Integrand size = 288, antiderivative size = 19 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx=\left (-e^{x^2}+2 x+(5+\log (2))^2\right )^4 \end {dmath*}
Time = 0.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx=\left (-e^{x^2}+2 x+(5+\log (2))^2\right )^4 \end {dmath*}
Integrate[125000 + 30000*x + 8*E^(4*x^2)*x + 2400*x^2 + 64*x^3 + (150000 + 24000*x + 960*x^2)*Log[2] + (75000 + 7200*x + 96*x^2)*Log[2]^2 + (20000 + 960*x)*Log[2]^3 + (3000 + 48*x)*Log[2]^4 + 240*Log[2]^5 + 8*Log[2]^6 + E^ (3*x^2)*(-8 - 600*x - 48*x^2 - 240*x*Log[2] - 24*x*Log[2]^2) + E^(2*x^2)*( 600 + 15048*x + 2400*x^2 + 96*x^3 + (240 + 12000*x + 960*x^2)*Log[2] + (24 + 3600*x + 96*x^2)*Log[2]^2 + 480*x*Log[2]^3 + 24*x*Log[2]^4) + E^x^2*(-1 5000 - 127400*x - 30096*x^2 - 2400*x^3 - 64*x^4 + (-12000 - 150960*x - 240 00*x^2 - 960*x^3)*Log[2] + (-3600 - 75096*x - 7200*x^2 - 96*x^3)*Log[2]^2 + (-480 - 20000*x - 960*x^2)*Log[2]^3 + (-24 - 3000*x - 48*x^2)*Log[2]^4 - 240*x*Log[2]^5 - 8*x*Log[2]^6),x]
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 0.71 (sec) , antiderivative size = 362, normalized size of antiderivative = 19.05, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.003, Rules used = {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.
| \(\displaystyle \int \left (64 x^3+2400 x^2+8 e^{4 x^2} x+e^{3 x^2} \left (-48 x^2-600 x-24 x \log ^2(2)-240 x \log (2)-8\right )+\left (96 x^2+7200 x+75000\right ) \log ^2(2)+\left (960 x^2+24000 x+150000\right ) \log (2)+e^{2 x^2} \left (96 x^3+2400 x^2+\left (96 x^2+3600 x+24\right ) \log ^2(2)+\left (960 x^2+12000 x+240\right ) \log (2)+15048 x+24 x \log ^4(2)+480 x \log ^3(2)+600\right )+e^{x^2} \left (-64 x^4-2400 x^3-30096 x^2+\left (-48 x^2-3000 x-24\right ) \log ^4(2)+\left (-960 x^2-20000 x-480\right ) \log ^3(2)+\left (-96 x^3-7200 x^2-75096 x-3600\right ) \log ^2(2)+\left (-960 x^3-24000 x^2-150960 x-12000\right ) \log (2)-127400 x-8 x \log ^6(2)-240 x \log ^5(2)-15000\right )+30000 x+(48 x+3000) \log ^4(2)+(960 x+20000) \log ^3(2)+125000+8 \log ^6(2)+240 \log ^5(2)\right ) \, dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -24 \sqrt {\pi } \text {erfi}(x)+12 \sqrt {\pi } \left (627+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right ) \text {erfi}(x)-12 \sqrt {\pi } (5+\log (2))^4 \text {erfi}(x)+16 