Integrand size = 462, antiderivative size = 24 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 x \left (4+e^x+x\right ) \left (-4+e^{-2 x} x^2+\log (3)\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(207\) vs. \(2(24)=48\).
Time = 0.27 (sec) , antiderivative size = 207, normalized size of antiderivative = 8.62 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 \left (e^{-7 x} x^9+e^{-8 x} x^9 (4+x)+4 e^{-5 x} x^7 (-4+\log (3))+6 e^{-3 x} x^5 (-4+\log (3))^2+4 e^{-x} x^3 (-4+\log (3))^3+e^x x (-4+\log (3))^4+\frac {1}{2} e^{-2 x} x^3 (-4+\log (3))^2 (-128+8 x (-4+\log (3))+38 \log (3)-3 \log (9))+\frac {3}{4} e^{-4 x} x^5 (-4+\log (3)) (-128+8 x (-4+\log (3))+34 \log (3)-\log (9))+\frac {1}{6} e^{-6 x} x^7 (-384+24 x (-4+\log (3))+98 \log (3)-\log (9))+\frac {1}{2} x^2 (-4+\log (3))^3 (-8+\log (9))+x (-4+\log (3))^3 (-16+\log (81))\right ) \]
Integrate[(576*x^8 - 352*x^9 - 128*x^10 + E^x*(144*x^8 - 112*x^9) + E^(3*x )*(-1792*x^6 + 1280*x^7 + (448*x^6 - 320*x^7)*Log[3]) + E^(2*x)*(-7168*x^6 + 4096*x^7 + 1536*x^8 + (1792*x^6 - 1024*x^7 - 384*x^8)*Log[3]) + E^(5*x) *(7680*x^4 - 4608*x^5 + (-3840*x^4 + 2304*x^5)*Log[3] + (480*x^4 - 288*x^5 )*Log[3]^2) + E^(4*x)*(30720*x^4 - 15360*x^5 - 6144*x^6 + (-15360*x^4 + 76 80*x^5 + 3072*x^6)*Log[3] + (1920*x^4 - 960*x^5 - 384*x^6)*Log[3]^2) + E^( 7*x)*(-12288*x^2 + 4096*x^3 + (9216*x^2 - 3072*x^3)*Log[3] + (-2304*x^2 + 768*x^3)*Log[3]^2 + (192*x^2 - 64*x^3)*Log[3]^3) + E^(6*x)*(-49152*x^2 + 1 6384*x^3 + 8192*x^4 + (36864*x^2 - 12288*x^3 - 6144*x^4)*Log[3] + (-9216*x ^2 + 3072*x^3 + 1536*x^4)*Log[3]^2 + (768*x^2 - 256*x^3 - 128*x^4)*Log[3]^ 3) + E^(9*x)*(4096 + 4096*x + (-4096 - 4096*x)*Log[3] + (1536 + 1536*x)*Lo g[3]^2 + (-256 - 256*x)*Log[3]^3 + (16 + 16*x)*Log[3]^4) + E^(8*x)*(16384 + 8192*x + (-16384 - 8192*x)*Log[3] + (6144 + 3072*x)*Log[3]^2 + (-1024 - 512*x)*Log[3]^3 + (64 + 32*x)*Log[3]^4))/E^(8*x),x]
16*(x^9/E^(7*x) + (x^9*(4 + x))/E^(8*x) + (4*x^7*(-4 + Log[3]))/E^(5*x) + (6*x^5*(-4 + Log[3])^2)/E^(3*x) + (4*x^3*(-4 + Log[3])^3)/E^x + E^x*x*(-4 + Log[3])^4 + (x^3*(-4 + Log[3])^2*(-128 + 8*x*(-4 + Log[3]) + 38*Log[3] - 3*Log[9]))/(2*E^(2*x)) + (3*x^5*(-4 + Log[3])*(-128 + 8*x*(-4 + Log[3]) + 34*Log[3] - Log[9]))/(4*E^(4*x)) + (x^7*(-384 + 24*x*(-4 + Log[3]) + 98*L og[3] - Log[9]))/(6*E^(6*x)) + (x^2*(-4 + Log[3])^3*(-8 + Log[9]))/2 + x*( -4 + Log[3])^3*(-16 + Log[81]))
Leaf count is larger than twice the leaf count of optimal. \(1292\) vs. \(2(24)=48\).
Time = 14.49 (sec) , antiderivative size = 1292, normalized size of antiderivative = 53.83, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used = {7239, 27, 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.
| \(\displaystyle \int e^{-8 x} \left (-128 x^{10}-352 x^9+576 x^8+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (1280 x^7-1792 x^6+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{5 x} \left (-4608 x^5+7680 x^4+\left (480 x^4-288 x^5\right ) \log ^2(3)+\left (2304 x^5-3840 x^4\right ) \log (3)\right )+e^{7 x} \left (4096 x^3-12288 x^2+\left (192 x^2-64 x^3\right ) \log ^3(3)+\left (768 x^3-2304 x^2\right ) \log ^2(3)+\left (9216 x^2-3072 x^3\right ) \log (3)\right )+e^{2 x} \left (1536 x^8+4096 x^7-7168 x^6+\left (-384 x^8-1024 x^7+1792 x^6\right ) \log (3)\right )+e^{4 x} \left (-6144 x^6-15360 x^5+30720 x^4+\left (-384 x^6-960 x^5+1920 x^4\right ) \log ^2(3)+\left (3072 x^6+7680 x^5-15360 x^4\right ) \log (3)\right )+e^{6 x} \left (8192 x^4+16384 x^3-49152 x^2+\left (-128 x^4-256 x^3+768 x^2\right ) \log ^3(3)+\left (1536 x^4+3072 x^3-9216 x^2\right ) \log ^2(3)+\left (-6144 x^4-12288 x^3+36864 x^2\right ) \log (3)\right )+e^{9 x} \left (4096 x+(16 x+16) \log ^4(3)+(-256 x-256) \log ^3(3)+(1536 x+1536) \log ^2(3)+(-4096 x-4096) \log (3)+4096\right )+e^{8 x} \left (8192 x+(32 x+64) \log ^4(3)+(-512 x-1024) \log ^3(3)+(3072 x+6144) \log ^2(3)+(-8192 x-16384) \log (3)+16384\right )\right ) \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int 16 e^{-8 x} \left (x^2+e^{2 x} (\log (3)-4)\right )^3 \left (-e^x (7 x-9) x^2-2 \left (4 x^2+11 x-18\right ) x^2+e^{2 x} (x (\log (9)-8)-16+\log (81))+e^{3 x} (x+1) (\log (3)-4)\right )dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 16 \int e^{-8 x} \left (x^2-e^{2 x} (4-\log (3))\right )^3 \left (e^x (9-7 x) x^2+2 \left (-4 x^2-11 x+18\right ) x^2-e^{2 x} ((8-\log (9)) x-\log (81)+16)-e^{3 x} (x+1) (4-\log (3))\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 16 \int \left (-e^{-7 x} (7 x-9) x^8-2 e^{-8 x} \left (4 x^2+11 