Integrand size = 230, antiderivative size = 35 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=(4-x)^2 \left (-3-e^{\log ^2(4)}+x-4 e^{-x} x (-x+\log (3))\right )^2 \] Output:
(x-4*x/exp(x)*(ln(3)-x)-exp(4*ln(2)^2)-3)^2*(4-x)^2
Leaf count is larger than twice the leaf count of optimal. \(181\) vs. \(2(35)=70\).
Time = 0.20 (sec) , antiderivative size = 181, normalized size of antiderivative = 5.17 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=e^{-2 x} x \left (e^{2 \left (x+\log ^2(4)\right )} (-8+x)-2 e^{2 x+\log ^2(4)} \left (40-11 x+x^2\right )+e^{2 x} \left (-168+73 x-14 x^2+x^3\right )-8 e^{x+\log ^2(4)} (-4+x)^2 (x-\log (3))+e^x \left (8 x^4+384 \log (3)+8 x^2 (40+11 \log (3))-2 x^3 (44+\log (81))-64 x (6+\log (243))\right )+8 x \left (2 x^4+32 \log ^2(3)-2 x^3 (8+\log (9))+x^2 \left (32+26 \log (3)+2 \log ^2(3)+\log (729)\right )-2 x \left (26 \log (3)+8 \log ^2(3)+\log (729)\right )\right )\right ) \] Input:
Integrate[(1024*x^3 - 1152*x^4 + 352*x^5 - 32*x^6 + E^(2*x + 2*Log[4]^2)*( -8 + 2*x) + E^(2*x)*(-168 + 146*x - 42*x^2 + 4*x^3) + (-1536*x^2 + 2048*x^ 3 - 672*x^4 + 64*x^5)*Log[3] + (512*x - 896*x^2 + 320*x^3 - 32*x^4)*Log[3] ^2 + E^x*(-768*x + 1344*x^2 - 672*x^3 + 128*x^4 - 8*x^5 + (384 - 1024*x + 584*x^2 - 120*x^3 + 8*x^4)*Log[3]) + E^Log[4]^2*(E^(2*x)*(-80 + 44*x - 6*x ^2) + E^x*(-256*x + 320*x^2 - 96*x^3 + 8*x^4 + (128 - 256*x + 88*x^2 - 8*x ^3)*Log[3])))/E^(2*x),x]
Output:
(x*(E^(2*(x + Log[4]^2))*(-8 + x) - 2*E^(2*x + Log[4]^2)*(40 - 11*x + x^2) + E^(2*x)*(-168 + 73*x - 14*x^2 + x^3) - 8*E^(x + Log[4]^2)*(-4 + x)^2*(x - Log[3]) + E^x*(8*x^4 + 384*Log[3] + 8*x^2*(40 + 11*Log[3]) - 2*x^3*(44 + Log[81]) - 64*x*(6 + Log[243])) + 8*x*(2*x^4 + 32*Log[3]^2 - 2*x^3*(8 + Log[9]) + x^2*(32 + 26*Log[3] + 2*Log[3]^2 + Log[729]) - 2*x*(26*Log[3] + 8*Log[3]^2 + Log[729]))))/E^(2*x)
Leaf count is larger than twice the leaf count of optimal. \(664\) vs. \(2(35)=70\).
Time = 12.82 (sec) , antiderivative size = 664, normalized size of antiderivative = 18.97, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used = {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.
| \(\displaystyle \int e^{-2 x} \left (-32 x^6+352 x^5-1152 x^4+1024 x^3+e^{2 x} \left (4 x^3-42 x^2+146 x-168\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-6 x^2+44 x-80\right )+e^x \left (8 x^4-96 x^3+320 x^2+\left (-8 x^3+88 x^2-256 x+128\right ) \log (3)-256 x\right )\right )+\left (-32 x^4+320 x^3-896 x^2+512 x\right ) \log ^2(3)+e^x \left (-8 x^5+128 x^4-672 x^3+1344 x^2+\left (8 x^4-120 x^3+584 x^2-1024 x+384\right ) \log (3)-768 x\right )+\left (64 x^5-672 x^4+2048 x^3-1536 x^2\right ) \log (3)+(2 x-8) e^{2 x+2 \log ^2(4)}\right ) \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-32 e^{-2 x} x^6+352 e^{-2 x} x^5-1152 e^{-2 x} x^4+1024 e^{-2 x} x^3+2 \left (2 x^3-21 x^2+73 x-84\right )-32 e^{-2 x} \left (x^3-10 x^2+28 x-16\right ) x \log ^2(3)+2 (4-x) e^{\log ^2(4)-x} \left (-4 x^3+32 x^2 \left (1+\frac {\log (3)}{8}\right )+3 e^x x-10 e^x-32 x \left (1+\frac {7 \log (3)}{8}\right )+16 \log (3)\right )+32 e^{-2 x} \left (2 x^3-21 x^2+64 x-48\right ) x^2 \log (3)+8 e^{-x} (4-x) \left (x^4-x^3 (12+\log (3))+x^2 (36+11 \log (3))-x (24+29 \log (3))+12 \log (3)\right )+2 (x-4) e^{2 \log ^2(4)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 