(4 + 3*Log[49])^2*(4 - x^2 + x*(2 - Log[49]) + 3*Log[49])*(20 + 8*Log[49] + Log[49]^2)) + (ArcTan[(2 + 2*x + Log[49])/Sqrt[12 + 8*Log[49] - Log[49]^2]]*(96 + 280*Log[49] + 248*Log[49]^2 + 58*Log[49]^3 - 10*Log[4 9]^4 - Log[49]^5))/(2*(4 + 3*Log[49])^3*(12 + 8*Log[49] - Log[49]^2)^(3/2) ) - (ArcTanh[(2 - 2*x - Log[49])/Sqrt[20 + 8*Log[49] + Log[49]^2]]*(160 - 88*Log[49] - 216*Log[49]^2 - 74*Log[49]^3 - 10*Log[49]^4 + Log[49]^5))/(2* (4 + 3*Log[49])^3*(20 + 8*Log[49] + Log[49]^2)^(3/2)) - (3*Log[49]*(2 + 2* x + Log[49])*(8 + 4*Log[49] - Log[49]^2))/(4*(4 + 3*Log[49])^2*(12 + 8*Log [49] - Log[49]^2)*(4 + x^2 + 3*Log[49] + x*(2 + Log[49]))) + (16 + 8*Log[4 9] - 11*Log[49]^2 - 5*Log[49]^3 + Log[49]^4 - x*Log[49]*(8 + 4*Log[49] - L og[49]^2))/(4*(4 + 3*Log[49])^2*(4 + x^2 + 3*Log[49] + x*(2 + Log[49]))^2) + (16 + 8*Log[49] + 13*Log[49]^2 + 5*Log[49]^3 + Log[49]^4 + x*Log[49]*(8 + 4*Log[49] + Log[49]^2))/(4*(4 + 3*Log[49])^2*(4 - x^2 + x*(2 - Log[49]) + 3*Log[49])^2) + (Log[49]*(4 + Log[49])*(36 + 64*Log[49] + 31*Log[49]^2 + Log[49]^3 - Log[49]^4) + x*(96 + 280*Log[49] + 248*Log[49]^2 + 58*Log...
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(25)=50\).
Time = 1.25 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.52
| method | result | size |
| norman | \(\frac {16 \ln \left (7\right )^{4}+32 \ln \left (7\right )^{3} x +24 \ln \left (7\right )^{2} x^{2}+8 \ln \left (7\right ) x^{3}+x^{4}}{\left (4 \ln \left (7\right )^{2} x^{2}+4 \ln \left (7\right ) x^{3}+x^{4}-36 \ln \left (7\right )^{2}-24 x \ln \left (7\right )-4 x^{2}-48 \ln \left (7\right )-16 x -16\right )^{2}}\) | \(81\) |
| gosper | \(\frac {16 \ln \left (7\right )^{4}+32 \ln \left (7\right )^{3} x +24 \ln \left (7\right )^{2} x^{2}+8 \ln \left (7\right ) x^{3}+x^{4}}{256+512 x +16 \ln \left (7\right )^{4} x^{4}+32 \ln \left (7\right )^{3} x^{5}+24 \ln \left (7\right )^{2} x^{6}+8 \ln \left (7\right ) x^{7}-288 \ln \left (7\right )^{4} x^{2}-480 \ln \left (7\right )^{3} x^{3}-296 \ln \left (7\right )^{2} x^{4}-80 \ln \left (7\right ) x^{5}-384 \ln \left (7\right )^{3} x^{2}-512 \ln \left (7\right )^{2} x^{3}-224 \ln \left (7\right ) x^{4}+1728 \ln \left (7\right )^{3} x +736 \ln \left (7\right )^{2} x^{2}+64 \ln \left (7\right ) x^{3}+3456 \ln \left (7\right )^{2} x +3456 \ln \left (7\right )^{2}+1152 x^{2} \ln \left (7\right )+1536 \ln \left (7\right )+x^{8}-8 x^{6}+384 x^{2}+128 x^{3}-16 x^{4}-32 x^{5}+1296 \ln \left (7\right )^{4}+3456 \ln \left (7\right )^{3}+2304 x \ln \left (7\right )}\) | \(227\) |