x-18\right ) x^8+e^{-6 x} \left (24 (4-\log (3)) x^2+(256-66 \log (3)+\log (9)) x+\log (81)+108 \log (3)-448\right ) x^6-4 e^{-5 x} (5 x-7) (-4+\log (3)) x^6+3 e^{-4 x} (4-\log (3)) \left (-8 (4-\log (3)) x^2-(80-22 \log (3)+\log (9)) x-\log (81)-36 \log (3)+160\right ) x^4-6 e^{-3 x} (3 x-5) (-4+\log (3))^2 x^4+e^{-2 x} (4-\log (3))^2 \left (8 (4-\log (3)) x^2+(64-\log (43046721)) x-3 (64-12 \log (3)-\log (81))\right ) x^2-4 e^{-x} (x-3) (-4+\log (3))^3 x^2+(-4+\log (3))^3 (\log (9) x-8 x+\log (81)-16)+e^x (x+1) (-4+\log (3))^4\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 16 \left (e^{-8 x} x^{10}+4 e^{-8 x} x^9+e^{-7 x} x^9-4 e^{-6 x} (4-\log (3)) x^8-\frac {1}{6} e^{-6 x} (256-66 \log (3)+\log (9)) x^7-\frac {16}{3} e^{-6 x} (4-\log (3)) x^7-4 e^{-5 x} (4-\log (3)) x^7+\frac {1}{6} e^{-6 x} (448-108 \log (3)-\log (81)) x^6-\frac {7}{36} e^{-6 x} (256-66 \log (3)+\log (9)) x^6+6 e^{-4 x} (4-\log (3))^2 x^6-\frac {56}{9} e^{-6 x} (4-\log (3)) x^6+\frac {1}{6} e^{-6 x} (448-108 \log (3)-\log (81)) x^5+\frac {3}{4} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^5-\frac {7}{36} e^{-6 x} (256-66 \log (3)+\log (9)) x^5+9 e^{-4 x} (4-\log (3))^2 x^5+6 e^{-3 x} (4-\log (3))^2 x^5-\frac {56}{9} e^{-6 x} (4-\log (3)) x^5-\frac {3}{4} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^4+\frac {5}{36} e^{-6 x} (448-108 \log (3)-\log (81)) x^4+\frac {15}{16} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^4-\frac {35}{216} e^{-6 x} (256-66 \log (3)+\log (9)) x^4-4 e^{-2 x} (4-\log (3))^3 x^4+\frac {45}{4} e^{-4 x} (4-\log (3))^2 x^4-\frac {140}{27} e^{-6 x} (4-\log (3)) x^4-\frac {1}{2} e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x^3-\frac {3}{4} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^3+\frac {5}{54} e^{-6 x} (448-108 \log (3)-\log (81)) x^3+\frac {15}{16} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^3-\frac {35}{324} e^{-6 x} (256-66 \log (3)+\log (9)) x^3-8 e^{-2 x} (4-\log (3))^3 x^3-4 e^{-x} (4-\log (3))^3 x^3+\frac {45}{4} e^{-4 x} (4-\log (3))^2 x^3-\frac {280}{81} e^{-6 x} (4-\log (3)) x^3-\frac {3}{4} e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x^2+\frac {3}{2} e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81)) x^2-\frac {9}{16} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^2+\frac {5}{108} e^{-6 x} (448-108 \log (3)-\log (81)) x^2+\frac {45}{64} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^2-\frac {35}{648} e^{-6 x} (256-66 \log (3)+\log (9)) x^2-12 e^{-2 x} (4-\log (3))^3 x^2+\frac {135}{16} e^{-4 x} (4-\log (3))^2 x^2-\frac {140}{81} e^{-6 x} (4-\log (3)) x^2-\frac {3}{4} e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x+\frac {3}{2} e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81)) x-\frac {9}{32} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x+\frac {5}{324} e^{-6 x} (448-108 \log (3)-\log (81)) x+\frac {45}{128} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x-\frac {35 e^{-6 x} (256-66 \log (3)+\log (9)) x}{1944}-12 e^{-2 x} (4-\log (3))^3 x+\frac {135}{32} e^{-4 x} (4-\log (3))^2 x-\frac {140}{243} e^{-6 x} (4-\log (3)) x+\frac {(4-\log (3))^3 (-\log (9) x+8 x-\log (81)+16)^2}{2 (8-\log (9))}-\frac {3}{8} e^{-2 x} (4-\log (3))^2 (64-\log (43046721))+\frac {3}{4} e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81))-\frac {9}{128} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81))+\frac {5 e^{-6 x} (448-108 \log (3)-\log (81))}{1944}+\frac {45}{512} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9))-\frac {35 e^{-6 x} (256-66 \log (3)+\log (9))}{11664}-e^x (4-\log (3))^4+e^x (x+1) (4-\log (3))^4-6 e^{-2 x} (4-\log (3))^3+\frac {135}{128} e^{-4 x} (4-\log (3))^2-\frac {70}{729} e^{-6 x} (4-\log (3))\right )\) |
Int[(576*x^8 - 352*x^9 - 128*x^10 + E^x*(144*x^8 - 112*x^9) + E^(3*x)*(-17 92*x^6 + 1280*x^7 + (448*x^6 - 320*x^7)*Log[3]) + E^(2*x)*(-7168*x^6 + 409 6*x^7 + 1536*x^8 + (1792*x^6 - 1024*x^7 - 384*x^8)*Log[3]) + E^(5*x)*(7680 *x^4 - 4608*x^5 + (-3840*x^4 + 2304*x^5)*Log[3] + (480*x^4 - 288*x^5)*Log[ 3]^2) + E^(4*x)*(30720*x^4 - 15360*x^5 - 6144*x^6 + (-15360*x^4 + 7680*x^5 + 3072*x^6)*Log[3] + (1920*x^4 - 960*x^5 - 384*x^6)*Log[3]^2) + E^(7*x)*( -12288*x^2 + 4096*x^3 + (9216*x^2 - 3072*x^3)*Log[3] + (-2304*x^2 + 768*x^ 3)*Log[3]^2 + (192*x^2 - 64*x^3)*Log[3]^3) + E^(6*x)*(-49152*x^2 + 16384*x ^3 + 8192*x^4 + (36864*x^2 - 12288*x^3 - 6144*x^4)*Log[3] + (-9216*x^2 + 3 072*x^3 + 1536*x^4)*Log[3]^2 + (768*x^2 - 256*x^3 - 128*x^4)*Log[3]^3) + E ^(9*x)*(4096 + 4096*x + (-4096 - 4096*x)*Log[3] + (1536 + 1536*x)*Log[3]^2 + (-256 - 256*x)*Log[3]^3 + (16 + 16*x)*Log[3]^4) + E^(8*x)*(16384 + 8192 *x + (-16384 - 8192*x)*Log[3] + (6144 + 3072*x)*Log[3]^2 + (-1024 - 512*x) *Log[3]^3 + (64 + 32*x)*Log[3]^4))/E^(8*x),x]