16 e^{-2 x} x^6-128 e^{-2 x} x^5+8 e^{-x} x^5-32 e^{-2 x} x^5 \log (3)+256 e^{-2 x} x^4+40 e^{-x} x^4+x^4-8 x^4 e^{\log ^2(4)-x}+16 e^{-2 x} x^4 \log ^2(3)-8 e^{-x} x^4 (16+\log (3))+256 e^{-2 x} x^4 \log (3)+160 e^{-x} x^3-14 x^3-32 x^3 e^{\log ^2(4)-x}+8 x^3 (12+\log (3)) e^{\log ^2(4)-x}-128 e^{-2 x} x^3 \log ^2(3)-2 x^3 e^{\log ^2(4)}+24 e^{-x} x^3 (28+\log (243))-32 e^{-x} x^3 (16+\log (3))-512 e^{-2 x} x^3 \log (3)+480 e^{-x} x^2+73 x^2-96 x^2 e^{\log ^2(4)-x}-8 x^2 (40+11 \log (3)) e^{\log ^2(4)-x}+24 x^2 (12+\log (3)) e^{\log ^2(4)-x}+256 e^{-2 x} x^2 \log ^2(3)+22 x^2 e^{\log ^2(4)}+72 e^{-x} x^2 (28+\log (243))-8 e^{-x} x^2 (168+73 \log (3))-96 e^{-x} x^2 (16+\log (3))+960 e^{-x} x-168 x+960 e^{-x}-192 x e^{\log ^2(4)-x}-16 x (40+11 \log (3)) e^{\log ^2(4)-x}+48 x (12+\log (3)) e^{\log ^2(4)-x}+256 x (1+\log (3)) e^{\log ^2(4)-x}-80 x e^{\log ^2(4)}-192 e^{\log ^2(4)-x}+(4-x)^2 e^{2 \log ^2(4)}-16 (40+11 \log (3)) e^{\log ^2(4)-x}+48 (12+\log (3)) e^{\log ^2(4)-x}+256 (1+\log (3)) e^{\log ^2(4)-x}-128 \log (3) e^{\log ^2(4)-x}+144 e^{-x} x (28+\log (243))+256 e^{-x} x (3+\log (81))-16 e^{-x} x (168+73 \log (3))-192 e^{-x} x (16+\log (3))+144 e^{-x} (28+\log (243))+256 e^{-x} (3+\log (81))-16 e^{-x} (168+73 \log (3))-192 e^{-x} (16+\log (3))-384 e^{-x} \log (3)\) |
Input:
Int[(1024*x^3 - 1152*x^4 + 352*x^5 - 32*x^6 + E^(2*x + 2*Log[4]^2)*(-8 + 2 *x) + E^(2*x)*(-168 + 146*x - 42*x^2 + 4*x^3) + (-1536*x^2 + 2048*x^3 - 67 2*x^4 + 64*x^5)*Log[3] + (512*x - 896*x^2 + 320*x^3 - 32*x^4)*Log[3]^2 + E ^x*(-768*x + 1344*x^2 - 672*x^3 + 128*x^4 - 8*x^5 + (384 - 1024*x + 584*x^ 2 - 120*x^3 + 8*x^4)*Log[3]) + E^Log[4]^2*(E^(2*x)*(-80 + 44*x - 6*x^2) + E^x*(-256*x + 320*x^2 - 96*x^3 + 8*x^4 + (128 - 256*x + 88*x^2 - 8*x^3)*Lo g[3])))/E^(2*x),x]
Output:
960/E^x - 192*E^(-x + Log[4]^2) + E^(2*Log[4]^2)*(4 - x)^2 - 168*x + (960* x)/E^x - 80*E^Log[4]^2*x - 192*E^(-x + Log[4]^2)*x + 73*x^2 + (480*x^2)/E^ x + 22*E^Log[4]^2*x^2 - 96*E^(-x + Log[4]^2)*x^2 - 14*x^3 + (160*x^3)/E^x - 2*E^Log[4]^2*x^3 - 32*E^(-x + Log[4]^2)*x^3 + x^4 + (256*x^4)/E^(2*x) + (40*x^4)/E^x - 8*E^(-x + Log[4]^2)*x^4 - (128*x^5)/E^(2*x) + (8*x^5)/E^x + (16*x^6)/E^(2*x) - (384*Log[3])/E^x - 128*E^(-x + Log[4]^2)*Log[3] - (512 *x^3*Log[3])/E^(2*x) + (256*x^4*Log[3])/E^(2*x) - (32*x^5*Log[3])/E^(2*x) + (256*x^2*Log[3]^2)/E^(2*x) - (128*x^3*Log[3]^2)/E^(2*x) + (16*x^4*Log[3] ^2)/E^(2*x) + 256*E^(-x + Log[4]^2)*(1 + Log[3]) + 256*E^(-x + Log[4]^2)*x *(1 + Log[3]) + 48*E^(-x + Log[4]^2)*(12 + Log[3]) + 48*E^(-x + Log[4]^2)* x*(12 + Log[3]) + 24*E^(-x + Log[4]^2)*x^2*(12 + Log[3]) + 8*E^(-x + Log[4 ]^2)*x^3*(12 + Log[3]) - (192*(16 + Log[3]))/E^x - (192*x*(16 + Log[3]))/E ^x - (96*x^2*(16 + Log[3]))/E^x - (32*x^3*(16 + Log[3]))/E^x - (8*x^4*(16 + Log[3]))/E^x - 16*E^(-x + Log[4]^2)*(40 + 11*Log[3]) - 16*E^(-x + Log[4] ^2)*x*(40 + 11*Log[3]) - 8*E^(-x + Log[4]^2)*x^2*(40 + 11*Log[3]) - (16*(1 68 + 73*Log[3]))/E^x - (16*x*(168 + 73*Log[3]))/E^x - (8*x^2*(168 + 73*Log [3]))/E^x + (256*(3 + Log[81]))/E^x + (256*x*(3 + Log[81]))/E^x + (144*(28 + Log[243]))/E^x + (144*x*(28 + Log[243]))/E^x + (72*x^2*(28 + Log[243])) /E^x + (24*x^3*(28 + Log[243]))/E^x
Leaf count of result is larger than twice the leaf count of optimal. \(252\) vs. \(2(35)=70\).
