3.51.0 ∫ e−2x(1024x3−1152x4+352x5−32x6+e2x+2 log2(4)(−8+2x)+e2x(−168+146x−42x2+4x3)+(−1536x2+2048x3− 672x4+64x5) log(3)+(512x−896x2+320x3−32x4) log2(3)+ex(−768x+1344x2−672x3+128x4−8x5+(384−1024x+584x2− 120x3 +8x4) log(3))+elog2(4)(e2x(−80+44x−6x2)+ex(−256x+320x2 −96x3 +8x4 +(128−256x+88x2 −8x3) log(3)))) dx [5078]

Integrand size = 230, antiderivative size = 35 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=(4-x)^2 \left (-3-e^{\log ^2(4)}+x-4 e^{-x} x (-x+\log (3))\right )^2 \]

Rubi [B] (veriﬁed)

Leaf count is larger than twice the leaf count of optimal. \(664\) vs. \(2(35)=70\).

Time = 13.08 (sec) , antiderivative size = 664, normalized size of antiderivative = 18.97, number of steps used = 104, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6874, 2207, 2225, 2227} \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=16 e^{-2 x} x^6-128 e^{-2 x} x^5+8 e^{-x} x^5-32 e^{-2 x} x^5 \log (3)+256 e^{-2 x} x^4+40 e^{-x} x^4+x^4-8 x^4 e^{\log ^2(4)-x}+16 e^{-2 x} x^4 \log ^2(3)-8 e^{-x} x^4 (16+\log (3))+256 e^{-2 x} x^4 \log (3)+160 e^{-x} x^3-14 x^3-32 x^3 e^{\log ^2(4)-x}+8 x^3 (12+\log (3)) e^{\log ^2(4)-x}-128 e^{-2 x} x^3 \log ^2(3)-2 x^3 e^{\log ^2(4)}+24 e^{-x} x^3 (28+\log (243))-32 e^{-x} x^3 (16+\log (3))-512 e^{-2 x} x^3 \log (3)+480 e^{-x} x^2+73 x^2-96 x^2 e^{\log ^2(4)-x}-8 x^2 (40+11 \log (3)) e^{\log ^2(4)-x}+24 x^2 (12+\log (3)) e^{\log ^2(4)-x}+256 e^{-2 x} x^2 \log ^2(3)+22 x^2 e^{\log ^2(4)}+72 e^{-x} x^2 (28+\log (243))-8 e^{-x} x^2 (168+73 \log (3))-96 e^{-x} x^2 (16+\log (3))+960 e^{-x} x-168 x+960 e^{-x}-192 x e^{\log ^2(4)-x}-16 x (40+11 \log (3)) e^{\log ^2(4)-x}+48 x (12+\log (3)) e^{\log ^2(4)-x}+256 x (1+\log (3)) e^{\log ^2(4)-x}-80 x e^{\log ^2(4)}-192 e^{\log ^2(4)-x}+(4-x)^2 e^{2 \log ^2(4)}-16 (40+11 \log (3)) e^{\log ^2(4)-x}+48 (12+\log (3)) e^{\log ^2(4)-x}+256 (1+\log (3)) e^{\log ^2(4)-x}-128 \log (3) e^{\log ^2(4)-x}+144 e^{-x} x (28+\log (243))+256 e^{-x} x (3+\log (81))-16 e^{-x} x (168+73 \log (3))-192 e^{-x} x (16+\log (3))+144 e^{-x} (28+\log (243))+256 e^{-x} (3+\log (81))-16 e^{-x} (168+73 \log (3))-192 e^{-x} (16+\log (3))-384 e^{-x} \log (3) \]

