Integrand size = 462, antiderivative size = 24 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 x \left (4+e^x+x\right ) \left (-4+e^{-2 x} x^2+\log (3)\right )^4 \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(1259\) vs. \(2(24)=48\).
Time = 93.12 (sec) , antiderivative size = 1259, normalized size of antiderivative = 52.46, number of steps used = 158, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6820, 12, 6874, 2227, 2207, 2225} \[ \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 e^{-8 x} x^{10}+64 e^{-8 x} x^9+16 e^{-7 x} x^9-64 e^{-6 x} (4-\log (3)) x^8-\frac {8}{3} e^{-6 x} (256-66 \log (3)+\log (9)) x^7-\frac {256}{3} e^{-6 x} (4-\log (3)) x^7-64 e^{-5 x} (4-\log (3)) x^7+\frac {8}{3} e^{-6 x} (448-108 \log (3)-\log (81)) x^6-\frac {28}{9} e^{-6 x} (256-66 \log (3)+\log (9)) x^6+96 e^{-4 x} (4-\log (3))^2 x^6-\frac {896}{9} e^{-6 x} (4-\log (3)) x^6+\frac {8}{3} e^{-6 x} (448-108 \log (3)-\log (81)) x^5+12 e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^5-\frac {28}{9} e^{-6 x} (256-66 \log (3)+\log (9)) x^5+144 e^{-4 x} (4-\log (3))^2 x^5+96 e^{-3 x} (4-\log (3))^2 x^5-\frac {896}{9} e^{-6 x} (4-\log (3)) x^5-12 e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^4+\frac {20}{9} e^{-6 x} (448-108 \log (3)-\log (81)) x^4+15 e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^4-\frac {70}{27} e^{-6 x} (256-66 \log (3)+\log (9)) x^4-64 e^{-2 x} (4-\log (3))^3 x^4+180 e^{-4 x} (4-\log (3))^2 x^4-\frac {2240}{27} e^{-6 x} (4-\log (3)) x^4-8 e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x^3-12 e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^3+\frac {40}{27} e^{-6 x} (448-108 \log (3)-\log (81)) x^3+15 e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^3-\frac {140}{81} e^{-6 x} (256-66 \log (3)+\log (9)) x^3-128 e^{-2 x} (4-\log (3))^3 x^3-64 e^{-x} (4-\log (3))^3 x^3+180 e^{-4 x} (4-\log (3))^2 x^3-\frac {4480}{81} e^{-6 x} (4-\log (3)) x^3-12 e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x^2+24 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81)) x^2-9 e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x^2+\frac {20}{27} e^{-6 x} (448-108 \log (3)-\log (81)) x^2+\frac {45}{4} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x^2-\frac {70}{81} e^{-6 x} (256-66 \log (3)+\log (9)) x^2-192 e^{-2 x} (4-\log (3))^3 x^2+135 e^{-4 x} (4-\log (3))^2 x^2-\frac {2240}{81} e^{-6 x} (4-\log (3)) x^2-12 e^{-2 x} (4-\log (3))^2 (64-\log (43046721)) x+24 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81)) x-\frac {9}{2} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81)) x+\frac {20}{81} e^{-6 x} (448-108 \log (3)-\log (81)) x+\frac {45}{8} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9)) x-\frac {70}{243} e^{-6 x} (256-66 \log (3)+\log (9)) x-192 e^{-2 x} (4-\log (3))^3 x+\frac {135}{2} e^{-4 x} (4-\log (3))^2 x-\frac {2240}{243} e^{-6 x} (4-\log (3)) x+\frac {8 (4-\log (3))^3 (-\log (9) x+8 x-\log (81)+16)^2}{8-\log (9)}-6 e^{-2 x} (4-\log (3))^2 (64-\log (43046721))+12 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81))-\frac {9}{8} e^{-4 x} (4-\log (3)) (160-36 \log (3)-\log (81))+\frac {10}{243} e^{-6 x} (448-108 \log (3)-\log (81))+\frac {45}{32} e^{-4 x} (4-\log (3)) (80-22 \log (3)+\log (9))-\frac {35}{729} e^{-6 x} (256-66 \log (3)+\log (9))-16 e^x (4-\log (3))^4+16 e^x (x+1) (4-\log (3))^4-96 e^{-2 x} (4-\log (3))^3+\frac {135}{8} e^{-4 x} (4-\log (3))^2-\frac {1120}{729} e^{-6 x} (4-\log (3)) \]
[In]
[Out]
Rule 12
Rule 2207
Rule 2225
Rule 2227
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int 16 e^{-8 x} \left (x^2+e^{2 x} (-4+\log (3))\right )^3 \left (-e^x x^2 (-9+7 x)-2 x^2 \left (-18+11 x+4 x^2\right )+e^{3 x} (1+x) (-4+\log (3))+e^{2 x} (-16+x (-8+\log (9))+\log (81))\right ) \, dx \\ & = 16 \int e^{-8 x} \left (x^2+e^{2 x} (-4+\log (3))\right )^3 \left (-e^x x^2 (-9+7 x)-2 x^2 \left (-18+11 x+4 x^2\right )+e^{3 x} (1+x) (-4+\log (3))+e^{2 x} (-16+x (-8+\log (9))+\log (81))\right ) \, dx \\ & = 16 \int \left (-e^{-7 x} x^8 (-9+7 x)-2 e^{-8 x} x^8 \left (-18+11 x+4 x^2\right )-4 e^{-5 x} x^6 (-7+5 x) (-4+\log (3))-6 e^{-3 x} x^4 (-5+3 x) (-4+\log (3))^2-4 e^{-x} (-3+x) x^2 (-4+\log (3))^3+e^x (1+x) (-4+\log (3))^4+3 e^{-4 x} x^4 (4-\log (3)) \left (160-8 x^2 (4-\log (3))-36 \log (3)-x (80-22 \log (3)+\log (9))-\log (81)\right )+(-4+\log (3))^3 (-16-8 x+x \log (9)+\log (81))+e^{-6 x} x^6 \left (-448+24 x^2 (4-\log (3))+108 \log (3)+x (256-66 \log (3)+\log (9))+\log (81)\right )+e^{-2 x} x^2 (4-\log (3))^2 \left (8 x^2 (4-\log (3))-3 (64-12 \log (3)-\log (81))+x (64-\log (43046721))\right )\right ) \, dx \\ & = \frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-16 \int e^{-7 x} x^8 (-9+7 x) \, dx+16 \int e^{-6 x} x^6 \left (-448+24 x^2 (4-\log (3))+108 \log (3)+x (256-66 \log (3)+\log (9))+\log (81)\right ) \, dx-32 \int e^{-8 x} x^8 \left (-18+11 x+4 x^2\right ) \, dx+(48 (4-\log (3))) \int e^{-4 x} x^4 \left (160-8 x^2 (4-\log (3))-36 \log (3)-x (80-22 \log (3)+\log (9))-\log (81)\right ) \, dx+(64 (4-\log (3))) \int e^{-5 x} x^6 (-7+5 x) \, dx+\left (16 (4-\log (3))^2\right ) \int e^{-2 x} x^2 \left (8 x^2 (4-\log (3))-3 (64-12 \log (3)-\log (81))+x (64-\log (43046721))\right ) \, dx-\left (96 (4-\log (3))^2\right ) \int e^{-3 x} x^4 (-5+3 x) \, dx+\left (64 (4-\log (3))^3\right ) \int e^{-x} (-3+x) x^2 \, dx+\left (16 (4-\log (3))^4\right ) \int e^x (1+x) \, dx \\ & = 16 e^x (1+x) (4-\log (3))^4+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-16 \int \left (-9 e^{-7 x} x^8+7 e^{-7 x} x^9\right ) \, dx+16 \int \left (-24 e^{-6 x} x^8 (-4+\log (3))-e^{-6 x} x^7 (-256+66 \log (3)-\log (9))+e^{-6 x} x^6 (-448+108 \log (3)+\log (81))\right ) \, dx-32 \int \left (-18 e^{-8 x} x^8+11 e^{-8 x} x^9+4 e^{-8 x} x^{10}\right ) \, dx+(48 (4-\log (3))) \int \left (8 e^{-4 