16*((4*x^9)/E^(8*x) + x^9/E^(7*x) + x^10/E^(8*x) - (70*(4 - Log[3]))/(729* E^(6*x)) - (140*x*(4 - Log[3]))/(243*E^(6*x)) - (140*x^2*(4 - Log[3]))/(81 *E^(6*x)) - (280*x^3*(4 - Log[3]))/(81*E^(6*x)) - (140*x^4*(4 - Log[3]))/( 27*E^(6*x)) - (56*x^5*(4 - Log[3]))/(9*E^(6*x)) - (56*x^6*(4 - Log[3]))/(9 *E^(6*x)) - (16*x^7*(4 - Log[3]))/(3*E^(6*x)) - (4*x^7*(4 - Log[3]))/E^(5* x) - (4*x^8*(4 - Log[3]))/E^(6*x) + (135*(4 - Log[3])^2)/(128*E^(4*x)) + ( 135*x*(4 - Log[3])^2)/(32*E^(4*x)) + (135*x^2*(4 - Log[3])^2)/(16*E^(4*x)) + (45*x^3*(4 - Log[3])^2)/(4*E^(4*x)) + (45*x^4*(4 - Log[3])^2)/(4*E^(4*x )) + (9*x^5*(4 - Log[3])^2)/E^(4*x) + (6*x^5*(4 - Log[3])^2)/E^(3*x) + (6* x^6*(4 - Log[3])^2)/E^(4*x) - (6*(4 - Log[3])^3)/E^(2*x) - (12*x*(4 - Log[ 3])^3)/E^(2*x) - (12*x^2*(4 - Log[3])^3)/E^(2*x) - (8*x^3*(4 - Log[3])^3)/ E^(2*x) - (4*x^3*(4 - Log[3])^3)/E^x - (4*x^4*(4 - Log[3])^3)/E^(2*x) - E^ x*(4 - Log[3])^4 + E^x*(1 + x)*(4 - Log[3])^4 - (35*(256 - 66*Log[3] + Log [9]))/(11664*E^(6*x)) - (35*x*(256 - 66*Log[3] + Log[9]))/(1944*E^(6*x)) - (35*x^2*(256 - 66*Log[3] + Log[9]))/(648*E^(6*x)) - (35*x^3*(256 - 66*Log [3] + Log[9]))/(324*E^(6*x)) - (35*x^4*(256 - 66*Log[3] + Log[9]))/(216*E^ (6*x)) - (7*x^5*(256 - 66*Log[3] + Log[9]))/(36*E^(6*x)) - (7*x^6*(256 - 6 6*Log[3] + Log[9]))/(36*E^(6*x)) - (x^7*(256 - 66*Log[3] + Log[9]))/(6*E^( 6*x)) + (45*(4 - Log[3])*(80 - 22*Log[3] + Log[9]))/(512*E^(4*x)) + (45*x* (4 - Log[3])*(80 - 22*Log[3] + Log[9]))/(128*E^(4*x)) + (45*x^2*(4 - Lo...
3.15.76.3.1 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]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(322\) vs. \(2(39)=78\).
Time = 0.24 (sec) , antiderivative size = 323, normalized size of antiderivative = 13.46
| method | result | size |
| risch | \(16 x^{2} \ln \left (3\right )^{4}+64 x \ln \left (3\right )^{4}-256 x^{2} \ln \left (3\right )^{3}-1024 x \ln \left (3\right )^{3}+1536 x^{2} \ln \left (3\right )^{2}+6144 x \ln \left (3\right )^{2}-4096 x^{2} \ln \left (3\right )-16384 x \ln \left (3\right )+4096 x^{2}+16384 x +16 \left (\ln \left (3\right )^{4}-16 \ln \left (3\right )^{3}+96 \ln \left (3\right )^{2}-256 \ln \left (3\right )+256\right ) x \,{\mathrm e}^{x}+64 \left (\ln \left (3\right )^{3}-12 \ln \left (3\right )^{2}+48 \ln \left (3\right )-64\right ) x^{3} {\mathrm e}^{-x}+\left (64 x^{4} \ln \left (3\right )^{3}+256 x^{3} \ln \left (3\right )^{3}-768 x^{4} \ln \left (3\right )^{2}-3072 x^{3} \ln \left (3\right )^{2}+3072 x^{4} \ln \left (3\right )+12288 x^{3} \ln \left (3\right )-4096 x^{4}-16384 x^{3}\right ) {\mathrm e}^{-2 x}+96 \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right ) x^{5} {\mathrm e}^{-3 x}+\left (96 x^{6} \ln \left (3\right )^{2}+384 x^{5} \ln \left (3\right )^{2}-768 x^{6} \ln \left (3\right )-3072 x^{5} \ln \left (3\right )+1536 x^{6}+6144 x^{5}\right ) {\mathrm e}^{-4 x}+64 \left (-4+\ln \left (3\right )\right ) x^{7} {\mathrm e}^{-5 x}+\left (64 x^{8} \ln \left (3\right )+256 \ln \left (3\right ) x^{7}-256 x^{8}-1024 x^{7}\right ) {\mathrm e}^{-6 x}+16 \,{\mathrm e}^{-7 x} x^{9}+\left (16 x^{10}+64 x^{9}\right ) {\mathrm e}^{-8 x}\) | \(323\) |
| parts | \(16384 x +1536 x \ln \left (3\right )^{2} {\mathrm e}^{x}-1024 x \ln \left (3\right )^{3}+16 \,{\mathrm e}^{x} \ln \left (3\right )^{4} x -256 \,{\mathrm e}^{x} \ln \left (3\right )^{3} x +6144 x \ln \left (3\right )^{2}+64 x \ln \left (3\right )^{4}-16384 x \ln \left (3\right )+4096 \,{\mathrm e}^{x} x -4096 x^{4} {\mathrm e}^{-2 x}-16384 \,{\mathrm e}^{-2 x} x^{3}-4096 x^{3} {\mathrm e}^{-x}-4096 x \ln \left (3\right ) {\mathrm e}^{x}+16 x^{2} \ln \left (3\right )^{4}+1536 x^{2} \ln \left (3\right )^{2}-4096 x^{2} \ln \left (3\right )+4096 x^{2}+64 \ln \left (3\right ) {\mathrm e}^{-6 x} x^{8}+96 \ln \left (3\right )^{2} {\mathrm e}^{-4 x} x^{6}+64 x^{7} {\mathrm e}^{-5 x} \ln \left (3\right )+256 \ln \left (3\right ) {\mathrm e}^{-6 x} x^{7}+64 \ln \left (3\right )^{3} {\mathrm e}^{-2 x} x^{4}+96 \ln \left (3\right )^{2} {\mathrm e}^{-3 x} x^{5}+384 \ln \left (3\right )^{2} {\mathrm e}^{-4 x} x^{5}-768 \ln \left (3\right ) {\mathrm e}^{-4 x} x^{6}+64 \ln \left (3\right )^{3} {\mathrm e}^{-x} x^{3}+256 \ln \left (3\right )^{3} {\mathrm e}^{-2 x} x^{3}-768 \ln \left (3\right )^{2} {\mathrm e}^{-2 x} x^{4}-768 \ln \left (3\right ) {\mathrm e}^{-3 x} x^{5}-3072 \ln \left (3\right ) {\mathrm e}^{-4 x} x^{5}-768 \ln \left (3\right )^{2} {\mathrm e}^{-x} x^{3}-3072 \ln \left (3\right )^{2} {\mathrm e}^{-2 x} x^{3}+3072 \ln \left (3\right ) {\mathrm e}^{-2 x} x^{4}+3072 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{3}+12288 \ln \left (3\right ) {\mathrm e}^{-2 x} x^{3}-256 x^{2} \ln \left (3\right )^{3}+16 \,{\mathrm e}^{-7 x} x^{9}+16 \,{\mathrm e}^{-8 x} x^{10}+64 \,{\mathrm e}^{-8 x} x^{9}-256 \,{\mathrm e}^{-6 x} x^{8}-256 x^{7} {\mathrm e}^{-5 x}-1024 \,{\mathrm e}^{-6 x} x^{7}+1536 \,{\mathrm e}^{-4 x} x^{6}+1536 x^{5} {\mathrm e}^{-3 x}+6144 \,{\mathrm e}^{-4 x} x^{5}\) | \(433\) |
| parallelrisch | \(\left (16 x^{9} {\mathrm e}^{x}+4096 x \,{\mathrm e}^{9 x}+16384 x \,{\mathrm e}^{8 x}+1536 x^{5} {\mathrm e}^{5 x}+16 x^{10}+64 x^{9}+1536 x^{6} {\mathrm e}^{4 x}+16 \ln \left (3\right )^{4} x^{2} {\mathrm e}^{8 x}-256 \ln \left (3\right )^{3} x^{2} {\mathrm e}^{8 x}+1536 \ln \left (3\right )^{2} x^{2} {\mathrm e}^{8 x}-4096 \ln \left (3\right ) x^{2} {\mathrm e}^{8 x}+16 \,{\mathrm e}^{9 x} \ln \left (3\right )^{4} x -256 \,{\mathrm e}^{9 x} \ln \left (3\right )^{3} x +64 \,{\mathrm e}^{8 x} \ln \left (3\right )^{4} x +64 \,{\mathrm e}^{7 x} \ln \left (3\right )^{3} x^{3}+64 \,{\mathrm e}^{6 x} \ln \left (3\right )^{3} x^{4}+1536 \,{\mathrm e}^{9 x} \ln \left (3\right )^{2} x -1024 \,{\mathrm e}^{8 x} \ln \left (3\right )^{3} x -768 \,{\mathrm e}^{7 x} \ln \left (3\right )^{2} x^{3}+256 \,{\mathrm e}^{6 x} \ln \left (3\right )^{3} x^{3}-768 \,{\mathrm e}^{6 x} \ln \left (3\right )^{2} x^{4}+96 \,{\mathrm e}^{5 x} \ln \left (3\right )^{2} x^{5}+96 \,{\mathrm e}^{4 x} \ln \left (3\right )^{2} x^{6}-4096 \,{\mathrm e}^{9 x} \ln \left (3\right ) x +6144 \,{\mathrm e}^{8 x} \ln \left (3\right )^{2} x +3072 \,{\mathrm e}^{7 x} \ln \left (3\right ) x^{3}-3072 \,{\mathrm e}^{6 x} \ln \left (3\right )^{2} x^{3}+3072 \,{\mathrm e}^{6 x} \ln \left (3\right ) x^{4}-768 \,{\mathrm e}^{5 x} \ln \left (3\right ) x^{5}+384 \,{\mathrm e}^{4 x} \ln \left (3\right )^{2} x^{5}-768 \,{\mathrm e}^{4 x} \ln \left (3\right ) x^{6}+64 \,{\mathrm e}^{3 x} \ln \left (3\right ) x^{7}+64 \,{\mathrm e}^{2 x} \ln \left (3\right ) x^{8}-16384 \,{\mathrm e}^{8 x} \ln \left (3\right ) x +12288 \,{\mathrm e}^{6 x} \ln \left (3\right ) x^{3}-3072 \,{\mathrm e}^{4 x} \ln \left (3\right ) x^{5}+256 \,{\mathrm e}^{2 x} \ln \left (3\right ) x^{7}+6144 x^{5} {\mathrm e}^{4 x}-256 \,{\mathrm e}^{2 x} x^{8}-1024 \,{\mathrm e}^{2 x} x^{7}-256 x^{7} {\mathrm e}^{3 x}+4096 x^{2} {\mathrm e}^{8 x}-16384 x^{3} {\mathrm e}^{6 x}-4096 \,{\mathrm e}^{7 x} x^{3}-4096 \,{\mathrm e}^{6 x} x^{4}\right ) {\mathrm e}^{-8 x}\) | \(478\) |
| default | \(\text {Expression too large to display}\) | \(1687\) |
int((((16*x+16)*ln(3)^4+(-256*x-256)*ln(3)^3+(1536*x+1536)*ln(3)^2+(-4096* x-4096)*ln(3)+4096*x+4096)*exp(x)^9+((32*x+64)*ln(3)^4+(-512*x-1024)*ln(3) ^3+(3072*x+6144)*ln(3)^2+(-8192*x-16384)*ln(3)+8192*x+16384)*exp(x)^8+((-6 4*x^3+192*x^2)*ln(3)^3+(768*x^3-2304*x^2)*ln(3)^2+(-3072*x^3+9216*x^2)*ln( 3)+4096*x^3-12288*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^2)*ln(3)^3+(1536* x^4+3072*x^3-9216*x^2)*ln(3)^2+(-6144*x^4-12288*x^3+36864*x^2)*ln(3)+8192* x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)*ln(3)^2+(2304*x^5-38 40*x^4)*ln(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6-960*x^5+1920*x^4)*ln( 3)^2+(3072*x^6+7680*x^5-15360*x^4)*ln(3)-6144*x^6-15360*x^5+30720*x^4)*exp (x)^4+((-320*x^7+448*x^6)*ln(3)+1280*x^7-1792*x^6)*exp(x)^3+((-384*x^8-102 4*x^7+1792*x^6)*ln(3)+1536*x^8+4096*x^7-7168*x^6)*exp(x)^2+(-112*x^9+144*x ^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp(x)^8,x,method=_RETURNVERBOSE)
16*x^2*ln(3)^4+64*x*ln(3)^4-256*x^2*ln(3)^3-1024*x*ln(3)^3+1536*x^2*ln(3)^ 2+6144*x*ln(3)^2-4096*x^2*ln(3)-16384*x*ln(3)+4096*x^2+16384*x+16*(ln(3)^4 -16*ln(3)^3+96*ln(3)^2-256*ln(3)+256)*x*exp(x)+64*(ln(3)^3-12*ln(3)^2+48*l n(3)-64)*x^3/exp(x)+(64*x^4*ln(3)^3+256*x^3*ln(3)^3-768*x^4*ln(3)^2-3072*x ^3*ln(3)^2+3072*x^4*ln(3)+12288*x^3*ln(3)-4096*x^4-16384*x^3)/exp(x)^2+96* (ln(3)^2-8*ln(3)+16)*x^5/exp(x)^3+(96*x^6*ln(3)^2+384*x^5*ln(3)^2-768*x^6* ln(3)-3072*x^5*ln(3)+1536*x^6+6144*x^5)/exp(x)^4+64*(-4+ln(3))*x^7/exp(x)^ 5+(64*x^8*ln(3)+256*ln(3)*x^7-256*x^8-1024*x^7)/exp(x)^6+16/exp(x)^7*x^9+( 16*x^10+64*x^9)/exp(x)^8
Leaf count of result is larger than twice the leaf count of optimal. 333 vs. \(2 (22) = 44\).