Rubi steps \begin{align*} \text {integral}& = \int \left (2 e^{2 \log ^2(4)} (-4+x)+1024 e^{-2 x} x^3-1152 e^{-2 x} x^4+352 e^{-2 x} x^5-32 e^{-2 x} x^6+2 \left (-84+73 x-21 x^2+2 x^3\right )+32 e^{-2 x} x^2 \left (-48+64 x-21 x^2+2 x^3\right ) \log (3)-32 e^{-2 x} x \left (-16+28 x-10 x^2+x^3\right ) \log ^2(3)+2 e^{-x+\log ^2(4)} (4-x) \left (-10 e^x+3 e^x x-4 x^3+32 x^2 \left (1+\frac {\log (3)}{8}\right )-32 x \left (1+\frac {7 \log (3)}{8}\right )+16 \log (3)\right )+8 e^{-x} (4-x) \left (x^4+12 \log (3)-x^3 (12+\log (3))+x^2 (36+11 \log (3))-x (24+29 \log (3))\right )\right ) \, dx \\ & = e^{2 \log ^2(4)} (4-x)^2+2 \int \left (-84+73 x-21 x^2+2 x^3\right ) \, dx+2 \int e^{-x+\log ^2(4)} (4-x) \left (-10 e^x+3 e^x x-4 x^3+32 x^2 \left (1+\frac {\log (3)}{8}\right )-32 x \left (1+\frac {7 \log (3)}{8}\right )+16 \log (3)\right ) \, dx+8 \int e^{-x} (4-x) \left (x^4+12 \log (3)-x^3 (12+\log (3))+x^2 (36+11 \log (3))-x (24+29 \log (3))\right ) \, dx-32 \int e^{-2 x} x^6 \, dx+352 \int e^{-2 x} x^5 \, dx+1024 \int e^{-2 x} x^3 \, dx-1152 \int e^{-2 x} x^4 \, dx+(32 \log (3)) \int e^{-2 x} x^2 \left (-48+64 x-21 x^2+2 x^3\right ) \, dx-\left (32 \log ^2(3)\right ) \int e^{-2 x} x \left (-16+28 x-10 x^2+x^3\right ) \, dx \\ & = e^{2 \log ^2(4)} (4-x)^2-168 x+73 x^2-14 x^3-512 e^{-2 x} x^3+x^4+576 e^{-2 x} x^4-176 e^{-2 x} x^5+16 e^{-2 x} x^6+2 \int \left (-e^{\log ^2(4)} \left (40-22 x+3 x^2\right )+4 e^{-x+\log ^2(4)} (4-x) \left (-x^3+4 \log (3)+x^2 (8+\log (3))-x (8+7 \log (3))\right )\right ) \, dx+8 \int \left (-e^{-x} x^5+48 e^{-x} \log (3)+e^{-x} x^4 (16+\log (3))+e^{-x} x^2 (168+73 \log (3))-32 e^{-x} x (3+\log (81))-3 e^{-x} x^3 (28+\log (243))\right ) \, dx-96 \int e^{-2 x} x^5 \, dx+880 \int e^{-2 x} x^4 \, dx+1536 \int e^{-2 x} x^2 \, dx-2304 \int e^{-2 x} x^3 \, dx+(32 \log (3)) \int \left (-48 e^{-2 x} x^2+64 e^{-2 x} x^3-21 e^{-2 x} x^4+2 e^{-2 x} x^5\right ) \, dx-\left (32 \log ^2(3)\right ) \int \left (-16 e^{-2 x} x+28 e^{-2 x} x^2-10 e^{-2 x} x^3+e^{-2 x} x^4\right ) \, dx \\ & = e^{2 \log ^2(4)} (4-x)^2-168 x+73 x^2-768 e^{-2 x} x^2-14 x^3+640 e^{-2 x} x^3+x^4+136 e^{-2 x} x^4-128 e^{-2 x} x^5+16 e^{-2 x} x^6-8 \int e^{-x} x^5 \, dx+8 \int e^{-x+\log ^2(4)} (4-x) \left (-x^3+4 \log (3)+x^2 (8+\log (3))-x (8+7 \log (3))\right ) \, dx-240 \int e^{-2 x} x^4 \, dx+1536 \int e^{-2 x} x \, dx+1760 \int e^{-2 x} x^3 \, dx-3456 \int e^{-2 x} x^2 \, dx-\left (2 e^{\log ^2(4)}\right ) \int \left (40-22 x+3 x^2\right ) \, dx+(64 \log (3)) \int e^{-2 x} x^5 \, dx+(384 \log (3)) \int e^{-x} \, dx-(672 \log (3)) \int e^{-2 x} x^4 \, dx-(1536 \log (3)) \int e^{-2 x} x^2 \, dx+(2048 \log (3)) \int e^{-2 x} x^3 \, dx-\left (32 \log ^2(3)\right ) \int e^{-2 x} x^4 \, dx+\left (320 \log ^2(3)\right ) \int e^{-2 x} x^3 \, dx+\left (512 \log ^2(3)\right ) \int e^{-2 x} x \, dx-\left (896 \log ^2(3)\right ) \int e^{-2 x} x^2 \, dx+(8 (16+\log (3))) \int e^{-x} x^4 \, dx+(8 (168+73 \log (3))) \int e^{-x} x^2 \, dx-(256 (3+\log (81))) \int e^{-x} x \, dx-(24 (28+\log (243))) \int e^{-x} x^3 \, dx \\ & = e^{2 \log ^2(4)} (4-x)^2-168 x-768 e^{-2 x} x-80 e^{\log ^2(4)} x+73 x^2+960 e^{-2 x} x^2+22 e^{\log ^2(4)} x^2-14 x^3-240 e^{-2 x} x^3-2 e^{\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6-384 e^{-x} \log (3)+768 e^{-2 x} x^2 \log (3)-1024 e^{-2 x} x^3 \log (3)+336 