| parallelrisch | \(\frac {16 \ln \left (7\right )^{4}+32 \ln \left (7\right )^{3} x +24 \ln \left (7\right )^{2} x^{2}+8 \ln \left (7\right ) x^{3}+x^{4}}{256+512 x +16 \ln \left (7\right )^{4} x^{4}+32 \ln \left (7\right )^{3} x^{5}+24 \ln \left (7\right )^{2} x^{6}+8 \ln \left (7\right ) x^{7}-288 \ln \left (7\right )^{4} x^{2}-480 \ln \left (7\right )^{3} x^{3}-296 \ln \left (7\right )^{2} x^{4}-80 \ln \left (7\right ) x^{5}-384 \ln \left (7\right )^{3} x^{2}-512 \ln \left (7\right )^{2} x^{3}-224 \ln \left (7\right ) x^{4}+1728 \ln \left (7\right )^{3} x +736 \ln \left (7\right )^{2} x^{2}+64 \ln \left (7\right ) x^{3}+3456 \ln \left (7\right )^{2} x +3456 \ln \left (7\right )^{2}+1152 x^{2} \ln \left (7\right )+1536 \ln \left (7\right )+x^{8}-8 x^{6}+384 x^{2}+128 x^{3}-16 x^{4}-32 x^{5}+1296 \ln \left (7\right )^{4}+3456 \ln \left (7\right )^{3}+2304 x \ln \left (7\right )}\) | \(227\) |
| risch | \(\frac {\ln \left (7\right )^{4}+2 \ln \left (7\right )^{3} x +\frac {3 \ln \left (7\right )^{2} x^{2}}{2}+\frac {\ln \left (7\right ) x^{3}}{2}+\frac {x^{4}}{16}}{16+32 x +\ln \left (7\right )^{4} x^{4}+2 \ln \left (7\right )^{3} x^{5}+\frac {3 \ln \left (7\right )^{2} x^{6}}{2}+\frac {\ln \left (7\right ) x^{7}}{2}-18 \ln \left (7\right )^{4} x^{2}-30 \ln \left (7\right )^{3} x^{3}-\frac {37 \ln \left (7\right )^{2} x^{4}}{2}-5 \ln \left (7\right ) x^{5}-24 \ln \left (7\right )^{3} x^{2}-32 \ln \left (7\right )^{2} x^{3}-14 \ln \left (7\right ) x^{4}+108 \ln \left (7\right )^{3} x +46 \ln \left (7\right )^{2} x^{2}+4 \ln \left (7\right ) x^{3}+216 \ln \left (7\right )^{2} x +216 \ln \left (7\right )^{2}+72 x^{2} \ln \left (7\right )+96 \ln \left (7\right )+\frac {x^{8}}{16}-\frac {x^{6}}{2}+24 x^{2}+8 x^{3}-x^{4}-2 x^{5}+81 \ln \left (7\right )^{4}+216 \ln \left (7\right )^{3}+144 x \ln \left (7\right )}\) | \(228\) |