x^4+800 x^3+32 x^3 \log ^2(2)+24 e^{2 x^2} x^2+15000 x^2+48 e^{x^2} x-8 e^{3 x^2} x-12 e^{2 x^2}+e^{4 x^2}+3600 x^2 \log ^2(2)-24 e^{x^2} x \left (627+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right )-4 e^{x^2} (5+\log (2))^2 \left (637+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right )+6 e^{2 x^2} \left (627+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right )-48 e^{x^2} x^2 (5+\log (2))^2+24 e^{2 x^2} x (5+\log (2))^2+48 e^{x^2} (5+\log (2))^2-4 e^{3 x^2} (5+\log (2))^2-32 e^{x^2} x^3+6 (2 x+125)^2 \log ^4(2)+\frac {40}{3} (6 x+125)^2 \log ^3(2)+75000 x \log ^2(2)+8 x \left (15625+\log ^6(2)+30 \log ^5(2)\right )+40 (2 x+25)^3 \log (2)\) |
Int[125000 + 30000*x + 8*E^(4*x^2)*x + 2400*x^2 + 64*x^3 + (150000 + 24000 *x + 960*x^2)*Log[2] + (75000 + 7200*x + 96*x^2)*Log[2]^2 + (20000 + 960*x )*Log[2]^3 + (3000 + 48*x)*Log[2]^4 + 240*Log[2]^5 + 8*Log[2]^6 + E^(3*x^2 )*(-8 - 600*x - 48*x^2 - 240*x*Log[2] - 24*x*Log[2]^2) + E^(2*x^2)*(600 + 15048*x + 2400*x^2 + 96*x^3 + (240 + 12000*x + 960*x^2)*Log[2] + (24 + 360 0*x + 96*x^2)*Log[2]^2 + 480*x*Log[2]^3 + 24*x*Log[2]^4) + E^x^2*(-15000 - 127400*x - 30096*x^2 - 2400*x^3 - 64*x^4 + (-12000 - 150960*x - 24000*x^2 - 960*x^3)*Log[2] + (-3600 - 75096*x - 7200*x^2 - 96*x^3)*Log[2]^2 + (-48 0 - 20000*x - 960*x^2)*Log[2]^3 + (-24 - 3000*x - 48*x^2)*Log[2]^4 - 240*x *Log[2]^5 - 8*x*Log[2]^6),x]
-12*E^(2*x^2) + E^(4*x^2) + 48*E^x^2*x - 8*E^(3*x^2)*x + 15000*x^2 + 24*E^ (2*x^2)*x^2 + 800*x^3 - 32*E^x^2*x^3 + 16*x^4 - 24*Sqrt[Pi]*Erfi[x] + 40*( 25 + 2*x)^3*Log[2] + 75000*x*Log[2]^2 + 3600*x^2*Log[2]^2 + 32*x^3*Log[2]^ 2 + (40*(125 + 6*x)^2*Log[2]^3)/3 + 6*(125 + 2*x)^2*Log[2]^4 + 48*E^x^2*(5 + Log[2])^2 - 4*E^(3*x^2)*(5 + Log[2])^2 + 24*E^(2*x^2)*x*(5 + Log[2])^2 - 48*E^x^2*x^2*(5 + Log[2])^2 - 12*Sqrt[Pi]*Erfi[x]*(5 + Log[2])^4 + 6*E^( 2*x^2)*(627 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log[2]^4) - 24*E^x ^2*x*(627 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log[2]^4) + 12*Sqrt[ Pi]*Erfi[x]*(627 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log[2]^4) - 4 *E^x^2*(5 + Log[2])^2*(637 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log [2]^4) + 8*x*(15625 + 30*Log[2]^5 + Log[2]^6)
3.4.57.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(284\) vs. \(2(18)=36\).