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)-256 e^{-2 x} x \log ^2(3)+448 e^{-2 x} x^2 \log ^2(3)-160 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)-8 e^{-x} x^4 (16+\log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} x (3+\log (81))+24 e^{-x} x^3 (28+\log (243))+8 \int \left (e^{-x+\log ^2(4)} x^4+16 e^{-x+\log ^2(4)} \log (3)-32 e^{-x+\log ^2(4)} x (1+\log (3))-e^{-x+\log ^2(4)} x^3 (12+\log (3))+e^{-x+\log ^2(4)} x^2 (40+11 \log (3))\right ) \, dx-40 \int e^{-x} x^4 \, dx-480 \int e^{-2 x} x^3 \, dx+768 \int e^{-2 x} \, dx+2640 \int e^{-2 x} x^2 \, dx-3456 \int e^{-2 x} x \, dx+(160 \log (3)) \int e^{-2 x} x^4 \, dx-(1344 \log (3)) \int e^{-2 x} x^3 \, dx-(1536 \log (3)) \int e^{-2 x} x \, dx+(3072 \log (3)) \int e^{-2 x} x^2 \, dx-\left (64 \log ^2(3)\right ) \int e^{-2 x} x^3 \, dx+\left (256 \log ^2(3)\right ) \int e^{-2 x} \, dx+\left (480 \log ^2(3)\right ) \int e^{-2 x} x^2 \, dx-\left (896 \log ^2(3)\right ) \int e^{-2 x} x \, dx+(32 (16+\log (3))) \int e^{-x} x^3 \, dx+(16 (168+73 \log (3))) \int e^{-x} x \, dx-(256 (3+\log (81))) \int e^{-x} \, dx-(72 (28+\log (243))) \int e^{-x} x^2 \, dx \\ & = -384 e^{-2 x}+e^{2 \log ^2(4)} (4-x)^2-168 x+960 e^{-2 x} x-80 e^{\log ^2(4)} x+73 x^2-360 e^{-2 x} x^2+22 e^{\log ^2(4)} x^2-14 x^3-2 e^{\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4+40 e^{-x} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6-384 e^{-x} \log (3)+768 e^{-2 x} x \log (3)-768 e^{-2 x} x^2 \log (3)-352 e^{-2 x} x^3 \log (3)+256 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)-128 e^{-2 x} \log ^2(3)+192 e^{-2 x} x \log ^2(3)+208 e^{-2 x} x^2 \log ^2(3)-128 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)-32 e^{-x} x^3 (16+\log (3))-8 e^{-x} x^4 (16+\log (3))-16 e^{-x} x (168+73 \log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} (3+\log (81))+256 e^{-x} x (3+\log (81))+72 e^{-x} x^2 (28+\log (243))+24 e^{-x} x^3 (28+\log (243))+8 \int e^{-x+\log ^2(4)} x^4 \, dx-160 \int e^{-x} x^3 \, dx-720 \int e^{-2 x} x^2 \, dx-1728 \int e^{-2 x} \, dx+2640 \int e^{-2 x} x \, dx+(128 \log (3)) \int e^{-x+\log ^2(4)} \, dx+(320 \log (3)) \int e^{-2 x} x^3 \, dx-(768 \log (3)) \int e^{-2 x} \, dx-(2016 \log (3)) \int e^{-2 x} x^2 \, dx+(3072 \log (3)) \int e^{-2 x} x \, dx-\left (96 \log ^2(3)\right ) \int e^{-2 x} x^2 \, dx-\left (448 \log ^2(3)\right ) \int e^{-2 x} \, dx+\left (480 \log ^2(3)\right ) \int e^{-2 x} x \, dx-(256 (1+\log (3))) \int e^{-x+\log ^2(4)} x \, dx-(8 (12+\log (3))) \int e^{-x+\log ^2(4)} x^3 \, dx+(96 (16+\log (3))) \int e^{-x} x^2 \, dx+(8 (40+11 \log (3))) \int e^{-x+\log ^2(4)} x^2 \, dx+(16 (168+73 \log (3))) \int e^{-x} \, dx-(144 (28+\log (243))) \int e^{-x} x \, dx \\ & = 480 e^{-2 x}+e^{2 \log ^2(4)} (4-x)^2-168 x-360 e^{-2 x} x-80 e^{\log ^2(4)} x+73 x^2+22 e^{\log ^2(4)} x^2-14 x^3+160 e^{-x} x^3-2 e^{\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4+40 e^{-x} x^4-8 e^{-x+\log ^2(4)} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6+384 e^{-2 x} \log (3)-384 e^{-x} \log (3)-128 e^{-x+\log ^2(4)} \log (3)-768 e^{-2 x} x \log (3)+240 e^{-2 x} x^2 \log (3)-512 e^{-2 x} x^3 \log (3)+256 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)+96 e^{-2 x} \log ^2(3)-48 e^{-2 x} x \log ^2(3)+256 e^{-2 x} x^2 \log ^2(3)-128 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)+256 