Time = 0.27 (sec) , antiderivative size = 333, normalized size of antiderivative = 13.88 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 \, {\left (x^{10} + x^{9} e^{x} + 4 \, x^{9} + {\left (x \log \left (3\right )^{4} - 16 \, x \log \left (3\right )^{3} + 96 \, x \log \left (3\right )^{2} - 256 \, x \log \left (3\right ) + 256 \, x\right )} e^{\left (9 \, x\right )} + {\left ({\left (x^{2} + 4 \, x\right )} \log \left (3\right )^{4} - 16 \, {\left (x^{2} + 4 \, x\right )} \log \left (3\right )^{3} + 96 \, {\left (x^{2} + 4 \, x\right )} \log \left (3\right )^{2} + 256 \, x^{2} - 256 \, {\left (x^{2} + 4 \, x\right )} \log \left (3\right ) + 1024 \, x\right )} e^{\left (8 \, x\right )} + 4 \, {\left (x^{3} \log \left (3\right )^{3} - 12 \, x^{3} \log \left (3\right )^{2} + 48 \, x^{3} \log \left (3\right ) - 64 \, x^{3}\right )} e^{\left (7 \, x\right )} - 4 \, {\left (64 \, x^{4} - {\left (x^{4} + 4 \, x^{3}\right )} \log \left (3\right )^{3} + 256 \, x^{3} + 12 \, {\left (x^{4} + 4 \, x^{3}\right )} \log \left (3\right )^{2} - 48 \, {\left (x^{4} + 4 \, x^{3}\right )} \log \left (3\right )\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{5} \log \left (3\right )^{2} - 8 \, x^{5} \log \left (3\right ) + 16 \, x^{5}\right )} e^{\left (5 \, x\right )} + 6 \, {\left (16 \, x^{6} + 64 \, x^{5} + {\left (x^{6} + 4 \, x^{5}\right )} \log \left (3\right )^{2} - 8 \, {\left (x^{6} + 4 \, x^{5}\right )} \log \left (3\right )\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x^{7} \log \left (3\right ) - 4 \, x^{7}\right )} e^{\left (3 \, x\right )} - 4 \, {\left (4 \, x^{8} + 16 \, x^{7} - {\left (x^{8} + 4 \, x^{7}\right )} \log \left (3\right )\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-8 \, x\right )} \]
integrate((((16*x+16)*log(3)^4+(-256*x-256)*log(3)^3+(1536*x+1536)*log(3)^ 2+(-4096*x-4096)*log(3)+4096*x+4096)*exp(x)^9+((32*x+64)*log(3)^4+(-512*x- 1024)*log(3)^3+(3072*x+6144)*log(3)^2+(-8192*x-16384)*log(3)+8192*x+16384) *exp(x)^8+((-64*x^3+192*x^2)*log(3)^3+(768*x^3-2304*x^2)*log(3)^2+(-3072*x ^3+9216*x^2)*log(3)+4096*x^3-12288*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^ 2)*log(3)^3+(1536*x^4+3072*x^3-9216*x^2)*log(3)^2+(-6144*x^4-12288*x^3+368 64*x^2)*log(3)+8192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)* log(3)^2+(2304*x^5-3840*x^4)*log(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6 -960*x^5+1920*x^4)*log(3)^2+(3072*x^6+7680*x^5-15360*x^4)*log(3)-6144*x^6- 15360*x^5+30720*x^4)*exp(x)^4+((-320*x^7+448*x^6)*log(3)+1280*x^7-1792*x^6 )*exp(x)^3+((-384*x^8-1024*x^7+1792*x^6)*log(3)+1536*x^8+4096*x^7-7168*x^6 )*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp(x)^8,x, algorithm=\
16*(x^10 + x^9*e^x + 4*x^9 + (x*log(3)^4 - 16*x*log(3)^3 + 96*x*log(3)^2 - 256*x*log(3) + 256*x)*e^(9*x) + ((x^2 + 4*x)*log(3)^4 - 16*(x^2 + 4*x)*lo g(3)^3 + 96*(x^2 + 4*x)*log(3)^2 + 256*x^2 - 256*(x^2 + 4*x)*log(3) + 1024 *x)*e^(8*x) + 4*(x^3*log(3)^3 - 12*x^3*log(3)^2 + 48*x^3*log(3) - 64*x^3)* e^(7*x) - 4*(64*x^4 - (x^4 + 4*x^3)*log(3)^3 + 256*x^3 + 12*(x^4 + 4*x^3)* log(3)^2 - 48*(x^4 + 4*x^3)*log(3))*e^(6*x) + 6*(x^5*log(3)^2 - 8*x^5*log( 3) + 16*x^5)*e^(5*x) + 6*(16*x^6 + 64*x^5 + (x^6 + 4*x^5)*log(3)^2 - 8*(x^ 6 + 4*x^5)*log(3))*e^(4*x) + 4*(x^7*log(3) - 4*x^7)*e^(3*x) - 4*(4*x^8 + 1 6*x^7 - (x^8 + 4*x^7)*log(3))*e^(2*x))*e^(-8*x)
Leaf count of result is larger than twice the leaf count of optimal. 366 vs. \(2 (42) = 84\).