x} x^6 (-4+\log (3))+e^{-4 x} x^5 (-80+22 \log (3)-\log (9))-e^{-4 x} x^4 (-160+36 \log (3)+\log (81))\right ) \, dx+(64 (4-\log (3))) \int \left (-7 e^{-5 x} x^6+5 e^{-5 x} x^7\right ) \, dx+\left (16 (4-\log (3))^2\right ) \int \left (-8 e^{-2 x} x^4 (-4+\log (3))+3 e^{-2 x} x^2 (-64+12 \log (3)+\log (81))-e^{-2 x} x^3 (-64+\log (43046721))\right ) \, dx-\left (96 (4-\log (3))^2\right ) \int \left (-5 e^{-3 x} x^4+3 e^{-3 x} x^5\right ) \, dx+\left (64 (4-\log (3))^3\right ) \int \left (-3 e^{-x} x^2+e^{-x} x^3\right ) \, dx-\left (16 (4-\log (3))^4\right ) \int e^x \, dx \\ & = -16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-112 \int e^{-7 x} x^9 \, dx-128 \int e^{-8 x} x^{10} \, dx+144 \int e^{-7 x} x^8 \, dx-352 \int e^{-8 x} x^9 \, dx+576 \int e^{-8 x} x^8 \, dx+(320 (4-\log (3))) \int e^{-5 x} x^7 \, dx+(384 (4-\log (3))) \int e^{-6 x} x^8 \, dx-(448 (4-\log (3))) \int e^{-5 x} x^6 \, dx-\left (288 (4-\log (3))^2\right ) \int e^{-3 x} x^5 \, dx-\left (384 (4-\log (3))^2\right ) \int e^{-4 x} x^6 \, dx+\left (480 (4-\log (3))^2\right ) \int e^{-3 x} x^4 \, dx+\left (64 (4-\log (3))^3\right ) \int e^{-x} x^3 \, dx+\left (128 (4-\log (3))^3\right ) \int e^{-2 x} x^4 \, dx-\left (192 (4-\log (3))^3\right ) \int e^{-x} x^2 \, dx+(16 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^7 \, dx-(48 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x^5 \, dx-(16 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^6 \, dx+(48 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} x^4 \, dx-\left (48 (4-\log (3))^2 (64-12 \log (3)-\log (81))\right ) \int e^{-2 x} x^2 \, dx+\left (16 (4-\log (3))^2 (64-\log (43046721))\right ) \int e^{-2 x} x^3 \, dx \\ & = -72 e^{-8 x} x^8-\frac {144}{7} e^{-7 x} x^8+44 e^{-8 x} x^9+16 e^{-7 x} x^9+16 e^{-8 x} x^{10}+\frac {448}{5} e^{-5 x} x^6 (4-\log (3))-64 e^{-5 x} x^7 (4-\log (3))-64 e^{-6 x} x^8 (4-\log (3))-160 e^{-3 x} x^4 (4-\log (3))^2+96 e^{-3 x} x^5 (4-\log (3))^2+96 e^{-4 x} x^6 (4-\log (3))^2+192 e^{-x} x^2 (4-\log (3))^3-64 e^{-x} x^3 (4-\log (3))^3-64 e^{-2 x} x^4 (4-\log (3))^3-16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4-\frac {8}{3} e^{-6 x} x^7 (256-66 \log (3)+\log (9))+12 e^{-4 x} x^5 (4-\log (3)) (80-22 \log (3)+\log (9))+\frac {8}{3} e^{-6 x} x^6 (448-108 \log (3)-\log (81))-12 e^{-4 x} x^4 (4-\log (3)) (160-36 \log (3)-\log (81))+24 e^{-2 x} x^2 (4-\log (3))^2 (64-12 \log (3)-\log (81))+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-8 e^{-2 x} x^3 (4-\log (3))^2 (64-\log (43046721))-144 \int e^{-7 x} x^8 \, dx-160 \int e^{-8 x} x^9 \, dx+\frac {1152}{7} \int e^{-7 x} x^7 \, dx-396 \int e^{-8 x} x^8 \, dx+576 \int e^{-8 x} x^7 \, dx+(448 (4-\log (3))) \int e^{-5 x} x^6 \, dx+(512 (4-\log (3))) \int e^{-6 x} x^7 \, dx-\frac {1}{5} (2688 (4-\log (3))) \int e^{-5 x} x^5 \, dx-\left (480 (4-\log (3))^2\right ) \int e^{-3 x} x^4 \, dx-\left (576 (4-\log (3))^2\right ) \int e^{-4 x} x^5 \, dx+\left (640 (4-\log (3))^2\right ) \int e^{-3 x} x^3 \, dx+\left (192 (4-\log (3))^3\right ) \int e^{-x} x^2 \, dx+\left (256 (4-\log (3))^3\right ) \int e^{-2 x} x^3 \, dx-\left (384 (4-\log (3))^3\right ) \int e^{-x} x \, dx+\frac {1}{3} (56 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^6 \, dx-(60 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x^4 \, dx-(16 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^5 \, dx+(48 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} x^3 \, dx-\left (48 (4-\log (3))^2 (64-12 \log (3)-\log (81))\right ) \int e^{-2 x} x \, dx+\left (24 (4-\log (3))^2 (64-\log (43046721))\right ) \int e^{-2 x} x^2 \, dx \\ & = -72 e^{-8 x} x^7-\frac {1152}{49} e^{-7 x} x^7-\frac {45}{2} e^{-8 x} x^8+64 e^{-8 x} x^9+16 e^{-7 x} x^9+16 e^{-8 x} x^{10}+\frac {2688}{25} e^{-5 x} x^5 (4-\log (3))-\frac {256}{3} e^{-6 x} x^7 (4-\log (3))-64 e^{-5 x} x^7 (4-\log (3))-64 e^{-6 x} x^8 (4-\log (3))-\frac {640}{3} e^{-3 x} x^3 (4-\log (3))^2+144 e^{-4 x} x^5 (4-\log (3))^2+96 e^{-3 x} x^5 (4-\log (3))^2+96 e^{-4 x} x^6 (4-\log (3))^2+384 e^{-x} x (4-\log (3))^3-128 e^{-2 x} x^3 (4-\log (3))^3-64 e^{-x} x^3 (4-\log (3))^3-64 e^{-2 x} x^4 (4-\log (3))^3-16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4-\frac {28}{9} e^{-6 x} x^6 (256-66 \log (3)+\log (9))-\frac {8}{3} e^{-6 x} x^7 (256-66 \log (3)+\log (9))+15 e^{-4 x} x^4 (4-\log (3)) (80-22 \log (3)+\log (9))+12 e^{-4 x} x^5 (4-\log (3)) (80-22 \log (3)+\log (9))+\frac {8}{3} e^{-6 x} x^5 (448-108 \log (3)-\log (81))+\frac {8}{3} e^{-6 x} x^6 (448-108 \log (3)-\log (81))-12 e^{-4 x} x^3 (4-\log (3)) (160-36 \log (3)-\log (81))-12 e^{-4 x} x^4 (4-\log (3)) (160-36 \log (3)-\log (81))+24 e^{-2 x} x (4-\log (3))^2 (64-12 \log (3)-\log (81))+24 e^{-2 x} x^2 (4-\log (3))^2 (64-12 \log (3)-\log (81))+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-12 e^{-2 x} x^2 (4-\log (3))^2 (64-\log (43046721))-8 e^{-2 x} x^3 (4-\log (3))^2 (64-\log (43046721))+\frac {1152}{7} \int e^{-7 x} x^6 \, dx-\frac {1152}{7} \int e^{-7 x} x^7 \, dx-180 \int e^{-8 x} x^8 \, dx-396 \int e^{-8 x} x^7 \, dx+504 \int e^{-8 x} x^6 \, dx-\frac {1}{5} (2688 (4-\log (3))) \int e^{-5 x} x^4 \, dx+\frac {1}{5} (2688 (4-\log (3))) \int e^{-5 x} x^5 \, dx+\frac {1}{3} (1792 (4-\log (3))) \int e^{-6 x} x^6 \, dx+\left (640 (4-\log (3))^2\right ) \int e^{-3 x} x^2 \, dx-\left (640 (4-\log (3))^2\right ) \int e^{-3 x} x^3 \, dx-\left (720 (4-\log (3))^2\right ) \int e^{-4 x} x^4 \, dx-\left (384 (4-\log (3))^3\right ) \int e^{-x} \, dx+\left (384 (4-\log (3))^3\right ) \int e^{-x} x \, dx+\left (384 (4-\log (3))^3\right ) \int e^{-2 x} x^2 \, dx+\frac {1}{3} (56 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^5 \, dx-(60 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x^3 \, dx-\frac {1}{3} (40 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^4 \, dx+(36 