e^{-x+\log ^2(4)} x (1+\log (3))+8 e^{-x+\log ^2(4)} x^3 (12+\log (3))-96 e^{-x} x^2 (16+\log (3))-32 e^{-x} x^3 (16+\log (3))-8 e^{-x} x^4 (16+\log (3))-8 e^{-x+\log ^2(4)} x^2 (40+11 \log (3))-16 e^{-x} (168+73 \log (3))-16 e^{-x} x (168+73 \log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} (3+\log (81))+256 e^{-x} x (3+\log (81))+144 e^{-x} x (28+\log (243))+72 e^{-x} x^2 (28+\log (243))+24 e^{-x} x^3 (28+\log (243))+32 \int e^{-x+\log ^2(4)} x^3 \, dx-480 \int e^{-x} x^2 \, dx-720 \int e^{-2 x} x \, dx+1320 \int e^{-2 x} \, dx+(480 \log (3)) \int e^{-2 x} x^2 \, dx+(1536 \log (3)) \int e^{-2 x} \, dx-(2016 \log (3)) \int e^{-2 x} x \, dx-\left (96 \log ^2(3)\right ) \int e^{-2 x} x \, dx+\left (240 \log ^2(3)\right ) \int e^{-2 x} \, dx-(256 (1+\log (3))) \int e^{-x+\log ^2(4)} \, dx-(24 (12+\log (3))) \int e^{-x+\log ^2(4)} x^2 \, dx+(192 (16+\log (3))) \int e^{-x} x \, dx+(16 (40+11 \log (3))) \int e^{-x+\log ^2(4)} x \, dx-(144 (28+\log (243))) \int e^{-x} \, dx \\ & = -180 e^{-2 x}+e^{2 \log ^2(4)} (4-x)^2-168 x-80 e^{\log ^2(4)} x+73 x^2+480 e^{-x} x^2+22 e^{\log ^2(4)} x^2-14 x^3+160 e^{-x} x^3-2 e^{\log ^2(4)} x^3-32 e^{-x+\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4+40 e^{-x} x^4-8 e^{-x+\log ^2(4)} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6-384 e^{-2 x} \log (3)-384 e^{-x} \log (3)-128 e^{-x+\log ^2(4)} \log (3)+240 e^{-2 x} x \log (3)-512 e^{-2 x} x^3 \log (3)+256 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)-24 e^{-2 x} \log ^2(3)+256 e^{-2 x} x^2 \log ^2(3)-128 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)+256 e^{-x+\log ^2(4)} (1+\log (3))+256 e^{-x+\log ^2(4)} x (1+\log (3))+24 e^{-x+\log ^2(4)} x^2 (12+\log (3))+8 e^{-x+\log ^2(4)} x^3 (12+\log (3))-192 e^{-x} x (16+\log (3))-96 e^{-x} x^2 (16+\log (3))-32 e^{-x} x^3 (16+\log (3))-8 e^{-x} x^4 (16+\log (3))-16 e^{-x+\log ^2(4)} x (40+11 \log (3))-8 e^{-x+\log ^2(4)} x^2 (40+11 \log (3))-16 e^{-x} (168+73 \log (3))-16 e^{-x} x (168+73 \log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} (3+\log (81))+256 e^{-x} x (3+\log (81))+144 e^{-x} (28+\log (243))+144 e^{-x} x (28+\log (243))+72 e^{-x} x^2 (28+\log (243))+24 e^{-x} x^3 (28+\log (243))+96 \int e^{-x+\log ^2(4)} x^2 \, dx-360 \int e^{-2 x} \, dx-960 \int e^{-x} x \, dx+(480 \log (3)) \int e^{-2 x} x \, dx-(1008 \log (3)) \int e^{-2 x} \, dx-\left (48 \log ^2(3)\right ) \int e^{-2 x} \, dx-(48 (12+\log (3))) \int e^{-x+\log ^2(4)} x \, dx+(192 (16+\log (3))) \int e^{-x} \, dx+(16 (40+11 \log (3))) \int e^{-x+\log ^2(4)} \, dx \\ & = e^{2 \log ^2(4)} (4-x)^2-168 x+960 e^{-x} x-80 e^{\log ^2(4)} x+73 x^2+480 e^{-x} x^2+22 e^{\log ^2(4)} x^2-96 e^{-x+\log ^2(4)} x^2-14 x^3+160 e^{-x} x^3-2 e^{\log ^2(4)} x^3-32 e^{-x+\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4+40 e^{-x} x^4-8 e^{-x+\log ^2(4)} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6+120 e^{-2 x} \log (3)-384 e^{-x} \log (3)-128 e^{-x+\log ^2(4)} \log (3)-512 e^{-2 x} x^3 \log (3)+256 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)+256 e^{-2 x} x^2 \log ^2(3)-128 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)+256 e^{-x+\log ^2(4)} (1+\log (3))+256 e^{-x+\log ^2(4)} x (1+\log (3))+48 e^{-x+\log ^2(4)} x (12+\log (3))+24 e^{-x+\log ^2(4)} x^2 (12+\log (3))+8 e^{-x+\log ^2(4)} x^3 (12+\log (3))-192 e^{-x} (16+\log (3))-192 e^{-x} x (16+\log (3))-96 e^{-x} x^2 (16+\log (3))-32 e^{-x} x^3 (16+\log (3))-8 e^{-x} x^4 (16+\log (3))-16 e^{-x+\log ^2(4)} (40+11 \log (3))-16 e^{-x+\log ^2(4)} x (40+11 \log (3))-8 e^{-x+\log ^2(4)} x^2 (40+11 \log (3))-16 e^{-x} (168+73 \log (3))-16 e^{-x} x (168+73 \log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} (3+\log (81))+256 e^{-x} x (3+\log (81))+144 e^{-x} (28+\log (243))+144 e^{-x} x (28+\log (243))+72 e^{-x} x^2 (28+\log (243))+24 e^{-x} x^3 (28+\log (243))+192 \int e^{-x+\log ^2(4)} x \, dx-960 \int e^{-x} \, dx+(240 \log (3)) \int e^{-2 x} \, dx-(48 (12+\log (3))) \int e^{-x+\log ^2(4)} \, dx \\ & = 960 e^{-x}+e^{2 \log ^2(4)} (4-x)^2-168 x+960 e^{-x} x-80 e^{\log ^2(4)} x-192 e^{-x+\log ^2(4)} x+73 x^2+480 e^{-x} x^2+22 e^{\log ^2(4)} x^2-96 e^{-x+\log ^2(4)} x^2-14 x^3+160 e^{-x} x^3-2 e^{\log ^2(4)} x^3-32 e^{-x+\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4+40 e^{-x} x^4-8 e^{-x+\log ^2(4)} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6-384 e^{-x} \log (3)-128 e^{-x+\log ^2(4)} \log (3)-512 e^{-2 x} x^3 \log (3)+256 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)+256 e^{-2 x} x^2 \log ^2(3)-128 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)+256 e^{-x+\log ^2(4)} (1+\log (3))+256 e^{-x+\log ^2(4)} x (1+\log (3))+48 e^{-x+\log ^2(4)} (12+\log (3))+48 e^{-x+\log ^2(4)} x (12+\log (3))+24 e^{-x+\log ^2(4)} x^2 (12+\log (3))+8 e^{-x+\log ^2(4)} x^3 (12+\log (3))-192 e^{-x} (16+\log (3))-192 e^{-x} x (16+\log (3))-96 e^{-x} x^2 (16+\log (3))-32 e^{-x} x^3 (16+\log (3))-8 e^{-x} x^4 (16+\log (3))-16 e^{-x+\log ^2(4)} (40+11 \log (3))-16 e^{-x+\log ^2(4)} x (40+11 \log (3))-8 e^{-x+\log ^2(4)} x^2 (40+11 \log (3))-16 e^{-x} (168+73 \log (3))-16 e^{-x} x (168+73 \log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} (3+\log (81))+256 e^{-x} x (3+\log (81))+144 e^{-x} (28+\log (243))+144 e^{-x} x (28+\log (243))+72 e^{-x} x^2 (28+\log (243))+24 e^{-x} x^3 (28+\log (243))+192 \int e^{-x+\log ^2(4)} \, dx \\ & = 960 e^{-x}-192 e^{-x+\log ^2(4)}+e^{2 \log ^2(4)} (4-x)^2-168 x+960 e^{-x} x-80 e^{\log ^2(4)} x-192 e^{-x+\log ^2(4)} x+73 x^2+480 e^{-x} x^2+22 e^{\log ^2(4)} x^2-96 e^{-x+\log ^2(4)} x^2-14 x^3+160 e^{-x} x^3-2 e^{\log ^2(4)} x^3-32 e^{-x+\log ^2(4)} x^3+x^4+256 e^{-2 x} x^4+40 e^{-x} x^4-8 e^{-x+\log ^2(4)} x^4-128 e^{-2 x} x^5+8 e^{-x} x^5+16 e^{-2 x} x^6-384 e^{-x} \log (3)-128 e^{-x+\log ^2(4)} \log (3)-512 e^{-2 x} x^3 \log (3)+256 e^{-2 x} x^4 \log (3)-32 e^{-2 x} x^5 \log (3)+256 e^{-2 x} x^2 \log ^2(3)-128 e^{-2 x} x^3 \log ^2(3)+16 e^{-2 x} x^4 \log ^2(3)+256 e^{-x+\log ^2(4)} (1+\log (3))+256 e^{-x+\log ^2(4)} x (1+\log (3))+48 e^{-x+\log ^2(4)} (12+\log (3))+48 e^{-x+\log ^2(4)} x (12+\log (3))+24 e^{-x+\log ^2(4)} x^2 (12+\log (3))+8 e^{-x+\log ^2(4)} x^3 (12+\log (3))-192 e^{-x} (16+\log (3))-192 e^{-x} x (16+\log (3))-96 e^{-x} x^2 (16+\log (3))-32 e^{-x} x^3 (16+\log (3))-8 e^{-x} x^4 (16+\log (3))-16 e^{-x+\log ^2(4)} (40+11 \log (3))-16 e^{-x+\log ^2(4)} x (40+11 \log (3))-8 e^{-x+\log ^2(4)} x^2 (40+11 \log (3))-16 e^{-x} (168+73 \log (3))-16 e^{-x} x (168+73 \log (3))-8 e^{-x} x^2 (168+73 \log (3))+256 e^{-x} (3+\log (81))+256 e^{-x} x (3+\log (81))+144 e^{-x} (28+\log (243))+144 e^{-x} x (28+\log (243))+72 e^{-x} x^2 (28+\log (243))+24 e^{-x} x^3 (28+\log (243)) \\ \end{align*}