Time = 20.35 (sec) , antiderivative size = 253, normalized size of antiderivative = 7.23
| method | result | size |
| norman | \(\left (\left (-128-32 \ln \left (3\right )\right ) x^{5}+\left (-512 \ln \left (3\right )-128 \ln \left (3\right )^{2}\right ) x^{3}+\left (256+256 \ln \left (3\right )+16 \ln \left (3\right )^{2}\right ) x^{4}+x^{4} {\mathrm e}^{2 x}+\left (-2 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-14\right ) x^{3} {\mathrm e}^{2 x}+\left (128 \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}}+384 \ln \left (3\right )\right ) x \,{\mathrm e}^{x}+\left (-8 \ln \left (3\right )-8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-88\right ) x^{4} {\mathrm e}^{x}+\left (-8 \,{\mathrm e}^{8 \ln \left (2\right )^{2}}-80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-168\right ) x \,{\mathrm e}^{2 x}+\left ({\mathrm e}^{8 \ln \left (2\right )^{2}}+22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}+73\right ) x^{2} {\mathrm e}^{2 x}+\left (-320 \ln \left (3\right )-128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}-384-64 \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}}\right ) x^{2} {\mathrm e}^{x}+\left (88 \ln \left (3\right )+64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}}+320+8 \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}}\right ) x^{3} {\mathrm e}^{x}+16 x^{6}+256 x^{2} \ln \left (3\right )^{2}+8 x^{5} {\mathrm e}^{x}\right ) {\mathrm e}^{-2 x}\) | \(253\) |
| risch | \(x^{4}-2 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}-14 x^{3}+x^{2} {\mathrm e}^{8 \ln \left (2\right )^{2}}+22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}+73 x^{2}-8 \,{\mathrm e}^{8 \ln \left (2\right )^{2}} x -80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x -168 x +\left (8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) x^{3}-8 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{4}-64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} \ln \left (3\right ) x^{2}+64 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}+128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x \ln \left (3\right )-128 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}-8 x^{4} \ln \left (3\right )+8 x^{5}+88 x^{3} \ln \left (3\right )-88 x^{4}-320 x^{2} \ln \left (3\right )+320 x^{3}+384 x \ln \left (3\right )-384 x^{2}\right ) {\mathrm e}^{-x}+\left (16 x^{4} \ln \left (3\right )^{2}-32 x^{5} \ln \left (3\right )+16 x^{6}-128 x^{3} \ln \left (3\right )^{2}+256 x^{4} \ln \left (3\right )-128 x^{5}+256 x^{2} \ln \left (3\right )^{2}-512 x^{3} \ln \left (3\right )+256 x^{4}\right ) {\mathrm e}^{-2 x}\) | \(272\) |
| parallelrisch | \(\left (-14 \,{\mathrm e}^{2 x} x^{3}-128 x^{3} \ln \left (3\right )^{2}-80 \,{\mathrm e}^{2 x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x +256 x^{4} \ln \left (3\right )+73 \,{\mathrm e}^{2 x} x^{2}+256 x^{2} \ln \left (3\right )^{2}-384 \,{\mathrm e}^{x} x^{2}-88 \,{\mathrm e}^{x} x^{4}+320 \,{\mathrm e}^{x} x^{3}+16 x^{4} \ln \left (3\right )^{2}+x^{4} {\mathrm e}^{2 x}-512 x^{3} \ln \left (3\right )-32 x^{5} \ln \left (3\right )-64 \,{\mathrm e}^{x} \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}+128 \,{\mathrm e}^{x} \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}} x +8 \,{\mathrm e}^{x} \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}-168 x \,{\mathrm e}^{2 x}+8 x^{5} {\mathrm e}^{x}+16 