Time = 0.24 (sec) , antiderivative size = 285, normalized size of antiderivative = 15.00
| method | result | size |
| norman | \({\mathrm e}^{4 x^{2}}+\left (-4 \ln \left (2\right )^{2}-40 \ln \left (2\right )-100\right ) {\mathrm e}^{3 x^{2}}+\left (32 \ln \left (2\right )^{2}+320 \ln \left (2\right )+800\right ) x^{3}+\left (6 \ln \left (2\right )^{4}+120 \ln \left (2\right )^{3}+900 \ln \left (2\right )^{2}+3000 \ln \left (2\right )+3750\right ) {\mathrm e}^{2 x^{2}}+\left (24 \ln \left (2\right )^{4}+480 \ln \left (2\right )^{3}+3600 \ln \left (2\right )^{2}+12000 \ln \left (2\right )+15000\right ) x^{2}+\left (-62500-4 \ln \left (2\right )^{6}-120 \ln \left (2\right )^{5}-1500 \ln \left (2\right )^{4}-75000 \ln \left (2\right )-37500 \ln \left (2\right )^{2}-10000 \ln \left (2\right )^{3}\right ) {\mathrm e}^{x^{2}}+\left (125000+8 \ln \left (2\right )^{6}+240 \ln \left (2\right )^{5}+3000 \ln \left (2\right )^{4}+150000 \ln \left (2\right )+75000 \ln \left (2\right )^{2}+20000 \ln \left (2\right )^{3}\right ) x +\left (-48 \ln \left (2\right )^{2}-480 \ln \left (2\right )-1200\right ) x^{2} {\mathrm e}^{x^{2}}+\left (24 \ln \left (2\right )^{2}+240 \ln \left (2\right )+600\right ) x \,{\mathrm e}^{2 x^{2}}+\left (-24 \ln \left (2\right )^{4}-480 \ln \left (2\right )^{3}-3600 \ln \left (2\right )^{2}-12000 \ln \left (2\right )-15000\right ) x \,{\mathrm e}^{x^{2}}+16 x^{4}+24 \,{\mathrm e}^{2 x^{2}} x^{2}-32 x^{3} {\mathrm e}^{x^{2}}-8 x \,{\mathrm e}^{3 x^{2}}\) | \(285\) |
| risch | \({\mathrm e}^{4 x^{2}}+\left (-4 \ln \left (2\right )^{2}-40 \ln \left (2\right )-8 x -100\right ) {\mathrm e}^{3 x^{2}}+\left (6 \ln \left (2\right )^{4}+120 \ln \left (2\right )^{3}+24 x \ln \left (2\right )^{2}+900 \ln \left (2\right )^{2}+240 x \ln \left (2\right )+24 x^{2}+3000 \ln \left (2\right )+600 x +3750\right ) {\mathrm e}^{2 x^{2}}+\left (-4 \ln \left (2\right )^{6}-120 \ln \left (2\right )^{5}-24 x \ln \left (2\right )^{4}-1500 \ln \left (2\right )^{4}-480 x \ln \left (2\right )^{3}-48 x^{2} \ln \left (2\right )^{2}-10000 \ln \left (2\right )^{3}-3600 x \ln \left (2\right )^{2}-480 x^{2} \ln \left (2\right )-32 x^{3}-37500 \ln \left (2\right )^{2}-12000 x \ln \left (2\right )-1200 x^{2}-75000 \ln \left (2\right )-15000 x -62500\right ) {\mathrm e}^{x^{2}}+8 x \ln \left (2\right )^{6}+240 x \ln \left (2\right )^{5}+24 x^{2} \ln \left (2\right )^{4}+3000 x \ln \left (2\right )^{4}+480 x^{2} \ln \left (2\right )^{3}+20000 x \ln \left (2\right )^{3}+32 x^{3} \ln \left (2\right )^{2}+3600 x^{2} \ln \left (2\right )^{2}+75000 x \ln \left (2\right )^{2}+320 x^{3} \ln \left (2\right )+12000 x^{2} \ln \left (2\right )+150000 x \ln \left (2\right )+625000 \ln \left (2\right )+16 x^{4}+800 x^{3}+15000 x^{2}+125000 x\) | \(289\) |