| default | \(-\frac {\left (-\frac {\ln \left (7\right )^{3}}{2}-\frac {\ln \left (7\right )}{4}-\frac {1}{2}\right ) x^{3}+\left (-2 \ln \left (7\right )^{4}-2 \ln \left (7\right )^{3}-\frac {\ln \left (7\right )^{2}}{4}-\ln \left (7\right )-1\right ) x^{2}+\left (-2 \ln \left (7\right )^{5}-10 \ln \left (7\right )^{4}+\frac {\ln \left (7\right )^{3}}{2}+10 \ln \left (7\right )^{2}+\ln \left (7\right )-2\right ) x -12 \ln \left (7\right )^{5}+\ln \left (7\right )^{4}+24 \ln \left (7\right )^{3}+9 \ln \left (7\right )^{2}-8 \ln \left (7\right )-4}{2 \left (3 \ln \left (7\right )+2\right ) \left (9 \ln \left (7\right )^{2}+12 \ln \left (7\right )+4\right ) \left (2 x \ln \left (7\right )+x^{2}+6 \ln \left (7\right )+2 x +4\right )^{2}}+\frac {\left (-\frac {\ln \left (7\right )^{3}}{2}-\frac {\ln \left (7\right )}{4}-\frac {1}{2}\right ) x^{3}+\left (-2 \ln \left (7\right )^{4}+2 \ln \left (7\right )^{3}-\frac {\ln \left (7\right )^{2}}{4}+\ln \left (7\right )+3\right ) x^{2}+\left (-2 \ln \left (7\right )^{5}+10 \ln \left (7\right )^{4}+\frac {17 \ln \left (7\right )^{3}}{2}+14 \ln \left (7\right )^{2}+9 \ln \left (7\right )-2\right ) x +12 \ln \left (7\right )^{5}+17 \ln \left (7\right )^{4}+24 \ln \left (7\right )^{3}+9 \ln \left (7\right )^{2}-8 \ln \left (7\right )-4}{2 \left (3 \ln \left (7\right )+2\right ) \left (9 \ln \left (7\right )^{2}+12 \ln \left (7\right )+4\right ) \left (2 x \ln \left (7\right )+x^{2}-6 \ln \left (7\right )-2 x -4\right )^{2}}\) | \(294\) |
Input:
int((-256*x*ln(7)^6+32*(-24*x^2-12)*ln(7)^5+16*(-60*x^3-44*x-64)*ln(7)^4+8 *(-80*x^4-60*x^2-224*x-64)*ln(7)^3+4*(-60*x^5-36*x^3-288*x^2-192*x)*ln(7)^ 2+2*(-24*x^6-8*x^4-160*x^3-192*x^2)*ln(7)-4*x^7-32*x^4-64*x^3)/(64*(x^6-27 *x^4+243*x^2-729)*ln(7)^6+32*(6*x^7-144*x^5-72*x^4+1134*x^3+1296*x^2-2916* x-5832)*ln(7)^5+16*(15*x^8-318*x^6-336*x^5+2139*x^4+5184*x^3-2268*x^2-1944 0*x-19440)*ln(7)^4+8*(20*x^9-372*x^7-624*x^6+2040*x^5+8208*x^4+4320*x^3-23 616*x^2-51840*x-34560)*ln(7)^3+4*(15*x^10-243*x^8-576*x^7+984*x^6+6432*x^5 +8496*x^4-11136*x^3-51072*x^2-69120*x-34560)*ln(7)^2+2*(6*x^11-84*x^9-264* x^8+192*x^7+2496*x^6+5184*x^5-384*x^4-21504*x^3-46080*x^2-46080*x-18432)*l n(7)+x^12-12*x^10-48*x^9+384*x^7+1088*x^6+768*x^5-3072*x^4-10240*x^3-15360 *x^2-12288*x-4096),x,method=_RETURNVERBOSE)
Output:
(16*ln(7)^4+32*ln(7)^3*x+24*ln(7)^2*x^2+8*ln(7)*x^3+x^4)/(4*ln(7)^2*x^2+4* ln(7)*x^3+x^4-36*ln(7)^2-24*x*ln(7)-4*x^2-48*ln(7)-16*x-16)^2
Leaf count of result is larger than twice the leaf count of optimal. 172 vs. \(2 (24) = 48\).