x^{6}+256 x^{4}-128 x^{5}+384 x \ln \left (3\right ) {\mathrm e}^{x}+64 \,{\mathrm e}^{x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}-128 \,{\mathrm e}^{x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}-8 \,{\mathrm e}^{x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{4}-8 \,{\mathrm e}^{x} x^{4} \ln \left (3\right )-8 \,{\mathrm e}^{2 x} {\mathrm e}^{8 \ln \left (2\right )^{2}} x +22 \,{\mathrm e}^{2 x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}+88 \,{\mathrm e}^{x} \ln \left (3\right ) x^{3}-320 \,{\mathrm e}^{x} \ln \left (3\right ) x^{2}-2 \,{\mathrm e}^{2 x} x^{3} {\mathrm e}^{4 \ln \left (2\right )^{2}}+{\mathrm e}^{8 \ln \left (2\right )^{2}} x^{2} {\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}\) | \(332\) |
| parts | \(-168 x -80 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x -8 \,{\mathrm e}^{8 \ln \left (2\right )^{2}} x +16 \,{\mathrm e}^{-2 x} x^{6}+8 \,{\mathrm e}^{-x} x^{5}-128 \,{\mathrm e}^{-2 x} x^{5}+256 \,{\mathrm e}^{-2 x} x^{4}+x^{2} {\mathrm e}^{8 \ln \left (2\right )^{2}}+8 \,{\mathrm e}^{-x} \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}-64 \,{\mathrm e}^{-x} \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}+128 \,{\mathrm e}^{-x} \ln \left (3\right ) {\mathrm e}^{4 \ln \left (2\right )^{2}} x +73 x^{2}-14 x^{3}+x^{4}+22 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}-2 \,{\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}-88 x^{4} {\mathrm e}^{-x}+320 x^{3} {\mathrm e}^{-x}-384 x^{2} {\mathrm e}^{-x}+256 \,{\mathrm e}^{-2 x} \ln \left (3\right )^{2} x^{2}-512 \,{\mathrm e}^{-2 x} \ln \left (3\right ) x^{3}-320 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{2}-128 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{2}+384 \,{\mathrm e}^{-x} \ln \left (3\right ) x +16 \,{\mathrm e}^{-2 x} \ln \left (3\right )^{2} x^{4}-32 \,{\mathrm e}^{-2 x} \ln \left (3\right ) x^{5}-8 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{4}-8 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{4}-128 \,{\mathrm e}^{-2 x} \ln \left (3\right )^{2} x^{3}+256 \,{\mathrm e}^{-2 x} \ln \left (3\right ) x^{4}+88 \,{\mathrm e}^{-x} \ln \left (3\right ) x^{3}+64 \,{\mathrm e}^{-x} {\mathrm e}^{4 \ln \left (2\right )^{2}} x^{3}\) | \(354\) |
| default | \(\text {Expression too large to display}\) | \(830\) |
Input:
int(((2*x-8)*exp(x)^2*exp(4*ln(2)^2)^2+((-6*x^2+44*x-80)*exp(x)^2+((-8*x^3 +88*x^2-256*x+128)*ln(3)+8*x^4-96*x^3+320*x^2-256*x)*exp(x))*exp(4*ln(2)^2 )+(4*x^3-42*x^2+146*x-168)*exp(x)^2+((8*x^4-120*x^3+584*x^2-1024*x+384)*ln (3)-8*x^5+128*x^4-672*x^3+1344*x^2-768*x)*exp(x)+(-32*x^4+320*x^3-896*x^2+ 512*x)*ln(3)^2+(64*x^5-672*x^4+2048*x^3-1536*x^2)*ln(3)-32*x^6+352*x^5-115 2*x^4+1024*x^3)/exp(x)^2,x,method=_RETURNVERBOSE)
Output:
((-128-32*ln(3))*x^5+(-512*ln(3)-128*ln(3)^2)*x^3+(256+256*ln(3)+16*ln(3)^ 2)*x^4+exp(x)^2*x^4+(-2*exp(ln(2)^2)^4-14)*x^3*exp(x)^2+(384*ln(3)+128*exp (ln(2)^2)^4*ln(3))*x*exp(x)+(-88-8*ln(3)-8*exp(ln(2)^2)^4)*x^4*exp(x)+(-8* exp(ln(2)^2)^8-80*exp(ln(2)^2)^4-168)*x*exp(x)^2+(exp(ln(2)^2)^8+22*exp(ln (2)^2)^4+73)*x^2*exp(x)^2+(-384-320*ln(3)-128*exp(ln(2)^2)^4-64*exp(ln(2)^ 2)^4*ln(3))*x^2*exp(x)+(320+88*ln(3)+64*exp(ln(2)^2)^4+8*exp(ln(2)^2)^4*ln (3))*x^3*exp(x)+16*x^6+256*x^2*ln(3)^2+8*x^5*exp(x))/exp(x)^2
Leaf count of result is larger than twice the leaf count of optimal. 205 vs. \(2 (33) = 66\).