| default | \(125000 x -12000 x \ln \left (2\right ) {\mathrm e}^{x^{2}}+24 \,{\mathrm e}^{2 x^{2}} x^{2}-75000 \ln \left (2\right ) {\mathrm e}^{x^{2}}-8 x \,{\mathrm e}^{3 x^{2}}+8 x \ln \left (2\right )^{6}-32 x^{3} {\mathrm e}^{x^{2}}+600 x \,{\mathrm e}^{2 x^{2}}-15000 \,{\mathrm e}^{x^{2}} x -100 \,{\mathrm e}^{3 x^{2}}+{\mathrm e}^{4 x^{2}}+3750 \,{\mathrm e}^{2 x^{2}}+240 x \ln \left (2\right )^{5}+24 \ln \left (2\right )^{2} \left (\frac {4}{3} x^{3}+150 x^{2}+3125 x \right )-62500 \,{\mathrm e}^{x^{2}}+16 x^{4}+800 x^{3}+15000 x^{2}-1200 x^{2} {\mathrm e}^{x^{2}}-24 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{4} x -480 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{3} x -3600 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2} x -480 \,{\mathrm e}^{x^{2}} \ln \left (2\right ) x^{2}+24 \ln \left (2\right )^{2} {\mathrm e}^{2 x^{2}} x +240 \ln \left (2\right ) {\mathrm e}^{2 x^{2}} x -48 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2} x^{2}+160 \ln \left (2\right )^{3} \left (3 x^{2}+125 x \right )+24 \ln \left (2\right )^{4} \left (x^{2}+125 x \right )-37500 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2}-1500 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{4}-10000 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{3}-120 \ln \left (2\right )^{5} {\mathrm e}^{x^{2}}-4 \ln \left (2\right )^{6} {\mathrm e}^{x^{2}}+40 \ln \left (2\right ) \left (2 x +25\right )^{3}+900 \ln \left (2\right )^{2} {\mathrm e}^{2 x^{2}}-4 \ln \left (2\right )^{2} {\mathrm e}^{3 x^{2}}+3000 \ln \left (2\right ) {\mathrm e}^{2 x^{2}}-40 \ln \left (2\right ) {\mathrm e}^{3 x^{2}}+6 \ln \left (2\right )^{4} {\mathrm e}^{2 x^{2}}+120 \ln \left (2\right )^{3} {\mathrm e}^{2 x^{2}}\) | \(391\) |
| parallelrisch | \(-12000 x \ln \left (2\right ) {\mathrm e}^{x^{2}}+24 \,{\mathrm e}^{2 x^{2}} x^{2}-75000 \ln \left (2\right ) {\mathrm e}^{x^{2}}+24 x^{2} \ln \left (2\right )^{4}+480 x^{2} \ln \left (2\right )^{3}-8 x \,{\mathrm e}^{3 x^{2}}+20000 x \ln \left (2\right )^{3}+3000 x \ln \left (2\right )^{4}-32 x^{3} {\mathrm e}^{x^{2}}+32 x^{3} \ln \left (2\right )^{2}+600 x \,{\mathrm e}^{2 x^{2}}+75000 x \ln \left (2\right )^{2}-15000 \,{\mathrm e}^{x^{2}} x +3600 x^{2} \ln \left (2\right )^{2}+150000 x \ln \left (2\right )+12000 x^{2} \ln \left (2\right )+320 x^{3} \ln \left (2\right )-100 \,{\mathrm e}^{3 x^{2}}+{\mathrm e}^{4 x^{2}}+3750 \,{\mathrm e}^{2 x^{2}}-62500 \,{\mathrm e}^{x^{2}}+16 x^{4}+800 x^{3}+15000 x^{2}-1200 x^{2} {\mathrm e}^{x^{2}}-24 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{4} x -480 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{3} x -3600 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2} x -480 \,{\mathrm e}^{x^{2}} \ln \left (2\right ) x^{2}+24 \ln \left (2\right )^{2} {\mathrm e}^{2 x^{2}} x +240 \ln \left (2\right ) {\mathrm e}^{2 x^{2}} x -48 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2} x^{2}-37500 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2}-1500 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{4}-10000 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{3}-120 \ln \left (2\right )^{5} {\mathrm e}^{x^{2}}-4 \ln \left (2\right )^{6} {\mathrm e}^{x^{2}}+\left (125000+8 \ln \left (2\right )^{6}+240 \ln \left (2\right )^{5}\right ) x +900 \ln \left (2\right )^{2} {\mathrm e}^{2 x^{2}}-4 \ln \left (2\right )^{2} {\mathrm e}^{3 x^{2}}+3000 \ln \left (2\right ) {\mathrm e}^{2 x^{2}}-40 \ln \left (2\right ) {\mathrm e}^{3 x^{2}}+6 \ln \left (2\right )^{4} {\mathrm e}^{2 x^{2}}+120 \ln \left (2\right )^{3} {\mathrm e}^{2 x^{2}}\) | \(407\) |
| parts | \(125000 x -12000 x \ln \left (2\right ) {\mathrm e}^{x^{2}}+24 \,{\mathrm e}^{2 x^{2}} x^{2}-75000 \ln \left (2\right ) {\mathrm e}^{x^{2}}+24 x^{2} \ln \left (2\right )^{4}+480 x^{2} \ln \left (2\right )^{3}-8 x \,{\mathrm e}^{3 x^{2}}+20000 x \ln \left (2\right )^{3}+8 x \ln \left (2\right )^{6}+3000 x \ln \left (2\right )^{4}-32 x^{3} {\mathrm e}^{x^{2}}+32 x^{3} \ln \left (2\right )^{2}+600 x \,{\mathrm e}^{2 x^{2}}+75000 x \ln \left (2\right )^{2}-15000 \,{\mathrm e}^{x^{2}} x +3600 x^{2} \ln \left (2\right )^{2}+150000 x \ln \left (2\right )+12000 x^{2} \ln \left (2\right )+320 x^{3} \ln \left (2\right )-100 \,{\mathrm e}^{3 x^{2}}+{\mathrm e}^{4 x^{2}}+3750 \,{\mathrm e}^{2 x^{2}}+240 x \ln \left (2\right )^{5}-62500 \,{\mathrm e}^{x^{2}}+16 x^{4}+800 x^{3}+15000 x^{2}-1200 x^{2} {\mathrm e}^{x^{2}}-24 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{4} x -480 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{3} x -3600 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2} x -480 \,{\mathrm e}^{x^{2}} \ln \left (2\right ) x^{2}+24 \ln \left (2\right )^{2} {\mathrm e}^{2 x^{2}} x +240 \ln \left (2\right ) {\mathrm e}^{2 x^{2}} x -48 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2} x^{2}-37500 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{2}-1500 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{4}-10000 \,{\mathrm e}^{x^{2}} \ln \left (2\right )^{3}-120 \ln \left (2\right )^{5} {\mathrm e}^{x^{2}}-4 \ln \left (2\right )^{6} {\mathrm e}^{x^{2}}+900 \ln \left (2\right )^{2} {\mathrm e}^{2 x^{2}}-4 \ln \left (2\right )^{2} {\mathrm e}^{3 x^{2}}+3000 \ln \left (2\right ) {\mathrm e}^{2 x^{2}}-40 \ln \left (2\right ) {\mathrm e}^{3 x^{2}}+6 \ln \left (2\right )^{4} {\mathrm e}^{2 x^{2}}+120 \ln \left (2\right )^{3} {\mathrm e}^{2 x^{2}}\) | \(408\) |