Time = 1.55 (sec) , antiderivative size = 366, normalized size of antiderivative = 15.25 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 x^{9} e^{- 7 x} + x^{2} \left (- 4096 \log {\left (3 \right )} - 256 \log {\left (3 \right )}^{3} + 16 \log {\left (3 \right )}^{4} + 1536 \log {\left (3 \right )}^{2} + 4096\right ) + x \left (- 16384 \log {\left (3 \right )} - 1024 \log {\left (3 \right )}^{3} + 64 \log {\left (3 \right )}^{4} + 6144 \log {\left (3 \right )}^{2} + 16384\right ) + \left (- 256 x^{7} + 64 x^{7} \log {\left (3 \right )}\right ) e^{- 5 x} + \left (16 x^{10} + 64 x^{9}\right ) e^{- 8 x} + \left (- 768 x^{5} \log {\left (3 \right )} + 96 x^{5} \log {\left (3 \right )}^{2} + 1536 x^{5}\right ) e^{- 3 x} + \left (- 4096 x^{3} - 768 x^{3} \log {\left (3 \right )}^{2} + 64 x^{3} \log {\left (3 \right )}^{3} + 3072 x^{3} \log {\left (3 \right )}\right ) e^{- x} + \left (- 256 x^{8} + 64 x^{8} \log {\left (3 \right )} - 1024 x^{7} + 256 x^{7} \log {\left (3 \right )}\right ) e^{- 6 x} + \left (- 4096 x \log {\left (3 \right )} - 256 x \log {\left (3 \right )}^{3} + 16 x \log {\left (3 \right )}^{4} + 1536 x \log {\left (3 \right )}^{2} + 4096 x\right ) e^{x} + \left (- 768 x^{6} \log {\left (3 \right )} + 96 x^{6} \log {\left (3 \right )}^{2} + 1536 x^{6} - 3072 x^{5} \log {\left (3 \right )} + 384 x^{5} \log {\left (3 \right )}^{2} + 6144 x^{5}\right ) e^{- 4 x} + \left (- 4096 x^{4} - 768 x^{4} \log {\left (3 \right )}^{2} + 64 x^{4} \log {\left (3 \right )}^{3} + 3072 x^{4} \log {\left (3 \right )} - 16384 x^{3} - 3072 x^{3} \log {\left (3 \right )}^{2} + 256 x^{3} \log {\left (3 \right )}^{3} + 12288 x^{3} \log {\left (3 \right )}\right ) e^{- 2 x} \]
integrate((((16*x+16)*ln(3)**4+(-256*x-256)*ln(3)**3+(1536*x+1536)*ln(3)** 2+(-4096*x-4096)*ln(3)+4096*x+4096)*exp(x)**9+((32*x+64)*ln(3)**4+(-512*x- 1024)*ln(3)**3+(3072*x+6144)*ln(3)**2+(-8192*x-16384)*ln(3)+8192*x+16384)* exp(x)**8+((-64*x**3+192*x**2)*ln(3)**3+(768*x**3-2304*x**2)*ln(3)**2+(-30 72*x**3+9216*x**2)*ln(3)+4096*x**3-12288*x**2)*exp(x)**7+((-128*x**4-256*x **3+768*x**2)*ln(3)**3+(1536*x**4+3072*x**3-9216*x**2)*ln(3)**2+(-6144*x** 4-12288*x**3+36864*x**2)*ln(3)+8192*x**4+16384*x**3-49152*x**2)*exp(x)**6+ ((-288*x**5+480*x**4)*ln(3)**2+(2304*x**5-3840*x**4)*ln(3)-4608*x**5+7680* x**4)*exp(x)**5+((-384*x**6-960*x**5+1920*x**4)*ln(3)**2+(3072*x**6+7680*x **5-15360*x**4)*ln(3)-6144*x**6-15360*x**5+30720*x**4)*exp(x)**4+((-320*x* *7+448*x**6)*ln(3)+1280*x**7-1792*x**6)*exp(x)**3+((-384*x**8-1024*x**7+17 92*x**6)*ln(3)+1536*x**8+4096*x**7-7168*x**6)*exp(x)**2+(-112*x**9+144*x** 8)*exp(x)-128*x**10-352*x**9+576*x**8)/exp(x)**8,x)
16*x**9*exp(-7*x) + x**2*(-4096*log(3) - 256*log(3)**3 + 16*log(3)**4 + 15 36*log(3)**2 + 4096) + x*(-16384*log(3) - 1024*log(3)**3 + 64*log(3)**4 + 6144*log(3)**2 + 16384) + (-256*x**7 + 64*x**7*log(3))*exp(-5*x) + (16*x** 10 + 64*x**9)*exp(-8*x) + (-768*x**5*log(3) + 96*x**5*log(3)**2 + 1536*x** 5)*exp(-3*x) + (-4096*x**3 - 768*x**3*log(3)**2 + 64*x**3*log(3)**3 + 3072 *x**3*log(3))*exp(-x) + (-256*x**8 + 64*x**8*log(3) - 1024*x**7 + 256*x**7 *log(3))*exp(-6*x) + (-4096*x*log(3) - 256*x*log(3)**3 + 16*x*log(3)**4 + 1536*x*log(3)**2 + 4096*x)*exp(x) + (-768*x**6*log(3) + 96*x**6*log(3)**2 + 1536*x**6 - 3072*x**5*log(3) + 384*x**5*log(3)**2 + 6144*x**5)*exp(-4*x) + (-4096*x**4 - 768*x**4*log(3)**2 + 64*x**4*log(3)**3 + 3072*x**4*log(3) - 16384*x**3 - 3072*x**3*log(3)**2 + 256*x**3*log(3)**3 + 12288*x**3*log( 3))*exp(-2*x)
Leaf count of result is larger than twice the leaf count of optimal. 1726 vs. \(2 (22) = 44\).