Time = 0.11 (sec) , antiderivative size = 205, normalized size of antiderivative = 5.86 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx={\left (16 \, x^{6} - 128 \, x^{5} + 256 \, x^{4} + 16 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \left (3\right )^{2} - 2 \, {\left ({\left (x^{3} - 11 \, x^{2} + 40 \, x\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} \log \left (3\right )\right )} e^{x}\right )} e^{\left (4 \, \log \left (2\right )^{2}\right )} + {\left (x^{2} - 8 \, x\right )} e^{\left (8 \, \log \left (2\right )^{2} + 2 \, x\right )} + {\left (x^{4} - 14 \, x^{3} + 73 \, x^{2} - 168 \, x\right )} e^{\left (2 \, x\right )} + 8 \, {\left (x^{5} - 11 \, x^{4} + 40 \, x^{3} - 48 \, x^{2} - {\left (x^{4} - 11 \, x^{3} + 40 \, x^{2} - 48 \, x\right )} \log \left (3\right )\right )} e^{x} - 32 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \left (3\right )\right )} e^{\left (-2 \, x\right )} \] Input:
integrate(((2*x-8)*exp(x)^2*exp(4*log(2)^2)^2+((-6*x^2+44*x-80)*exp(x)^2+( (-8*x^3+88*x^2-256*x+128)*log(3)+8*x^4-96*x^3+320*x^2-256*x)*exp(x))*exp(4 *log(2)^2)+(4*x^3-42*x^2+146*x-168)*exp(x)^2+((8*x^4-120*x^3+584*x^2-1024* x+384)*log(3)-8*x^5+128*x^4-672*x^3+1344*x^2-768*x)*exp(x)+(-32*x^4+320*x^ 3-896*x^2+512*x)*log(3)^2+(64*x^5-672*x^4+2048*x^3-1536*x^2)*log(3)-32*x^6 +352*x^5-1152*x^4+1024*x^3)/exp(x)^2,x, algorithm="fricas")
Output:
(16*x^6 - 128*x^5 + 256*x^4 + 16*(x^4 - 8*x^3 + 16*x^2)*log(3)^2 - 2*((x^3 - 11*x^2 + 40*x)*e^(2*x) + 4*(x^4 - 8*x^3 + 16*x^2 - (x^3 - 8*x^2 + 16*x) *log(3))*e^x)*e^(4*log(2)^2) + (x^2 - 8*x)*e^(8*log(2)^2 + 2*x) + (x^4 - 1 4*x^3 + 73*x^2 - 168*x)*e^(2*x) + 8*(x^5 - 11*x^4 + 40*x^3 - 48*x^2 - (x^4 - 11*x^3 + 40*x^2 - 48*x)*log(3))*e^x - 32*(x^5 - 8*x^4 + 16*x^3)*log(3)) *e^(-2*x)
Leaf count of result is larger than twice the leaf count of optimal. 291 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 291, normalized size of antiderivative = 8.31 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=x^{4} + x^{3} \left (-14 - 2 e^{4 \log {\left (2 \right )}^{2}}\right ) + x^{2} \left (e^{8 \log {\left (2 \right )}^{2}} + 73 + 22 e^{4 \log {\left (2 \right )}^{2}}\right ) + x \left (- 80 e^{4 \log {\left (2 \right )}^{2}} - 8 e^{8 \log {\left (2 \right )}^{2}} - 168\right ) + \left (16 x^{6} - 128 x^{5} - 32 x^{5} \log {\left (3 \right )} + 16 x^{4} \log {\left (3 \right )}^{2} + 256 x^{4} + 256 x^{4} \log {\left (3 \right )} - 512 x^{3} \log {\left (3 \right )} - 128 x^{3} \log {\left (3 \right )}^{2} + 256 x^{2} \log {\left (3 \right )}^{2}\right ) e^{- 2 x} + \left (8 x^{5} - 88 x^{4} - 8 x^{4} e^{4 \log {\left (2 \right )}^{2}} - 8 x^{4} \log {\left (3 \right )} + 8 x^{3} e^{4 \log {\left (2 \right )}^{2}} \log {\left (3 \right )} + 88 x^{3} \log {\left (3 \right )} + 320 x^{3} + 64 x^{3} e^{4 \log {\left (2 \right )}^{2}} - 128 x^{2} e^{4 \log {\left (2 \right )}^{2}} - 64 x^{2} e^{4 \log {\left (2 \right )}^{2}} \log {\left (3 \right )} - 384 x^{2} - 320 x^{2} \log {\left (3 \right )} + 384 x \log {\left (3 \right )} + 128 x e^{4 \log {\left (2 \right )}^{2}} \log {\left (3 \right )}\right ) e^{- x} \] Input:
integrate(((2*x-8)*exp(x)**2*exp(4*ln(2)**2)**2+((-6*x**2+44*x-80)*exp(x)* *2+((-8*x**3+88*x**2-256*x+128)*ln(3)+8*x**4-96*x**3+320*x**2-256*x)*exp(x ))*exp(4*ln(2)**2)+(4*x**3-42*x**2+146*x-168)*exp(x)**2+((8*x**4-120*x**3+ 584*x**2-1024*x+384)*ln(3)-8*x**5+128*x**4-672*x**3+1344*x**2-768*x)*exp(x )+(-32*x**4+320*x**3-896*x**2+512*x)*ln(3)**2+(64*x**5-672*x**4+2048*x**3- 1536*x**2)*ln(3)-32*x**6+352*x**5-1152*x**4+1024*x**3)/exp(x)**2,x)
Output:
x**4 + x**3*(-14 - 2*exp(4*log(2)**2)) + x**2*(exp(8*log(2)**2) + 73 + 22* exp(4*log(2)**2)) + x*(-80*exp(4*log(2)**2) - 8*exp(8*log(2)**2) - 168) + (16*x**6 - 128*x**5 - 32*x**5*log(3) + 16*x**4*log(3)**2 + 256*x**4 + 256* x**4*log(3) - 512*x**3*log(3) - 128*x**3*log(3)**2 + 256*x**2*log(3)**2)*e xp(-2*x) + (8*x**5 - 88*x**4 - 8*x**4*exp(4*log(2)**2) - 8*x**4*log(3) + 8 *x**3*exp(4*log(2)**2)*log(3) + 88*x**3*log(3) + 320*x**3 + 64*x**3*exp(4* log(2)**2) - 128*x**2*exp(4*log(2)**2) - 64*x**2*exp(4*log(2)**2)*log(3) - 384*x**2 - 320*x**2*log(3) + 384*x*log(3) + 128*x*exp(4*log(2)**2)*log(3) )*exp(-x)
Leaf count of result is larger than twice the leaf count of optimal. 855 vs. \(2 (33) = 66\).