int(8*x*exp(x^2)^4+(-24*x*ln(2)^2-240*x*ln(2)-48*x^2-600*x-8)*exp(x^2)^3+( 24*x*ln(2)^4+480*x*ln(2)^3+(96*x^2+3600*x+24)*ln(2)^2+(960*x^2+12000*x+240 )*ln(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*ln(2)^6-240*x*ln(2)^ 5+(-48*x^2-3000*x-24)*ln(2)^4+(-960*x^2-20000*x-480)*ln(2)^3+(-96*x^3-7200 *x^2-75096*x-3600)*ln(2)^2+(-960*x^3-24000*x^2-150960*x-12000)*ln(2)-64*x^ 4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*ln(2)^6+240*ln(2)^5+(48*x+ 3000)*ln(2)^4+(960*x+20000)*ln(2)^3+(96*x^2+7200*x+75000)*ln(2)^2+(960*x^2 +24000*x+150000)*ln(2)+64*x^3+2400*x^2+30000*x+125000,x,method=_RETURNVERB OSE)
exp(x^2)^4+(-4*ln(2)^2-40*ln(2)-100)*exp(x^2)^3+(32*ln(2)^2+320*ln(2)+800) *x^3+(6*ln(2)^4+120*ln(2)^3+900*ln(2)^2+3000*ln(2)+3750)*exp(x^2)^2+(24*ln (2)^4+480*ln(2)^3+3600*ln(2)^2+12000*ln(2)+15000)*x^2+(-62500-4*ln(2)^6-12 0*ln(2)^5-1500*ln(2)^4-75000*ln(2)-37500*ln(2)^2-10000*ln(2)^3)*exp(x^2)+( 125000+8*ln(2)^6+240*ln(2)^5+3000*ln(2)^4+150000*ln(2)+75000*ln(2)^2+20000 *ln(2)^3)*x+(-48*ln(2)^2-480*ln(2)-1200)*x^2*exp(x^2)+(24*ln(2)^2+240*ln(2 )+600)*x*exp(x^2)^2+(-24*ln(2)^4-480*ln(2)^3-3600*ln(2)^2-12000*ln(2)-1500 0)*x*exp(x^2)+16*x^4+24*x^2*exp(x^2)^2-32*x^3*exp(x^2)-8*exp(x^2)^3*x
Leaf count of result is larger than twice the leaf count of optimal. 257 vs. \(2 (18) = 36\).
Time = 0.28 (sec) , antiderivative size = 257, normalized size of antiderivative = 13.53 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx=8 \, x \log \left (2\right )^{6} + 240 \, x \log \left (2\right )^{5} + 24 \, {\left (x^{2} + 125 \, x\right )} \log \left (2\right )^{4} + 16 \, x^{4} + 160 \, {\left (3 \, x^{2} + 125 \, x\right )} \log \left (2\right )^{3} + 800 \, x^{3} + 8 \, {\left (4 \, x^{3} + 450 \, x^{2} + 9375 \, x\right )} \log \left (2\right )^{2} + 15000 \, x^{2} - 4 \, {\left (\log \left (2\right )^{2} + 2 \, x + 10 \, \log \left (2\right ) + 25\right )} e^{\left (3 \, x^{2}\right )} + 6 \, {\left (\log \left (2\right )^{4} + 2 \, {\left (2 \, x + 75\right )} \log \left (2\right )^{2} + 20 \, \log \left (2\right )^{3} + 4 \, x^{2} + 20 \, {\left (2 \, x + 25\right )} \log \left (2\right ) + 100 \, x + 625\right )} e^{\left (2 \, x^{2}\right )} - 4 \, {\left (\log \left (2\right )^{6} + 3 \, {\left (2 \, x + 125\right )} \log \left (2\right )^{4} + 30 \, \log \left (2\right )^{5} + 20 \, {\left (6 \, x + 125\right )} \log \left (2\right )^{3} + 8 \, x^{3} + 3 \, {\left (4 \, x^{2} + 300 \, x + 3125\right )} \log \left (2\right )^{2} + 300 \, x^{2} + 30 \, {\left (4 \, x^{2} + 100 \, x + 625\right )} \log \left (2\right ) + 3750 \, x + 15625\right )} e^{\left (x^{2}\right )} + 80 \, {\left (4 \, x^{3} + 150 \, x^{2} + 1875 \, x\right )} \log \left (2\right ) + 125000 \, x + e^{\left (4 \, x^{2}\right )} \end {dmath*}