Time = 0.26 (sec) , antiderivative size = 1726, normalized size of antiderivative = 71.92 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=\text {Too large to display} \]
integrate((((16*x+16)*log(3)^4+(-256*x-256)*log(3)^3+(1536*x+1536)*log(3)^ 2+(-4096*x-4096)*log(3)+4096*x+4096)*exp(x)^9+((32*x+64)*log(3)^4+(-512*x- 1024)*log(3)^3+(3072*x+6144)*log(3)^2+(-8192*x-16384)*log(3)+8192*x+16384) *exp(x)^8+((-64*x^3+192*x^2)*log(3)^3+(768*x^3-2304*x^2)*log(3)^2+(-3072*x ^3+9216*x^2)*log(3)+4096*x^3-12288*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^ 2)*log(3)^3+(1536*x^4+3072*x^3-9216*x^2)*log(3)^2+(-6144*x^4-12288*x^3+368 64*x^2)*log(3)+8192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)* log(3)^2+(2304*x^5-3840*x^4)*log(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6 -960*x^5+1920*x^4)*log(3)^2+(3072*x^6+7680*x^5-15360*x^4)*log(3)-6144*x^6- 15360*x^5+30720*x^4)*exp(x)^4+((-320*x^7+448*x^6)*log(3)+1280*x^7-1792*x^6 )*exp(x)^3+((-384*x^8-1024*x^7+1792*x^6)*log(3)+1536*x^8+4096*x^7-7168*x^6 )*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp(x)^8,x, algorithm=\
16*x^2*log(3)^4 + 16*(x - 1)*e^x*log(3)^4 - 256*x^2*log(3)^3 + 64*(x^3 + 3 *x^2 + 6*x + 6)*e^(-x)*log(3)^3 - 192*(x^2 + 2*x + 2)*e^(-x)*log(3)^3 + 32 *(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^3 + 32*(4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^3 - 192*(2*x^2 + 2*x + 1)*e^(-2*x)*log(3)^3 - 25 6*(x - 1)*e^x*log(3)^3 + 64*x*log(3)^4 + 16*e^x*log(3)^4 + 1536*x^2*log(3) ^2 - 768*(x^3 + 3*x^2 + 6*x + 6)*e^(-x)*log(3)^2 + 2304*(x^2 + 2*x + 2)*e^ (-x)*log(3)^2 - 384*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^2 - 384*(4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^2 + 2304*(2*x^2 + 2*x + 1)*e ^(-2*x)*log(3)^2 + 32/27*(81*x^5 + 135*x^4 + 180*x^3 + 180*x^2 + 120*x + 4 0)*e^(-3*x)*log(3)^2 - 160/27*(27*x^4 + 36*x^3 + 36*x^2 + 24*x + 8)*e^(-3* x)*log(3)^2 + 3/8*(256*x^6 + 384*x^5 + 480*x^4 + 480*x^3 + 360*x^2 + 180*x + 45)*e^(-4*x)*log(3)^2 + 15/8*(128*x^5 + 160*x^4 + 160*x^3 + 120*x^2 + 6 0*x + 15)*e^(-4*x)*log(3)^2 - 15*(32*x^4 + 32*x^3 + 24*x^2 + 12*x + 3)*e^( -4*x)*log(3)^2 + 1536*(x - 1)*e^x*log(3)^2 - 1024*x*log(3)^3 - 256*e^x*log (3)^3 - 4096*x^2*log(3) + 3072*(x^3 + 3*x^2 + 6*x + 6)*e^(-x)*log(3) - 921 6*(x^2 + 2*x + 2)*e^(-x)*log(3) + 1536*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e ^(-2*x)*log(3) + 1536*(4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3) - 9216*(2* x^2 + 2*x + 1)*e^(-2*x)*log(3) - 256/27*(81*x^5 + 135*x^4 + 180*x^3 + 180* x^2 + 120*x + 40)*e^(-3*x)*log(3) + 1280/27*(27*x^4 + 36*x^3 + 36*x^2 + 24 *x + 8)*e^(-3*x)*log(3) - 3*(256*x^6 + 384*x^5 + 480*x^4 + 480*x^3 + 36...
Leaf count of result is larger than twice the leaf count of optimal. 351 vs. \(2 (22) = 44\).
Time = 0.30 (sec) , antiderivative size = 351, normalized size of antiderivative = 14.62 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 \, x^{9} e^{\left (-7 \, x\right )} + 16 \, x^{2} \log \left (3\right )^{4} - 256 \, x^{2} \log \left (3\right )^{3} + 64 \, x \log \left (3\right )^{4} + 1536 \, x^{2} \log \left (3\right )^{2} - 1024 \, x \log \left (3\right )^{3} - 4096 \, x^{2} \log \left (3\right ) + 6144 \, x \log \left (3\right )^{2} + 4096 \, x^{2} + 64 \, {\left (x^{3} \log \left (3\right )^{3} - 12 \, x^{3} \log \left (3\right )^{2} + 48 \, x^{3} \log \left (3\right ) - 64 \, x^{3}\right )} e^{\left (-x\right )} + 64 \, {\left (x^{4} \log \left (3\right )^{3} - 12 \, x^{4} \log \left (3\right )^{2} + 4 \, x^{3} \log \left (3\right )^{3} + 48 \, x^{4} \log \left (3\right ) - 48 \, x^{3} \log \left (3\right )^{2} - 64 \, x^{4} + 192 \, x^{3} \log \left (3\right ) - 256 \, x^{3}\right )} e^{\left (-2 \, x\right )} + 96 \, {\left (x^{5} \log \left (3\right )^{2} - 8 \, x^{5} \log \left (3\right ) + 16 \, x^{5}\right )} e^{\left (-3 \, x\right )} + 96 \, {\left (x^{6} \log \left (3\right )^{2} - 8 \, x^{6} \log \left (3\right ) + 4 \, x^{5} \log \left (3\right )^{2} + 16 \, x^{6} - 32 \, x^{5} \log \left (3\right ) + 64 \, x^{5}\right )} e^{\left (-4 \, x\right )} + 64 \, {\left (x^{7} \log \left (3\right ) - 4 \, x^{7}\right )} e^{\left (-5 \, x\right )} + 64 \, {\left (x^{8} \log \left (3\right ) - 4 \, x^{8} + 4 \, x^{7} \log \left (3\right ) - 16 \, x^{7}\right )} e^{\left (-6 \, x\right )} + 16 \, {\left (x^{10} + 4 \, x^{9}\right )} e^{\left (-8 \, x\right )} + 16 \, {\left (x \log \left (3\right )^{4} - 16 \, x \log \left (3\right )^{3} + 96 \, x \log \left (3\right )^{2} - 256 \, x \log \left (3\right ) + 256 \, x\right )} e^{x} - 16384 \, x \log \left (3\right ) + 16384 \, x \]