Mathematica [B] (veriﬁed)

Leaf count is larger than twice the leaf count of optimal. \(181\) vs. \(2(35)=70\).

Time = 0.33 (sec) , antiderivative size = 181, normalized size of antiderivative = 5.17 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=e^{-2 x} x \left (e^{2 \left (x+\log ^2(4)\right )} (-8+x)-2 e^{2 x+\log ^2(4)} \left (40-11 x+x^2\right )+e^{2 x} \left (-168+73 x-14 x^2+x^3\right )-8 e^{x+\log ^2(4)} (-4+x)^2 (x-\log (3))+e^x \left (8 x^4+384 \log (3)+8 x^2 (40+11 \log (3))-2 x^3 (44+\log (81))-64 x (6+\log (243))\right )+8 x \left (2 x^4+32 \log ^2(3)-2 x^3 (8+\log (9))+x^2 \left (32+26 \log (3)+2 \log ^2(3)+\log (729)\right )-2 x \left (26 \log (3)+8 \log ^2(3)+\log (729)\right )\right )\right ) \]

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(252\) vs. \(2(35)=70\).

Time = 0.16 (sec) , antiderivative size = 253, normalized size of antiderivative = 7.23


method	result	size

norman	\(\left (\left (-128-32 \ln \left (3\right )\right ) x^{5}+\left (-512 \ln \left (3\right )-128 \ln \left (3\right )^{2}\right ) x^{3}+\left (256+256 \ln \left (3\right )+16 \ln \left (3\right )^{2}\right ) x^{4}+{\mathrm e}^{2 x} x^{4}+\left (-2 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-14\right ) x^{3} {\mathrm e}^{2 x}+\left (128 \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}}+384 \ln \left (3\right )\right ) x \,{\mathrm e}^{x}+\left (-8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-8 \ln \left (3\right )-88\right ) x^{4} {\mathrm e}^{x}+\left (-8 \,{\mathrm e}^{8 \ln \left (2\right )^{2}}-80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-168\right ) x \,{\mathrm e}^{2 x}+\left ({\mathrm e}^{8 \ln \left (2\right )^{2}}+22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}+73\right ) x^{2} {\mathrm e}^{2 x}+\left (-128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-320 \ln \left (3\right )-64 \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}}-384\right ) x^{2} {\mathrm e}^{x}+\left (64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}+88 \ln \left (3\right )+8 \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}}+320\right ) x^{3} {\mathrm e}^{x}+16 x^{6}+256 x^{2} \ln \left (3\right )^{2}+8 x^{5} {\mathrm e}^{x}\right ) {\mathrm e}^{-2 x}\)	\(253\)
risch	\(x^{4}-2 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}-14 x^{3}+22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}+x^{2} {\mathrm e}^{8 \ln \left (2\right )^{2}}+73 x^{2}-8 \,{\mathrm e}^{8 \ln \left (2\right )^{2}} x -80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x -168 x +\left (8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) x^{3}-8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{4}-64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2} \ln \left (3\right )+64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}+128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x \ln \left (3\right )-128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}-8 x^{4} \ln \left (3\right )+8 x^{5}+88 x^{3} \ln \left (3\right )-88 x^{4}-320 x^{2} \ln \left (3\right )+320 x^{3}+384 x \ln \left (3\right )-384 x^{2}\right ) {\mathrm e}^{-x}+\left (16 x^{4} \ln \left (3\right )^{2}-32 x^{5} \ln \left (3\right )+16 x^{6}-128 x^{3} \ln \left (3\right )^{2}+256 x^{4} \ln \left (3\right )-128 x^{5}+256 x^{2} \ln \left (3\right )^{2}-512 x^{3} \ln \left (3\right )+256 x^{4}\right ) {\mathrm e}^{-2 x}\)	\(272\)
parallelrisch	\(\left (-8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} {\mathrm e}^{x} x^{4}-8 \ln \left (3\right ) {\mathrm e}^{x} x^{4}+{\mathrm e}^{2 x} x^{4}-14 \,{\mathrm e}^{2 x} x^{3}-128 x^{3} \ln \left (3\right )^{2}+73 \,{\mathrm e}^{2 x} x^{2}-168 x \,{\mathrm e}^{2 x}-32 x^{5} \ln \left (3\right )-512 x^{3} \ln \left (3\right )-88 \,{\mathrm e}^{x} x^{4}-384 \,{\mathrm e}^{x} x^{2}+320 \,{\mathrm e}^{x} x^{3}-320 x^{2} \ln \left (3\right ) {\mathrm e}^{x}+8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) {\mathrm e}^{x} x^{3}-64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) {\mathrm e}^{x} x^{2}+128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) {\mathrm e}^{x} x +384 x \ln \left (3\right ) {\mathrm e}^{x}+256 x^{2} \ln \left (3\right )^{2}+16 x^{4} \ln \left (3\right )^{2}+256 x^{4} \ln \left (3\right )+8 x^{5} {\mathrm e}^{x}+16 x^{6}-128 x^{5}+256 x^{4}+64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} {\mathrm e}^{x} x^{3}-128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} {\mathrm e}^{x} x^{2}+{\mathrm e}^{8 \ln \left (2\right )^{2}} x^{2} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x} x^{3} {\mathrm e}^{4 \ln \left (2\right )^{2}}-80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} {\mathrm e}^{2 x} x -8 \,{\mathrm e}^{2 x} {\mathrm e}^{8 \ln \left (2\right )^{2}} x +22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} {\mathrm e}^{2 x} x^{2}+88 \ln \left (3\right ) {\mathrm e}^{x} x^{3}\right ) {\mathrm e}^{-2 x}\)	\(332\)
parts	\(16 \,{\mathrm e}^{-2 x} x^{6}+8 \,{\mathrm e}^{-x} x^{5}-128 \,{\mathrm e}^{-2 x} x^{5}-88 \,{\mathrm e}^{-x} x^{4}+320 \,{\mathrm e}^{-x} x^{3}+256 \,{\mathrm e}^{-2 x} x^{4}+16 \,{\mathrm e}^{-2 x} \ln \left (3\right )^{2} x^{4}-32 \,{\mathrm e}^{-2 x} \ln \left (3\right ) x^{5}-8 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{4}-8 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{4}-128 \,{\mathrm e}^{-2 x} \ln \left (3\right )^{2} x^{3}+256 \,{\mathrm e}^{-2 x} \ln \left (3\right ) x^{4}+64 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}+88 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{3}+256 \,{\mathrm e}^{-2 x} \ln \left (3\right )^{2} x^{2}-512 \,{\mathrm e}^{-2 x} \ln \left (3\right ) x^{3}-128 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}-320 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{2}+384 \,{\mathrm e}^{-x} \ln \left (3\right ) x +22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}-8 \,{\mathrm e}^{8 \ln \left (2\right )^{2}} x -2 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}+x^{2} {\mathrm e}^{8 \ln \left (2\right )^{2}}-80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x -168 x +8 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) x^{3}-64 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) x^{2}+128 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) x -384 x^{2} {\mathrm e}^{-x}+x^{4}-14 x^{3}+73 x^{2}\)	\(354\)
default	\(\text {Expression too large to display}\)	\(830\)