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} x^2 \, dx-\left (24 (4-\log (3))^2 (64-12 \log (3)-\log (81))\right ) \int e^{-2 x} \, dx+\left (24 (4-\log (3))^2 (64-\log (43046721))\right ) \int e^{-2 x} x \, dx \\ & = -63 e^{-8 x} x^6-\frac {1152}{49} e^{-7 x} x^6-\frac {45}{2} e^{-8 x} x^7+64 e^{-8 x} x^9+16 e^{-7 x} x^9+16 e^{-8 x} x^{10}+\frac {2688}{25} e^{-5 x} x^4 (4-\log (3))-\frac {896}{9} e^{-6 x} x^6 (4-\log (3))-\frac {256}{3} e^{-6 x} x^7 (4-\log (3))-64 e^{-5 x} x^7 (4-\log (3))-64 e^{-6 x} x^8 (4-\log (3))-\frac {640}{3} e^{-3 x} x^2 (4-\log (3))^2+180 e^{-4 x} x^4 (4-\log (3))^2+144 e^{-4 x} x^5 (4-\log (3))^2+96 e^{-3 x} x^5 (4-\log (3))^2+96 e^{-4 x} x^6 (4-\log (3))^2+384 e^{-x} (4-\log (3))^3-192 e^{-2 x} x^2 (4-\log (3))^3-128 e^{-2 x} x^3 (4-\log (3))^3-64 e^{-x} x^3 (4-\log (3))^3-64 e^{-2 x} x^4 (4-\log (3))^3-16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4-\frac {28}{9} e^{-6 x} x^5 (256-66 \log (3)+\log (9))-\frac {28}{9} e^{-6 x} x^6 (256-66 \log (3)+\log (9))-\frac {8}{3} e^{-6 x} x^7 (256-66 \log (3)+\log (9))+15 e^{-4 x} x^3 (4-\log (3)) (80-22 \log (3)+\log (9))+15 e^{-4 x} x^4 (4-\log (3)) (80-22 \log (3)+\log (9))+12 e^{-4 x} x^5 (4-\log (3)) (80-22 \log (3)+\log (9))+\frac {20}{9} e^{-6 x} x^4 (448-108 \log (3)-\log (81))+\frac {8}{3} e^{-6 x} x^5 (448-108 \log (3)-\log (81))+\frac {8}{3} e^{-6 x} x^6 (448-108 \log (3)-\log (81))-9 e^{-4 x} x^2 (4-\log (3)) (160-36 \log (3)-\log (81))-12 e^{-4 x} x^3 (4-\log (3)) (160-36 \log (3)-\log (81))-12 e^{-4 x} x^4 (4-\log (3)) (160-36 \log (3)-\log (81))+12 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81))+24 e^{-2 x} x (4-\log (3))^2 (64-12 \log (3)-\log (81))+24 e^{-2 x} x^2 (4-\log (3))^2 (64-12 \log (3)-\log (81))+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-12 e^{-2 x} x (4-\log (3))^2 (64-\log (43046721))-12 e^{-2 x} x^2 (4-\log (3))^2 (64-\log (43046721))-8 e^{-2 x} x^3 (4-\log (3))^2 (64-\log (43046721))+\frac {6912}{49} \int e^{-7 x} x^5 \, dx-\frac {1152}{7} \int e^{-7 x} x^6 \, dx-180 \int e^{-8 x} x^7 \, dx-\frac {693}{2} \int e^{-8 x} x^6 \, dx+378 \int e^{-8 x} x^5 \, dx-\frac {1}{25} (10752 (4-\log (3))) \int e^{-5 x} x^3 \, dx+\frac {1}{5} (2688 (4-\log (3))) \int e^{-5 x} x^4 \, dx+\frac {1}{3} (1792 (4-\log (3))) \int e^{-6 x} x^5 \, dx+\frac {1}{3} \left (1280 (4-\log (3))^2\right ) \int e^{-3 x} x \, dx-\left (640 (4-\log (3))^2\right ) \int e^{-3 x} x^2 \, dx-\left (720 (4-\log (3))^2\right ) \int e^{-4 x} x^3 \, dx+\left (384 (4-\log (3))^3\right ) \int e^{-x} \, dx+\left (384 (4-\log (3))^3\right ) \int e^{-2 x} x \, dx+\frac {1}{9} (140 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^4 \, dx-(45 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x^2 \, dx-\frac {1}{9} (80 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^3 \, dx+(18 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} x \, dx+\left (12 (4-\log (3))^2 (64-\log (43046721))\right ) \int e^{-2 x} \, dx \\ & = -\frac {189}{4} e^{-8 x} x^5-\frac {6912}{343} e^{-7 x} x^5-\frac {315}{16} e^{-8 x} x^6+64 e^{-8 x} x^9+16 e^{-7 x} x^9+16 e^{-8 x} x^{10}+\frac {10752}{125} e^{-5 x} x^3 (4-\log (3))-\frac {896}{9} e^{-6 x} x^5 (4-\log (3))-\frac {896}{9} e^{-6 x} x^6 (4-\log (3))-\frac {256}{3} e^{-6 x} x^7 (4-\log (3))-64 e^{-5 x} x^7 (4-\log (3))-64 e^{-6 x} x^8 (4-\log (3))-\frac {1280}{9} e^{-3 x} x (4-\log (3))^2+180 e^{-4 x} x^3 (4-\log (3))^2+180 e^{-4 x} x^4 (4-\log (3))^2+144 e^{-4 x} x^5 (4-\log (3))^2+96 e^{-3 x} x^5 (4-\log (3))^2+96 e^{-4 x} x^6 (4-\log (3))^2-192 e^{-2 x} x (4-\log (3))^3-192 e^{-2 x} x^2 (4-\log (3))^3-128 e^{-2 x} x^3 (4-\log (3))^3-64 e^{-x} x^3 (4-\log (3))^3-64 e^{-2 x} x^4 (4-\log (3))^3-16 e^x (4-\log (3))^4+16 e^x (1+x) (4-\log (3))^4-\frac {70}{27} e^{-6 x} x^4 (256-66 \log (3)+\log (9))-\frac {28}{9} e^{-6 x} x^5 (256-66 \log (3)+\log (9))-\frac {28}{9} e^{-6 x} x^6 (256-66 \log (3)+\log (9))-\frac {8}{3} e^{-6 x} x^7 (256-66 \log (3)+\log (9))+\frac {45}{4} e^{-4 x} x^2 (4-\log (3)) (80-22 \log (3)+\log (9))+15 e^{-4 x} x^3 (4-\log (3)) (80-22 \log (3)+\log (9))+15 e^{-4 x} x^4 (4-\log (3)) (80-22 \log (3)+\log (9))+12 e^{-4 x} x^5 (4-\log (3)) (80-22 \log (3)+\log (9))+\frac {40}{27} e^{-6 x} x^3 (448-108 \log (3)-\log (81))+\frac {20}{9} e^{-6 x} x^4 (448-108 \log (3)-\log (81))+\frac {8}{3} e^{-6 x} x^5 (448-108 \log (3)-\log (81))+\frac {8}{3} e^{-6 x} x^6 (448-108 \log (3)-\log (81))-\frac {9}{2} e^{-4 x} x (4-\log (3)) (160-36 \log (3)-\log (81))-9 e^{-4 x} x^2 (4-\log (3)) (160-36 \log (3)-\log (81))-12 e^{-4 x} x^3 (4-\log (3)) (160-36 \log (3)-\log (81))-12 e^{-4 x} x^4 (4-\log (3)) (160-36 \log (3)-\log (81))+12 e^{-2 x} (4-\log (3))^2 (64-12 \log (3)-\log (81))+24 e^{-2 x} x (4-\log (3))^2 (64-12 \log (3)-\log (81))+24 e^{-2 x} x^2 (4-\log (3))^2 (64-12 \log (3)-\log (81))+\frac {8 (4-\log (3))^3 (16+8 x-x \log (9)-\log (81))^2}{8-\log (9)}-6 e^{-2 x} (4-\log (3))^2 (64-\log (43046721))-12 e^{-2 x} x (4-\log (3))^2 (64-\log (43046721))-12 e^{-2 x} x^2 (4-\log (3))^2 (64-\log (43046721))-8 e^{-2 x} x^3 (4-\log (3))^2 (64-\log (43046721))+\frac {34560}{343} \int e^{-7 x} x^4 \, dx-\frac {6912}{49} \int e^{-7 x} x^5 \, dx-\frac {315}{2} \int e^{-8 x} x^6 \, dx+\frac {945}{4} \int e^{-8 x} x^4 \, dx-\frac {2079}{8} \int e^{-8 x} x^5 \, dx-\frac {1}{125} (32256 (4-\log (3))) \int e^{-5 x} x^2 \, dx+\frac {1}{25} (10752 (4-\log (3))) \int e^{-5 x} x^3 \, dx+\frac {1}{9} (4480 (4-\log (3))) \int e^{-6 x} x^4 \, dx+\frac {1}{9} \left (1280 (4-\log (3))^2\right ) \int e^{-3 x} \, dx-\frac {1}{3} \left (1280 (4-\log (3))^2\right ) \int e^{-3 x} x \, dx-\left (540 (4-\log (3))^2\right ) \int e^{-4 x} x^2 \, dx+\left (192 (4-\log (3))^3\right ) \int e^{-2 x} \, dx+\frac {1}{27} (280 (256-66 \log (3)+\log (9))) \int e^{-6 x} x^3 \, dx-\frac {1}{2} (45 (4-\log (3)) (80-22 \log (3)+\log (9))) \int e^{-4 x} x \, dx-\frac {1}{9} (40 (448-108 \log (3)-\log (81))) \int e^{-6 x} x^2 \, dx+\frac {1}{2} (9 (4-\log (3)) (160-36 \log (3)-\log (81))) \int e^{-4 x} \, dx \\ & = \text {Too large to display} \\ \end{align*}