Time = 0.08 (sec) , antiderivative size = 172, normalized size of antiderivative = 7.48 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\frac {x^{4} + 8 \, x^{3} \log \left (7\right ) + 24 \, x^{2} \log \left (7\right )^{2} + 32 \, x \log \left (7\right )^{3} + 16 \, \log \left (7\right )^{4}}{x^{8} - 8 \, x^{6} - 32 \, x^{5} + 16 \, {\left (x^{4} - 18 \, x^{2} + 81\right )} \log \left (7\right )^{4} - 16 \, x^{4} + 32 \, {\left (x^{5} - 15 \, x^{3} - 12 \, x^{2} + 54 \, x + 108\right )} \log \left (7\right )^{3} + 128 \, x^{3} + 8 \, {\left (3 \, x^{6} - 37 \, x^{4} - 64 \, x^{3} + 92 \, x^{2} + 432 \, x + 432\right )} \log \left (7\right )^{2} + 384 \, x^{2} + 8 \, {\left (x^{7} - 10 \, x^{5} - 28 \, x^{4} + 8 \, x^{3} + 144 \, x^{2} + 288 \, x + 192\right )} \log \left (7\right ) + 512 \, x + 256} \] Input:
integrate((-256*x*log(7)^6+32*(-24*x^2-12)*log(7)^5+16*(-60*x^3-44*x-64)*l og(7)^4+8*(-80*x^4-60*x^2-224*x-64)*log(7)^3+4*(-60*x^5-36*x^3-288*x^2-192 *x)*log(7)^2+2*(-24*x^6-8*x^4-160*x^3-192*x^2)*log(7)-4*x^7-32*x^4-64*x^3) /(64*(x^6-27*x^4+243*x^2-729)*log(7)^6+32*(6*x^7-144*x^5-72*x^4+1134*x^3+1 296*x^2-2916*x-5832)*log(7)^5+16*(15*x^8-318*x^6-336*x^5+2139*x^4+5184*x^3 -2268*x^2-19440*x-19440)*log(7)^4+8*(20*x^9-372*x^7-624*x^6+2040*x^5+8208* x^4+4320*x^3-23616*x^2-51840*x-34560)*log(7)^3+4*(15*x^10-243*x^8-576*x^7+ 984*x^6+6432*x^5+8496*x^4-11136*x^3-51072*x^2-69120*x-34560)*log(7)^2+2*(6 *x^11-84*x^9-264*x^8+192*x^7+2496*x^6+5184*x^5-384*x^4-21504*x^3-46080*x^2 -46080*x-18432)*log(7)+x^12-12*x^10-48*x^9+384*x^7+1088*x^6+768*x^5-3072*x ^4-10240*x^3-15360*x^2-12288*x-4096),x, algorithm="fricas")
Output:
(x^4 + 8*x^3*log(7) + 24*x^2*log(7)^2 + 32*x*log(7)^3 + 16*log(7)^4)/(x^8 - 8*x^6 - 32*x^5 + 16*(x^4 - 18*x^2 + 81)*log(7)^4 - 16*x^4 + 32*(x^5 - 15 *x^3 - 12*x^2 + 54*x + 108)*log(7)^3 + 128*x^3 + 8*(3*x^6 - 37*x^4 - 64*x^ 3 + 92*x^2 + 432*x + 432)*log(7)^2 + 384*x^2 + 8*(x^7 - 10*x^5 - 28*x^4 + 8*x^3 + 144*x^2 + 288*x + 192)*log(7) + 512*x + 256)
Leaf count of result is larger than twice the leaf count of optimal. 207 vs. \(2 (19) = 38\).
Time = 16.62 (sec) , antiderivative size = 207, normalized size of antiderivative = 9.00 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=- \frac {- x^{4} - 8 x^{3} \log {\left (7 \right )} - 24 x^{2} \log {\left (7 \right )}^{2} - 32 x \log {\left (7 \right )}^{3} - 16 \log {\left (7 \right )}^{4}}{x^{8} + 8 x^{7} \log {\left (7 \right )} + x^{6} \left (-8 + 24 \log {\left (7 \right )}^{2}\right ) + x^{5} \left (- 80 \log {\left (7 \right )} - 32 + 32 \log {\left (7 \right )}^{3}\right ) + x^{4} \left (- 296 \log {\left (7 \right )}^{2} - 224 \log {\left (7 \right )} - 16 + 16 \log {\left (7 \right )}^{4}\right ) + x^{3} \left (- 480 \log {\left (7 \right )}^{3} - 512 \log {\left (7 \right )}^{2} + 64 \log {\left (7 \right )} + 128\right ) + x^{2} \left (- 288 \log {\left (7 \right )}^{4} - 384 \log {\left (7 \right )}^{3} + 384 + 1152 \log {\left (7 \right )} + 736 \log {\left (7 \right )}^{2}\right ) + x \left (512 + 2304 \log {\left (7 \right )} + 1728 \log {\left (7 \right )}^{3} + 3456 \log {\left (7 \right )}^{2}\right ) + 256 + 1536 \log {\left (7 \right )} + 3456 \log {\left (7 \right )}^{2} + 1296 \log {\left (7 \right )}^{4} + 3456 \log {\left (7 \right )}^{3}} \] Input:
integrate((-256*x*ln(7)**6+32*(-24*x**2-12)*ln(7)**5+16*(-60*x**3-44*x-64) *ln(7)**4+8*(-80*x**4-60*x**2-224*x-64)*ln(7)**3+4*(-60*x**5-36*x**3-288*x **2-192*x)*ln(7)**2+2*(-24*x**6-8*x**4-160*x**3-192*x**2)*ln(7)-4*x**7-32* x**4-64*x**3)/(64*(x**6-27*x**4+243*x**2-729)*ln(7)**6+32*(6*x**7-144*x**5 -72*x**4+1134*x**3+1296*x**2-2916*x-5832)*ln(7)**5+16*(15*x**8-318*x**6-33 6*x**5+2139*x**4+5184*x**3-2268*x**2-19440*x-19440)*ln(7)**4+8*(20*x**9-37 2*x**7-624*x**6+2040*x**5+8208*x**4+4320*x**3-23616*x**2-51840*x-34560)*ln (7)**3+4*(15*x**10-243*x**8-576*x**7+984*x**6+6432*x**5+8496*x**4-11136*x* *3-51072*x**2-69120*x-34560)*ln(7)**2+2*(6*x**11-84*x**9-264*x**8+192*x**7 +2496*x**6+5184*x**5-384*x**4-21504*x**3-46080*x**2-46080*x-18432)*ln(7)+x **12-12*x**10-48*x**9+384*x**7+1088*x**6+768*x**5-3072*x**4-10240*x**3-153 60*x**2-12288*x-4096),x)
Output:
-(-x**4 - 8*x**3*log(7) - 24*x**2*log(7)**2 - 32*x*log(7)**3 - 16*log(7)** 4)/(x**8 + 8*x**7*log(7) + x**6*(-8 + 24*log(7)**2) + x**5*(-80*log(7) - 3 2 + 32*log(7)**3) + x**4*(-296*log(7)**2 - 224*log(7) - 16 + 16*log(7)**4) + x**3*(-480*log(7)**3 - 512*log(7)**2 + 64*log(7) + 128) + x**2*(-288*lo g(7)**4 - 384*log(7)**3 + 384 + 1152*log(7) + 736*log(7)**2) + x*(512 + 23 04*log(7) + 1728*log(7)**3 + 3456*log(7)**2) + 256 + 1536*log(7) + 3456*lo g(7)**2 + 1296*log(7)**4 + 3456*log(7)**3)
Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (24) = 48\).
Time = 0.07 (sec) , antiderivative size = 196, normalized size of antiderivative = 8.52 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\frac {x^{4} + 8 \, x^{3} \log \left (7\right ) + 24 \, x^{2} \log \left (7\right )^{2} + 32 \, x \log \left (7\right )^{3} + 16 \, \log \left (7\right )^{4}}{x^{8} + 8 \, x^{7} \log \left (7\right ) + 8 \, {\left (3 \, \log \left (7\right )^{2} - 1\right )} x^{6} + 16 \, {\left (2 \, \log \left (7\right )^{3} - 5 \, \log \left (7\right ) - 2\right )} x^{5} + 8 \, {\left (2 \, \log \left (7\right )^{4} - 37 \, \log \left (7\right )^{2} - 28 \, \log \left (7\right ) - 2\right )} x^{4} - 32 \, {\left (15 \, \log \left (7\right )^{3} + 16 \, \log \left (7\right )^{2} - 2 \, \log \left (7\right ) - 4\right )} x^{3} + 1296 \, \log \left (7\right )^{4} - 32 \, {\left (9 \, \log \left (7\right )^{4} + 12 \, \log \left (7\right )^{3} - 23 \, \log \left (7\right )^{2} - 36 \, \log \left (7\right ) - 12\right )} x^{2} + 3456 \, \log \left (7\right )^{3} + 64 \, {\left (27 \, \log \left (7\right )^{3} + 54 \, \log \left (7\right )^{2} + 36 \, \log \left (7\right ) + 8\right )} x + 3456 \, \log \left (7\right )^{2} + 1536 \, \log \left (7\right ) + 256} \] Input:
integrate((-256*x*log(7)^6+32*(-24*x^2-12)*log(7)^5+16*(-60*x^3-44*x-64)*l og(7)^4+8*(-80*x^4-60*x^2-224*x-64)*log(7)^3+4*(-60*x^5-36*x^3-288*x^2-192 *x)*log(7)^2+2*(-24*x^6-8*x^4-160*x^3-192*x^2)*log(7)-4*x^7-32*x^4-64*x^3) /(64*(x^6-27*x^4+243*x^2-729)*log(7)^6+32*(6*x^7-144*x^5-72*x^4+1134*x^3+1 296*x^2-2916*x-5832)*log(7)^5+16*(15*x^8-318*x^6-336*x^5+2139*x^4+5184*x^3 -2268*x^2-19440*x-19440)*log(7)^4+8*(20*x^9-372*x^7-624*x^6+2040*x^5+8208* x^4+4320*x^3-23616*x^2-51840*x-34560)*log(7)^3+4*(15*x^10-243*x^8-576*x^7+ 984*x^6+6432*x^5+8496*x^4-11136*x^3-51072*x^2-69120*x-34560)*log(7)^2+2*(6 *x^11-84*x^9-264*x^8+192*x^7+2496*x^6+5184*x^5-384*x^4-21504*x^3-46080*x^2 -46080*x-18432)*log(7)+x^12-12*x^10-48*x^9+384*x^7+1088*x^6+768*x^5-3072*x ^4-10240*x^3-15360*x^2-12288*x-4096),x, algorithm="maxima")
Output:
(x^4 + 8*x^3*log(7) + 24*x^2*log(7)^2 + 32*x*log(7)^3 + 16*log(7)^4)/(x^8 + 8*x^7*log(7) + 8*(3*log(7)^2 - 1)*x^6 + 16*(2*log(7)^3 - 5*log(7) - 2)*x ^5 + 8*(2*log(7)^4 - 37*log(7)^2 - 28*log(7) - 2)*x^4 - 32*(15*log(7)^3 + 16*log(7)^2 - 2*log(7) - 4)*x^3 + 1296*log(7)^4 - 32*(9*log(7)^4 + 12*log( 7)^3 - 23*log(7)^2 - 36*log(7) - 12)*x^2 + 3456*log(7)^3 + 64*(27*log(7)^3 + 54*log(7)^2 + 36*log(7) + 8)*x + 3456*log(7)^2 + 1536*log(7) + 256)
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (24) = 48\).
Time = 0.19 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.48 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\frac {x^{4} + 8 \, x^{3} \log \left (7\right ) + 24 \, x^{2} \log \left (7\right )^{2} + 32 \, x \log \left (7\right )^{3} + 16 \, \log \left (7\right )^{4}}{{\left (x^{4} + 4 \, x^{3} \log \left (7\right ) + 4 \, x^{2} \log \left (7\right )^{2} - 4 \, x^{2} - 24 \, x \log \left (7\right ) - 36 \, \log \left (7\right )^{2} - 16 \, x - 48 \, \log \left (7\right ) - 16\right )}^{2}} \] Input:
integrate((-256*x*log(7)^6+32*(-24*x^2-12)*log(7)^5+16*(-60*x^3-44*x-64)*l og(7)^4+8*(-80*x^4-60*x^2-224*x-64)*log(7)^3+4*(-60*x^5-36*x^3-288*x^2-192 *x)*log(7)^2+2*(-24*x^6-8*x^4-160*x^3-192*x^2)*log(7)-4*x^7-32*x^4-64*x^3) /(64*(x^6-27*x^4+243*x^2-729)*log(7)^6+32*(6*x^7-144*x^5-72*x^4+1134*x^3+1 296*x^2-2916*x-5832)*log(7)^5+16*(15*x^8-318*x^6-336*x^5+2139*x^4+5184*x^3 -2268*x^2-19440*x-19440)*log(7)^4+8*(20*x^9-372*x^7-624*x^6+2040*x^5+8208* x^4+4320*x^3-23616*x^2-51840*x-34560)*log(7)^3+4*(15*x^10-243*x^8-576*x^7+ 984*x^6+6432*x^5+8496*x^4-11136*x^3-51072*x^2-69120*x-34560)*log(7)^2+2*(6 *x^11-84*x^9-264*x^8+192*x^7+2496*x^6+5184*x^5-384*x^4-21504*x^3-46080*x^2 -46080*x-18432)*log(7)+x^12-12*x^10-48*x^9+384*x^7+1088*x^6+768*x^5-3072*x ^4-10240*x^3-15360*x^2-12288*x-4096),x, algorithm="giac")
Output:
(x^4 + 8*x^3*log(7) + 24*x^2*log(7)^2 + 32*x*log(7)^3 + 16*log(7)^4)/(x^4 + 4*x^3*log(7) + 4*x^2*log(7)^2 - 4*x^2 - 24*x*log(7) - 36*log(7)^2 - 16*x - 48*log(7) - 16)^2
Timed out. \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\text {Hanged} \] Input:
int((2*log(7)*(192*x^2 + 160*x^3 + 8*x^4 + 24*x^6) + 4*log(7)^2*(192*x + 2 88*x^2 + 36*x^3 + 60*x^5) + 16*log(7)^4*(44*x + 60*x^3 + 64) + 256*x*log(7 )^6 + 32*log(7)^5*(24*x^2 + 12) + 8*log(7)^3*(224*x + 60*x^2 + 80*x^4 + 64 ) + 64*x^3 + 32*x^4 + 4*x^7)/(12288*x + 4*log(7)^2*(69120*x + 51072*x^2 + 11136*x^3 - 8496*x^4 - 6432*x^5 - 984*x^6 + 576*x^7 + 243*x^8 - 15*x^10 + 34560) + 32*log(7)^5*(2916*x - 1296*x^2 - 1134*x^3 + 72*x^4 + 144*x^5 - 6* x^7 + 5832) + 16*log(7)^4*(19440*x + 2268*x^2 - 5184*x^3 - 2139*x^4 + 336* x^5 + 318*x^6 - 15*x^8 + 19440) - 64*log(7)^6*(243*x^2 - 27*x^4 + x^6 - 72 9) + 15360*x^2 + 10240*x^3 + 3072*x^4 - 768*x^5 - 1088*x^6 - 384*x^7 + 48* x^9 + 12*x^10 - x^12 + 8*log(7)^3*(51840*x + 23616*x^2 - 4320*x^3 - 8208*x ^4 - 2040*x^5 + 624*x^6 + 372*x^7 - 20*x^9 + 34560) + 2*log(7)*(46080*x + 46080*x^2 + 21504*x^3 + 384*x^4 - 5184*x^5 - 2496*x^6 - 192*x^7 + 264*x^8 + 84*x^9 - 6*x^11 + 18432) + 4096),x)
Output:
\text{Hanged}
Time = 0.40 (sec) , antiderivative size = 226, normalized size of antiderivative = 9.83 \[ \int \frac {-64 x^3-32 x^4-4 x^7+\left (-192 x^2-160 x^3-8 x^4-24 x^6\right ) \log (49)+\left (-192 x-288 x^2-36 x^3-60 x^5\right ) \log ^2(49)+\left (-64-224 x-60 x^2-80 x^4\right ) \log ^3(49)+\left (-64-44 x-60 x^3\right ) \log ^4(49)+\left (-12-24 x^2\right ) \log ^5(49)-4 x \log ^6(49)}{-4096-12288 x-15360 x^2-10240 x^3-3072 x^4+768 x^5+1088 x^6+384 x^7-48 x^9-12 x^{10}+x^{12}+\left (-18432-46080 x-46080 x^2-21504 x^3-384 x^4+5184 x^5+2496 x^6+192 x^7-264 x^8-84 x^9+6 x^{11}\right ) \log (49)+\left (-34560-69120 x-51072 x^2-11136 x^3+8496 x^4+6432 x^5+984 x^6-576 x^7-243 x^8+15 x^{10}\right ) \log ^2(49)+\left (-34560-51840 x-23616 x^2+4320 x^3+8208 x^4+2040 x^5-624 x^6-372 x^7+20 x^9\right ) \log ^3(49)+\left (-19440-19440 x-2268 