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 205 vs. \(2 (33) = 66\).

Time = 0.25 (sec) , antiderivative size = 205, normalized size of antiderivative = 5.86 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx={\left (16 \, x^{6} - 128 \, x^{5} + 256 \, x^{4} + 16 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \left (3\right )^{2} - 2 \, {\left ({\left (x^{3} - 11 \, x^{2} + 40 \, x\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} \log \left (3\right )\right )} e^{x}\right )} e^{\left (4 \, \log \left (2\right )^{2}\right )} + {\left (x^{2} - 8 \, x\right )} e^{\left (8 \, \log \left (2\right )^{2} + 2 \, x\right )} + {\left (x^{4} - 14 \, x^{3} + 73 \, x^{2} - 168 \, x\right )} e^{\left (2 \, x\right )} + 8 \, {\left (x^{5} - 11 \, x^{4} + 40 \, x^{3} - 48 \, x^{2} - {\left (x^{4} - 11 \, x^{3} + 40 \, x^{2} - 48 \, x\right )} \log \left (3\right )\right )} e^{x} - 32 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \left (3\right )\right )} e^{\left (-2 \, x\right )} \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 291 vs. \(2 (29) = 58\).

Time = 0.23 (sec) , antiderivative size = 291, normalized size of antiderivative = 8.31 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=x^{4} + x^{3} \left (-14 - 2 e^{4 \log {\left (2 \right )}^{2}}\right ) + x^{2} \left (e^{8 \log {\left (2 \right )}^{2}} + 73 + 22 e^{4 \log {\left (2 \right )}^{2}}\right ) + x \left (- 80 e^{4 \log {\left (2 \right )}^{2}} - 8 e^{8 \log {\left (2 \right )}^{2}} - 168\right ) + \left (16 x^{6} - 128 x^{5} - 32 x^{5} \log {\left (3 \right )} + 16 x^{4} \log {\left (3 \right )}^{2} + 256 x^{4} + 256 x^{4} \log {\left (3 \right )} - 512 x^{3} \log {\left (3 \right )} - 128 x^{3} \log {\left (3 \right )}^{2} + 256 x^{2} \log {\left (3 \right )}^{2}\right ) e^{- 2 x} + \left (8 x^{5} - 88 x^{4} - 8 x^{4} e^{4 \log {\left (2 \right )}^{2}} - 8 x^{4} \log {\left (3 \right )} + 8 x^{3} e^{4 \log {\left (2 \right )}^{2}} \log {\left (3 \right )} + 88 x^{3} \log {\left (3 \right )} + 320 x^{3} + 64 x^{3} e^{4 \log {\left (2 \right )}^{2}} - 128 x^{2} e^{4 \log {\left (2 \right )}^{2}} - 64 x^{2} e^{4 \log {\left (2 \right )}^{2}} \log {\left (3 \right )} - 384 x^{2} - 320 x^{2} \log {\left (3 \right )} + 384 x \log {\left (3 \right )} + 128 x e^{4 \log {\left (2 \right )}^{2}} \log {\left (3 \right )}\right ) e^{- x} \]