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 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=16 \left (e^{-7 x} x^9+e^{-8 x} x^9 (4+x)+4 e^{-5 x} x^7 (-4+\log (3))+6 e^{-3 x} x^5 (-4+\log (3))^2+4 e^{-x} x^3 (-4+\log (3))^3+e^x x (-4+\log (3))^4+\frac {1}{2} e^{-2 x} x^3 (-4+\log (3))^2 (-128+8 x (-4+\log (3))+38 \log (3)-3 \log (9))+\frac {3}{4} e^{-4 x} x^5 (-4+\log (3)) (-128+8 x (-4+\log (3))+34 \log (3)-\log (9))+\frac {1}{6} e^{-6 x} x^7 (-384+24 x (-4+\log (3))+98 \log (3)-\log (9))+\frac {1}{2} x^2 (-4+\log (3))^3 (-8+\log (9))+x (-4+\log (3))^3 (-16+\log (81))\right ) \]
[In]
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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 | \(\text {Expression too large to display}\) | \(1687\) |
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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 )} \]
[In]
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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} \]
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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 \[ \int e^{-8 x} \left (576 x^8-352 x^9-128 x^{10}+e^x \left (144 x^8-112 x^9\right )+e^{3 x} \left (-1792 x^6+1280 x^7+\left (448 x^6-320 x^7\right ) \log (3)\right )+e^{2 x} \left (-7168 x^6+4096 x^7+1536 x^8+\left (1792 x^6-1024 x^7-384 x^8\right ) \log (3)\right )+e^{5 x} \left (7680 x^4-4608 x^5+\left (-3840 x^4+2304 x^5\right ) \log (3)+\left (480 x^4-288 x^5\right ) \log ^2(3)\right )+e^{4 x} \left (30720 x^4-15360 x^5-6144 x^6+\left (-15360 x^4+7680 x^5+3072 x^6\right ) \log (3)+\left (1920 x^4-960 x^5-384 x^6\right ) \log ^2(3)\right )+e^{7 x} \left (-12288 x^2+4096 x^3+\left (9216 x^2-3072 x^3\right ) \log (3)+\left (-2304 x^2+768 x^3\right ) \log ^2(3)+\left (192 x^2-64 x^3\right ) \log ^3(3)\right )+e^{6 x} \left (-49152 x^2+16384 x^3+8192 x^4+\left (36864 x^2-12288 x^3-6144 x^4\right ) \log (3)+\left (-9216 x^2+3072 x^3+1536 x^4\right ) \log ^2(3)+\left (768 x^2-256 x^3-128 x^4\right ) \log ^3(3)\right )+e^{9 x} \left (4096+4096 x+(-4096-4096 x) \log (3)+(1536+1536 x) \log ^2(3)+(-256-256 x) \log ^3(3)+(16+16 x) \log ^4(3)\right )+e^{8 x} \left (16384+8192 x+(-16384-8192 x) \log (3)+(6144+3072 x) \log ^2(3)+(-1024-512 x) \log ^3(3)+(64+32 x) \log ^4(3)\right )\right ) \, dx=\text {Too large to display} \]
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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 \]
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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 \]
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