x^2+5184 x^3+2139 x^4-336 x^5-318 x^6+15 x^8\right ) \log ^4(49)+\left (-5832-2916 x+1296 x^2+1134 x^3-72 x^4-144 x^5+6 x^7\right ) \log ^5(49)+\left (-729+243 x^2-27 x^4+x^6\right ) \log ^6(49)} \, dx=\frac {16 \mathrm {log}\left (7\right )^{4}+32 \mathrm {log}\left (7\right )^{3} x +24 \mathrm {log}\left (7\right )^{2} x^{2}+8 \,\mathrm {log}\left (7\right ) x^{3}+x^{4}}{256+512 x +1728 \mathrm {log}\left (7\right )^{3} x +736 \mathrm {log}\left (7\right )^{2} x^{2}+64 \,\mathrm {log}\left (7\right ) x^{3}+16 \mathrm {log}\left (7\right )^{4} x^{4}-288 \mathrm {log}\left (7\right )^{4} x^{2}+32 \mathrm {log}\left (7\right )^{3} x^{5}-480 \mathrm {log}\left (7\right )^{3} x^{3}-384 \mathrm {log}\left (7\right )^{3} x^{2}+24 \mathrm {log}\left (7\right )^{2} x^{6}-296 \mathrm {log}\left (7\right )^{2} x^{4}-512 \mathrm {log}\left (7\right )^{2} x^{3}+3456 \mathrm {log}\left (7\right )^{2} x +8 \,\mathrm {log}\left (7\right ) x^{7}-80 \,\mathrm {log}\left (7\right ) x^{5}-224 \,\mathrm {log}\left (7\right ) x^{4}+2304 \,\mathrm {log}\left (7\right ) x +384 x^{2}+1536 \,\mathrm {log}\left (7\right )+1152 x^{2} \mathrm {log}\left (7\right )-32 x^{5}+128 x^{3}+x^{8}-8 x^{6}-16 x^{4}+1296 \mathrm {log}\left (7\right )^{4}+3456 \mathrm {log}\left (7\right )^{3}+3456 \mathrm {log}\left (7\right )^{2}} \] Input:
int((-256*x*log(7)^6+32*(-24*x^2-12)*log(7)^5+16*(-60*x^3-44*x-64)*log(7)^ 4+8*(-80*x^4-60*x^2-224*x-64)*log(7)^3+4*(-60*x^5-36*x^3-288*x^2-192*x)*lo g(7)^2+2*(-24*x^6-8*x^4-160*x^3-192*x^2)*log(7)-4*x^7-32*x^4-64*x^3)/(64*( x^6-27*x^4+243*x^2-729)*log(7)^6+32*(6*x^7-144*x^5-72*x^4+1134*x^3+1296*x^ 2-2916*x-5832)*log(7)^5+16*(15*x^8-318*x^6-336*x^5+2139*x^4+5184*x^3-2268* x^2-19440*x-19440)*log(7)^4+8*(20*x^9-372*x^7-624*x^6+2040*x^5+8208*x^4+43 20*x^3-23616*x^2-51840*x-34560)*log(7)^3+4*(15*x^10-243*x^8-576*x^7+984*x^ 6+6432*x^5+8496*x^4-11136*x^3-51072*x^2-69120*x-34560)*log(7)^2+2*(6*x^11- 84*x^9-264*x^8+192*x^7+2496*x^6+5184*x^5-384*x^4-21504*x^3-46080*x^2-46080 *x-18432)*log(7)+x^12-12*x^10-48*x^9+384*x^7+1088*x^6+768*x^5-3072*x^4-102 40*x^3-15360*x^2-12288*x-4096),x)
Output:
(16*log(7)**4 + 32*log(7)**3*x + 24*log(7)**2*x**2 + 8*log(7)*x**3 + x**4) /(16*log(7)**4*x**4 - 288*log(7)**4*x**2 + 1296*log(7)**4 + 32*log(7)**3*x **5 - 480*log(7)**3*x**3 - 384*log(7)**3*x**2 + 1728*log(7)**3*x + 3456*lo g(7)**3 + 24*log(7)**2*x**6 - 296*log(7)**2*x**4 - 512*log(7)**2*x**3 + 73 6*log(7)**2*x**2 + 3456*log(7)**2*x + 3456*log(7)**2 + 8*log(7)*x**7 - 80* log(7)*x**5 - 224*log(7)*x**4 + 64*log(7)*x**3 + 1152*log(7)*x**2 + 2304*l og(7)*x + 1536*log(7) + x**8 - 8*x**6 - 32*x**5 - 16*x**4 + 128*x**3 + 384 *x**2 + 512*x + 256)