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 855 vs. \(2 (33) = 66\).

Time = 0.32 (sec) , antiderivative size = 855, normalized size of antiderivative = 24.43 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=\text {Too large to display} \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 349 vs. \(2 (33) = 66\).

Time = 0.27 (sec) , antiderivative size = 349, normalized size of antiderivative = 9.97 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=16 \, x^{6} e^{\left (-2 \, x\right )} - 32 \, x^{5} e^{\left (-2 \, x\right )} \log \left (3\right ) + 16 \, x^{4} e^{\left (-2 \, x\right )} \log \left (3\right )^{2} + 8 \, x^{5} e^{\left (-x\right )} - 128 \, x^{5} e^{\left (-2 \, x\right )} - 8 \, x^{4} e^{\left (-x\right )} \log \left (3\right ) + 256 \, x^{4} e^{\left (-2 \, x\right )} \log \left (3\right ) - 128 \, x^{3} e^{\left (-2 \, x\right )} \log \left (3\right )^{2} - 8 \, x^{4} e^{\left (4 \, \log \left (2\right )^{2} - x\right )} - 88 \, x^{4} e^{\left (-x\right )} + 256 \, x^{4} e^{\left (-2 \, x\right )} + 8 \, x^{3} e^{\left (4 \, \log \left (2\right )^{2} - x\right )} \log \left (3\right ) + 88 \, x^{3} e^{\left (-x\right )} \log \left (3\right ) - 512 \, x^{3} e^{\left (-2 \, x\right )} \log \left (3\right ) + 256 \, x^{2} e^{\left (-2 \, x\right )} \log \left (3\right )^{2} + x^{4} - 2 \, x^{3} e^{\left (4 \, \log \left (2\right )^{2}\right )} + 64 \, x^{3} e^{\left (4 \, \log \left (2\right )^{2} - x\right )} + 320 \, x^{3} e^{\left (-x\right )} - 64 \, x^{2} e^{\left (4 \, \log \left (2\right )^{2} - x\right )} \log \left (3\right ) - 320 \, x^{2} e^{\left (-x\right )} \log \left (3\right ) - 14 \, x^{3} + x^{2} e^{\left (8 \, \log \left (2\right )^{2}\right )} + 22 \, x^{2} e^{\left (4 \, \log \left (2\right )^{2}\right )} - 128 \, x^{2} e^{\left (4 \, \log \left (2\right )^{2} - x\right )} - 384 \, x^{2} e^{\left (-x\right )} + 128 \, x e^{\left (4 \, \log \left (2\right )^{2} - x\right )} \log \left (3\right ) + 384 \, x e^{\left (-x\right )} \log \left (3\right ) + 73 \, x^{2} - 8 \, x e^{\left (8 \, \log \left (2\right )^{2}\right )} - 80 \, x e^{\left (4 \, \log \left (2\right )^{2}\right )} - 168 \, x \]

Mupad [B] (veriﬁcation not implemented)

Time = 16.32 (sec) , antiderivative size = 229, normalized size of antiderivative = 6.54 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx={\mathrm {e}}^{-x}\,\left (8\,x^5+\left (-8\,\ln \left (3\right )-8\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}-88\right )\,x^4+\left (88\,\ln \left (3\right )+64\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+8\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}\,\ln \left (3\right )+320\right )\,x^3+\left (-320\,\ln \left (3\right )-128\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}-64\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}\,\ln \left (3\right )-384\right )\,x^2+128\,\ln \left (3\right )\,\left ({\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+3\right )\,x\right )-x\,\left (80\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+8\,{\mathrm {e}}^{8\,{\ln \left (2\right )}^2}+168\right )+x^2\,\left (22\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+{\mathrm {e}}^{8\,{\ln \left (2\right )}^2}+73\right )-x^3\,\left (2\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+14\right )+{\mathrm {e}}^{-2\,x}\,\left (16\,x^6+\left (-32\,\ln \left (3\right )-128\right )\,x^5+\left (256\,\ln \left (3\right )+16\,{\ln \left (3\right )}^2+256\right )\,x^4-128\,\ln \left (3\right )\,\left (\ln \left (3\right )+4\right )\,x^3+256\,{\ln \left (3\right )}^2\,x^2\right )+x^4 \]

Optimal result