integrate((((16*x+16)*log(3)^4+(-256*x-256)*log(3)^3+(1536*x+1536)*log(3)^ 2+(-4096*x-4096)*log(3)+4096*x+4096)*exp(x)^9+((32*x+64)*log(3)^4+(-512*x- 1024)*log(3)^3+(3072*x+6144)*log(3)^2+(-8192*x-16384)*log(3)+8192*x+16384) *exp(x)^8+((-64*x^3+192*x^2)*log(3)^3+(768*x^3-2304*x^2)*log(3)^2+(-3072*x ^3+9216*x^2)*log(3)+4096*x^3-12288*x^2)*exp(x)^7+((-128*x^4-256*x^3+768*x^ 2)*log(3)^3+(1536*x^4+3072*x^3-9216*x^2)*log(3)^2+(-6144*x^4-12288*x^3+368 64*x^2)*log(3)+8192*x^4+16384*x^3-49152*x^2)*exp(x)^6+((-288*x^5+480*x^4)* log(3)^2+(2304*x^5-3840*x^4)*log(3)-4608*x^5+7680*x^4)*exp(x)^5+((-384*x^6 -960*x^5+1920*x^4)*log(3)^2+(3072*x^6+7680*x^5-15360*x^4)*log(3)-6144*x^6- 15360*x^5+30720*x^4)*exp(x)^4+((-320*x^7+448*x^6)*log(3)+1280*x^7-1792*x^6 )*exp(x)^3+((-384*x^8-1024*x^7+1792*x^6)*log(3)+1536*x^8+4096*x^7-7168*x^6 )*exp(x)^2+(-112*x^9+144*x^8)*exp(x)-128*x^10-352*x^9+576*x^8)/exp(x)^8,x, algorithm=\
16*x^9*e^(-7*x) + 16*x^2*log(3)^4 - 256*x^2*log(3)^3 + 64*x*log(3)^4 + 153 6*x^2*log(3)^2 - 1024*x*log(3)^3 - 4096*x^2*log(3) + 6144*x*log(3)^2 + 409 6*x^2 + 64*(x^3*log(3)^3 - 12*x^3*log(3)^2 + 48*x^3*log(3) - 64*x^3)*e^(-x ) + 64*(x^4*log(3)^3 - 12*x^4*log(3)^2 + 4*x^3*log(3)^3 + 48*x^4*log(3) - 48*x^3*log(3)^2 - 64*x^4 + 192*x^3*log(3) - 256*x^3)*e^(-2*x) + 96*(x^5*lo g(3)^2 - 8*x^5*log(3) + 16*x^5)*e^(-3*x) + 96*(x^6*log(3)^2 - 8*x^6*log(3) + 4*x^5*log(3)^2 + 16*x^6 - 32*x^5*log(3) + 64*x^5)*e^(-4*x) + 64*(x^7*lo g(3) - 4*x^7)*e^(-5*x) + 64*(x^8*log(3) - 4*x^8 + 4*x^7*log(3) - 16*x^7)*e ^(-6*x) + 16*(x^10 + 4*x^9)*e^(-8*x) + 16*(x*log(3)^4 - 16*x*log(3)^3 + 96 *x*log(3)^2 - 256*x*log(3) + 256*x)*e^x - 16384*x*log(3) + 16384*x
Time = 9.02 (sec) , antiderivative size = 183, normalized size of antiderivative = 7.62 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=64\,x\,{\left (\ln \left (3\right )-4\right )}^4+16\,x^2\,{\left (\ln \left (3\right )-4\right )}^4+{\mathrm {e}}^{-8\,x}\,\left (16\,x^{10}+64\,x^9\right )+16\,x^9\,{\mathrm {e}}^{-7\,x}+{\mathrm {e}}^{-6\,x}\,\left (\left (64\,\ln \left (3\right )-256\right )\,x^8+\left (256\,\ln \left (3\right )-1024\right )\,x^7\right )+{\mathrm {e}}^{-2\,x}\,\left (64\,{\left (\ln \left (3\right )-4\right )}^3\,x^4+256\,{\left (\ln \left (3\right )-4\right )}^3\,x^3\right )+{\mathrm {e}}^{-4\,x}\,\left (96\,{\left (\ln \left (3\right )-4\right )}^2\,x^6+384\,{\left (\ln \left (3\right )-4\right )}^2\,x^5\right )+x^7\,{\mathrm {e}}^{-5\,x}\,\left (64\,\ln \left (3\right )-256\right )+64\,x^3\,{\mathrm {e}}^{-x}\,{\left (\ln \left (3\right )-4\right )}^3+96\,x^5\,{\mathrm {e}}^{-3\,x}\,{\left (\ln \left (3\right )-4\right )}^2+16\,x\,{\mathrm {e}}^x\,{\left (\ln \left (3\right )-4\right )}^4 \]
int(exp(-8*x)*(exp(3*x)*(log(3)*(448*x^6 - 320*x^7) - 1792*x^6 + 1280*x^7) + exp(x)*(144*x^8 - 112*x^9) - exp(2*x)*(log(3)*(1024*x^7 - 1792*x^6 + 38 4*x^8) + 7168*x^6 - 4096*x^7 - 1536*x^8) - exp(4*x)*(log(3)^2*(960*x^5 - 1 920*x^4 + 384*x^6) - log(3)*(7680*x^5 - 15360*x^4 + 3072*x^6) - 30720*x^4 + 15360*x^5 + 6144*x^6) - exp(6*x)*(log(3)^3*(256*x^3 - 768*x^2 + 128*x^4) - log(3)^2*(3072*x^3 - 9216*x^2 + 1536*x^4) + log(3)*(12288*x^3 - 36864*x ^2 + 6144*x^4) + 49152*x^2 - 16384*x^3 - 8192*x^4) + 576*x^8 - 352*x^9 - 1 28*x^10 + exp(7*x)*(log(3)*(9216*x^2 - 3072*x^3) - 12288*x^2 + 4096*x^3 + log(3)^3*(192*x^2 - 64*x^3) - log(3)^2*(2304*x^2 - 768*x^3)) - exp(5*x)*(l og(3)*(3840*x^4 - 2304*x^5) - 7680*x^4 + 4608*x^5 - log(3)^2*(480*x^4 - 28 8*x^5)) + exp(9*x)*(4096*x - log(3)*(4096*x + 4096) + log(3)^4*(16*x + 16) - log(3)^3*(256*x + 256) + log(3)^2*(1536*x + 1536) + 4096) + exp(8*x)*(8 192*x - log(3)*(8192*x + 16384) + log(3)^4*(32*x + 64) - log(3)^3*(512*x + 1024) + log(3)^2*(3072*x + 6144) + 16384)),x)
64*x*(log(3) - 4)^4 + 16*x^2*(log(3) - 4)^4 + exp(-8*x)*(64*x^9 + 16*x^10) + 16*x^9*exp(-7*x) + exp(-6*x)*(x^8*(64*log(3) - 256) + x^7*(256*log(3) - 1024)) + exp(-2*x)*(256*x^3*(log(3) - 4)^3 + 64*x^4*(log(3) - 4)^3) + exp (-4*x)*(384*x^5*(log(3) - 4)^2 + 96*x^6*(log(3) - 4)^2) + x^7*exp(-5*x)*(6 4*log(3) - 256) + 64*x^3*exp(-x)*(log(3) - 4)^3 + 96*x^5*exp(-3*x)*(log(3) - 4)^2 + 16*x*exp(x)*(log(3) - 4)^4