Time = 0.17 (sec) , antiderivative size = 855, normalized size of antiderivative = 24.43 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=\text {Too large to display} \] Input:
integrate(((2*x-8)*exp(x)^2*exp(4*log(2)^2)^2+((-6*x^2+44*x-80)*exp(x)^2+( (-8*x^3+88*x^2-256*x+128)*log(3)+8*x^4-96*x^3+320*x^2-256*x)*exp(x))*exp(4 *log(2)^2)+(4*x^3-42*x^2+146*x-168)*exp(x)^2+((8*x^4-120*x^3+584*x^2-1024* x+384)*log(3)-8*x^5+128*x^4-672*x^3+1344*x^2-768*x)*exp(x)+(-32*x^4+320*x^ 3-896*x^2+512*x)*log(3)^2+(64*x^5-672*x^4+2048*x^3-1536*x^2)*log(3)-32*x^6 +352*x^5-1152*x^4+1024*x^3)/exp(x)^2,x, algorithm="maxima")
Output:
x^4 - 2*x^3*e^(4*log(2)^2) + 8*(2*x^4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)* log(3)^2 - 40*(4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3)^2 + 224*(2*x^2 + 2 *x + 1)*e^(-2*x)*log(3)^2 - 128*(2*x + 1)*e^(-2*x)*log(3)^2 - 14*x^3 + x^2 *e^(8*log(2)^2) + 22*x^2*e^(4*log(2)^2) - 8*(x^4 + 4*x^3 + 12*x^2 + 24*x + 24)*e^(-x)*log(3) + 8*(x^3*e^(4*log(2)^2) + 3*x^2*e^(4*log(2)^2) + 6*x*e^ (4*log(2)^2) + 6*e^(4*log(2)^2))*e^(-x)*log(3) + 120*(x^3 + 3*x^2 + 6*x + 6)*e^(-x)*log(3) - 88*(x^2*e^(4*log(2)^2) + 2*x*e^(4*log(2)^2) + 2*e^(4*lo g(2)^2))*e^(-x)*log(3) - 584*(x^2 + 2*x + 2)*e^(-x)*log(3) + 256*(x*e^(4*l og(2)^2) + e^(4*log(2)^2))*e^(-x)*log(3) + 1024*(x + 1)*e^(-x)*log(3) - 8* (4*x^5 + 10*x^4 + 20*x^3 + 30*x^2 + 30*x + 15)*e^(-2*x)*log(3) + 168*(2*x^ 4 + 4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3) - 256*(4*x^3 + 6*x^2 + 6*x + 3)*e^(-2*x)*log(3) + 384*(2*x^2 + 2*x + 1)*e^(-2*x)*log(3) + 73*x^2 - 8*x* e^(8*log(2)^2) - 80*x*e^(4*log(2)^2) + 8*(x^5 + 5*x^4 + 20*x^3 + 60*x^2 + 120*x + 120)*e^(-x) - 8*(x^4*e^(4*log(2)^2) + 4*x^3*e^(4*log(2)^2) + 12*x^ 2*e^(4*log(2)^2) + 24*x*e^(4*log(2)^2) + 24*e^(4*log(2)^2))*e^(-x) - 128*( x^4 + 4*x^3 + 12*x^2 + 24*x + 24)*e^(-x) + 96*(x^3*e^(4*log(2)^2) + 3*x^2* e^(4*log(2)^2) + 6*x*e^(4*log(2)^2) + 6*e^(4*log(2)^2))*e^(-x) + 672*(x^3 + 3*x^2 + 6*x + 6)*e^(-x) - 320*(x^2*e^(4*log(2)^2) + 2*x*e^(4*log(2)^2) + 2*e^(4*log(2)^2))*e^(-x) - 1344*(x^2 + 2*x + 2)*e^(-x) + 256*(x*e^(4*log( 2)^2) + e^(4*log(2)^2))*e^(-x) + 768*(x + 1)*e^(-x) + 4*(4*x^6 + 12*x^5...
Leaf count of result is larger than twice the leaf count of optimal. 349 vs. \(2 (33) = 66\).
Time = 0.12 (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 \] Input:
integrate(((2*x-8)*exp(x)^2*exp(4*log(2)^2)^2+((-6*x^2+44*x-80)*exp(x)^2+( (-8*x^3+88*x^2-256*x+128)*log(3)+8*x^4-96*x^3+320*x^2-256*x)*exp(x))*exp(4 *log(2)^2)+(4*x^3-42*x^2+146*x-168)*exp(x)^2+((8*x^4-120*x^3+584*x^2-1024* x+384)*log(3)-8*x^5+128*x^4-672*x^3+1344*x^2-768*x)*exp(x)+(-32*x^4+320*x^ 3-896*x^2+512*x)*log(3)^2+(64*x^5-672*x^4+2048*x^3-1536*x^2)*log(3)-32*x^6 +352*x^5-1152*x^4+1024*x^3)/exp(x)^2,x, algorithm="giac")
Output:
16*x^6*e^(-2*x) - 32*x^5*e^(-2*x)*log(3) + 16*x^4*e^(-2*x)*log(3)^2 + 8*x^ 5*e^(-x) - 128*x^5*e^(-2*x) - 8*x^4*e^(-x)*log(3) + 256*x^4*e^(-2*x)*log(3 ) - 128*x^3*e^(-2*x)*log(3)^2 - 8*x^4*e^(4*log(2)^2 - x) - 88*x^4*e^(-x) + 256*x^4*e^(-2*x) + 8*x^3*e^(4*log(2)^2 - x)*log(3) + 88*x^3*e^(-x)*log(3) - 512*x^3*e^(-2*x)*log(3) + 256*x^2*e^(-2*x)*log(3)^2 + x^4 - 2*x^3*e^(4* log(2)^2) + 64*x^3*e^(4*log(2)^2 - x) + 320*x^3*e^(-x) - 64*x^2*e^(4*log(2 )^2 - x)*log(3) - 320*x^2*e^(-x)*log(3) - 14*x^3 + x^2*e^(8*log(2)^2) + 22 *x^2*e^(4*log(2)^2) - 128*x^2*e^(4*log(2)^2 - x) - 384*x^2*e^(-x) + 128*x* e^(4*log(2)^2 - x)*log(3) + 384*x*e^(-x)*log(3) + 73*x^2 - 8*x*e^(8*log(2) ^2) - 80*x*e^(4*log(2)^2) - 168*x
Time = 4.66 (sec) , antiderivative size = 229, normalized size of antiderivative = 6.54 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx={\mathrm {e}}^{-x}\,\left (8\,x^5+\left (-8\,\ln \left (3\right )-8\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}-88\right )\,x^4+\left (88\,\ln \left (3\right )+64\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+8\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}\,\ln \left (3\right )+320\right )\,x^3+\left (-320\,\ln \left (3\right )-128\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}-64\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}\,\ln \left (3\right )-384\right )\,x^2+128\,\ln \left (3\right )\,\left ({\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+3\right )\,x\right )-x\,\left (80\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+8\,{\mathrm {e}}^{8\,{\ln \left (2\right )}^2}+168\right )+x^2\,\left (22\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+{\mathrm {e}}^{8\,{\ln \left (2\right )}^2}+73\right )-x^3\,\left (2\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}+14\right )+{\mathrm {e}}^{-2\,x}\,\left (16\,x^6+\left (-32\,\ln \left (3\right )-128\right )\,x^5+\left (256\,\ln \left (3\right )+16\,{\ln \left (3\right )}^2+256\right )\,x^4-128\,\ln \left (3\right )\,\left (\ln \left (3\right )+4\right )\,x^3+256\,{\ln \left (3\right )}^2\,x^2\right )+x^4 \] Input:
int(exp(-2*x)*(log(3)^2*(512*x - 896*x^2 + 320*x^3 - 32*x^4) - log(3)*(153 6*x^2 - 2048*x^3 + 672*x^4 - 64*x^5) + exp(2*x)*(146*x - 42*x^2 + 4*x^3 - 168) + 1024*x^3 - 1152*x^4 + 352*x^5 - 32*x^6 - exp(4*log(2)^2)*(exp(2*x)* (6*x^2 - 44*x + 80) + exp(x)*(256*x + log(3)*(256*x - 88*x^2 + 8*x^3 - 128 ) - 320*x^2 + 96*x^3 - 8*x^4)) - exp(x)*(768*x - log(3)*(584*x^2 - 1024*x - 120*x^3 + 8*x^4 + 384) - 1344*x^2 + 672*x^3 - 128*x^4 + 8*x^5) + exp(2*x )*exp(8*log(2)^2)*(2*x - 8)),x)
Output:
exp(-x)*(x^3*(88*log(3) + 64*exp(4*log(2)^2) + 8*exp(4*log(2)^2)*log(3) + 320) - x^4*(8*log(3) + 8*exp(4*log(2)^2) + 88) - x^2*(320*log(3) + 128*exp (4*log(2)^2) + 64*exp(4*log(2)^2)*log(3) + 384) + 8*x^5 + 128*x*log(3)*(ex p(4*log(2)^2) + 3)) - x*(80*exp(4*log(2)^2) + 8*exp(8*log(2)^2) + 168) + x ^2*(22*exp(4*log(2)^2) + exp(8*log(2)^2) + 73) - x^3*(2*exp(4*log(2)^2) + 14) + exp(-2*x)*(256*x^2*log(3)^2 - x^5*(32*log(3) + 128) + x^4*(256*log(3 ) + 16*log(3)^2 + 256) + 16*x^6 - 128*x^3*log(3)*(log(3) + 4)) + x^4
Time = 0.18 (sec) , antiderivative size = 333, normalized size of antiderivative = 9.51 \[ \int e^{-2 x} \left (1024 x^3-1152 x^4+352 x^5-32 x^6+e^{2 x+2 \log ^2(4)} (-8+2 x)+e^{2 x} \left (-168+146 x-42 x^2+4 x^3\right )+\left (-1536 x^2+2048 x^3-672 x^4+64 x^5\right ) \log (3)+\left (512 x-896 x^2+320 x^3-32 x^4\right ) \log ^2(3)+e^x \left (-768 x+1344 x^2-672 x^3+128 x^4-8 x^5+\left (384-1024 x+584 x^2-120 x^3+8 x^4\right ) \log (3)\right )+e^{\log ^2(4)} \left (e^{2 x} \left (-80+44 x-6 x^2\right )+e^x \left (-256 x+320 x^2-96 x^3+8 x^4+\left (128-256 x+88 x^2-8 x^3\right ) \log (3)\right )\right )\right ) \, dx=\frac {x \left (-32 \,\mathrm {log}\left (3\right ) x^{4}+e^{2 x} x^{3}-14 e^{2 x} x^{2}+8 e^{x} x^{4}-88 e^{x} x^{3}+256 \,\mathrm {log}\left (3\right ) x^{3}+256 \mathrm {log}\left (3\right )^{2} x +16 x^{5}-128 \mathrm {log}\left (3\right )^{2} x^{2}+256 x^{3}+320 e^{x} x^{2}+73 e^{2 x} x -8 e^{8 \mathrm {log}\left (2\right )^{2}+2 x}-80 e^{4 \mathrm {log}\left (2\right )^{2}+2 x}+e^{8 \mathrm {log}\left (2\right )^{2}+2 x} x -2 e^{4 \mathrm {log}\left (2\right )^{2}+2 x} x^{2}+22 e^{4 \mathrm {log}\left (2\right )^{2}+2 x} x +128 e^{4 \mathrm {log}\left (2\right )^{2}+x} \mathrm {log}\left (3\right )-8 e^{4 \mathrm {log}\left (2\right )^{2}+x} x^{3}+64 e^{4 \mathrm {log}\left (2\right )^{2}+x} x^{2}-128 e^{4 \mathrm {log}\left (2\right )^{2}+x} x +384 e^{x} \mathrm {log}\left (3\right )-168 e^{2 x}-128 x^{4}-384 e^{x} x +8 e^{4 \mathrm {log}\left (2\right )^{2}+x} \mathrm {log}\left (3\right ) x^{2}-64 e^{4 \mathrm {log}\left (2\right )^{2}+x} \mathrm {log}\left (3\right ) x -8 e^{x} \mathrm {log}\left (3\right ) x^{3}+88 e^{x} \mathrm {log}\left (3\right ) x^{2}-320 e^{x} \mathrm {log}\left (3\right ) x +16 \mathrm {log}\left (3\right )^{2} x^{3}-512 \,\mathrm {log}\left (3\right ) x^{2}\right )}{e^{2 x}} \] Input:
int(((2*x-8)*exp(x)^2*exp(4*log(2)^2)^2+((-6*x^2+44*x-80)*exp(x)^2+((-8*x^ 3+88*x^2-256*x+128)*log(3)+8*x^4-96*x^3+320*x^2-256*x)*exp(x))*exp(4*log(2 )^2)+(4*x^3-42*x^2+146*x-168)*exp(x)^2+((8*x^4-120*x^3+584*x^2-1024*x+384) *log(3)-8*x^5+128*x^4-672*x^3+1344*x^2-768*x)*exp(x)+(-32*x^4+320*x^3-896* x^2+512*x)*log(3)^2+(64*x^5-672*x^4+2048*x^3-1536*x^2)*log(3)-32*x^6+352*x ^5-1152*x^4+1024*x^3)/exp(x)^2,x)
Output:
(x*(e**(8*log(2)**2 + 2*x)*x - 8*e**(8*log(2)**2 + 2*x) - 2*e**(4*log(2)** 2 + 2*x)*x**2 + 22*e**(4*log(2)**2 + 2*x)*x - 80*e**(4*log(2)**2 + 2*x) + 8*e**(4*log(2)**2 + x)*log(3)*x**2 - 64*e**(4*log(2)**2 + x)*log(3)*x + 12 8*e**(4*log(2)**2 + x)*log(3) - 8*e**(4*log(2)**2 + x)*x**3 + 64*e**(4*log (2)**2 + x)*x**2 - 128*e**(4*log(2)**2 + x)*x + e**(2*x)*x**3 - 14*e**(2*x )*x**2 + 73*e**(2*x)*x - 168*e**(2*x) - 8*e**x*log(3)*x**3 + 88*e**x*log(3 )*x**2 - 320*e**x*log(3)*x + 384*e**x*log(3) + 8*e**x*x**4 - 88*e**x*x**3 + 320*e**x*x**2 - 384*e**x*x + 16*log(3)**2*x**3 - 128*log(3)**2*x**2 + 25 6*log(3)**2*x - 32*log(3)*x**4 + 256*log(3)*x**3 - 512*log(3)*x**2 + 16*x* *5 - 128*x**4 + 256*x**3))/e**(2*x)