integrate(8*x*exp(x^2)^4+(-24*x*log(2)^2-240*x*log(2)-48*x^2-600*x-8)*exp( x^2)^3+(24*x*log(2)^4+480*x*log(2)^3+(96*x^2+3600*x+24)*log(2)^2+(960*x^2+ 12000*x+240)*log(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*log(2)^6 -240*x*log(2)^5+(-48*x^2-3000*x-24)*log(2)^4+(-960*x^2-20000*x-480)*log(2) ^3+(-96*x^3-7200*x^2-75096*x-3600)*log(2)^2+(-960*x^3-24000*x^2-150960*x-1 2000)*log(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*log(2)^6 +240*log(2)^5+(48*x+3000)*log(2)^4+(960*x+20000)*log(2)^3+(96*x^2+7200*x+7 5000)*log(2)^2+(960*x^2+24000*x+150000)*log(2)+64*x^3+2400*x^2+30000*x+125 000,x, algorithm=\
8*x*log(2)^6 + 240*x*log(2)^5 + 24*(x^2 + 125*x)*log(2)^4 + 16*x^4 + 160*( 3*x^2 + 125*x)*log(2)^3 + 800*x^3 + 8*(4*x^3 + 450*x^2 + 9375*x)*log(2)^2 + 15000*x^2 - 4*(log(2)^2 + 2*x + 10*log(2) + 25)*e^(3*x^2) + 6*(log(2)^4 + 2*(2*x + 75)*log(2)^2 + 20*log(2)^3 + 4*x^2 + 20*(2*x + 25)*log(2) + 100 *x + 625)*e^(2*x^2) - 4*(log(2)^6 + 3*(2*x + 125)*log(2)^4 + 30*log(2)^5 + 20*(6*x + 125)*log(2)^3 + 8*x^3 + 3*(4*x^2 + 300*x + 3125)*log(2)^2 + 300 *x^2 + 30*(4*x^2 + 100*x + 625)*log(2) + 3750*x + 15625)*e^(x^2) + 80*(4*x ^3 + 150*x^2 + 1875*x)*log(2) + 125000*x + e^(4*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 296 vs. \(2 (15) = 30\).
Time = 0.21 (sec) , antiderivative size = 296, normalized size of antiderivative = 15.58 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx=16 x^{4} + x^{3} \cdot \left (32 \log {\left (2 \right )}^{2} + 320 \log {\left (2 \right )} + 800\right ) + x^{2} \cdot \left (24 \log {\left (2 \right )}^{4} + 480 \log {\left (2 \right )}^{3} + 3600 \log {\left (2 \right )}^{2} + 12000 \log {\left (2 \right )} + 15000\right ) + x \left (8 \log {\left (2 \right )}^{6} + 240 \log {\left (2 \right )}^{5} + 3000 \log {\left (2 \right )}^{4} + 20000 \log {\left (2 \right )}^{3} + 75000 \log {\left (2 \right )}^{2} + 150000 \log {\left (2 \right )} + 125000\right ) + \left (- 8 x - 100 - 40 \log {\left (2 \right )} - 4 \log {\left (2 \right )}^{2}\right ) e^{3 x^{2}} + \left (24 x^{2} + 24 x \log {\left (2 \right )}^{2} + 240 x \log {\left (2 \right )} + 600 x + 6 \log {\left (2 \right )}^{4} + 120 \log {\left (2 \right )}^{3} + 900 \log {\left (2 \right )}^{2} + 3000 \log {\left (2 \right )} + 3750\right ) e^{2 x^{2}} + \left (- 32 x^{3} - 1200 x^{2} - 480 x^{2} \log {\left (2 \right )} - 48 x^{2} \log {\left (2 \right )}^{2} - 15000 x - 12000 x \log {\left (2 \right )} - 3600 x \log {\left (2 \right )}^{2} - 480 x \log {\left (2 \right )}^{3} - 24 x \log {\left (2 \right )}^{4} - 62500 - 75000 \log {\left (2 \right )} - 37500 \log {\left (2 \right )}^{2} - 10000 \log {\left (2 \right )}^{3} - 1500 \log {\left (2 \right )}^{4} - 120 \log {\left (2 \right )}^{5} - 4 \log {\left (2 \right )}^{6}\right ) e^{x^{2}} + e^{4 x^{2}} \end {dmath*}
integrate(8*x*exp(x**2)**4+(-24*x*ln(2)**2-240*x*ln(2)-48*x**2-600*x-8)*ex p(x**2)**3+(24*x*ln(2)**4+480*x*ln(2)**3+(96*x**2+3600*x+24)*ln(2)**2+(960 *x**2+12000*x+240)*ln(2)+96*x**3+2400*x**2+15048*x+600)*exp(x**2)**2+(-8*x *ln(2)**6-240*x*ln(2)**5+(-48*x**2-3000*x-24)*ln(2)**4+(-960*x**2-20000*x- 480)*ln(2)**3+(-96*x**3-7200*x**2-75096*x-3600)*ln(2)**2+(-960*x**3-24000* x**2-150960*x-12000)*ln(2)-64*x**4-2400*x**3-30096*x**2-127400*x-15000)*ex p(x**2)+8*ln(2)**6+240*ln(2)**5+(48*x+3000)*ln(2)**4+(960*x+20000)*ln(2)** 3+(96*x**2+7200*x+75000)*ln(2)**2+(960*x**2+24000*x+150000)*ln(2)+64*x**3+ 2400*x**2+30000*x+125000,x)
16*x**4 + x**3*(32*log(2)**2 + 320*log(2) + 800) + x**2*(24*log(2)**4 + 48 0*log(2)**3 + 3600*log(2)**2 + 12000*log(2) + 15000) + x*(8*log(2)**6 + 24 0*log(2)**5 + 3000*log(2)**4 + 20000*log(2)**3 + 75000*log(2)**2 + 150000* log(2) + 125000) + (-8*x - 100 - 40*log(2) - 4*log(2)**2)*exp(3*x**2) + (2 4*x**2 + 24*x*log(2)**2 + 240*x*log(2) + 600*x + 6*log(2)**4 + 120*log(2)* *3 + 900*log(2)**2 + 3000*log(2) + 3750)*exp(2*x**2) + (-32*x**3 - 1200*x* *2 - 480*x**2*log(2) - 48*x**2*log(2)**2 - 15000*x - 12000*x*log(2) - 3600 *x*log(2)**2 - 480*x*log(2)**3 - 24*x*log(2)**4 - 62500 - 75000*log(2) - 3 7500*log(2)**2 - 10000*log(2)**3 - 1500*log(2)**4 - 120*log(2)**5 - 4*log( 2)**6)*exp(x**2) + exp(4*x**2)
Leaf count of result is larger than twice the leaf count of optimal. 259 vs. \(2 (18) = 36\).
Time = 0.31 (sec) , antiderivative size = 259, normalized size of antiderivative = 13.63 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx=8 \, x \log \left (2\right )^{6} + 240 \, x \log \left (2\right )^{5} + 24 \, {\left (x^{2} + 125 \, x\right )} \log \left (2\right )^{4} + 16 \, x^{4} + 160 \, {\left (3 \, x^{2} + 125 \, x\right )} \log \left (2\right )^{3} + 800 \, x^{3} + 8 \, {\left (4 \, x^{3} + 450 \, x^{2} + 9375 \, x\right )} \log \left (2\right )^{2} + 15000 \, x^{2} - 4 \, {\left (\log \left (2\right )^{2} + 2 \, x + 10 \, \log \left (2\right ) + 25\right )} e^{\left (3 \, x^{2}\right )} + 6 \, {\left (\log \left (2\right )^{4} + 20 \, \log \left (2\right )^{3} + 4 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x + 4 \, x^{2} + 150 \, \log \left (2\right )^{2} + 500 \, \log \left (2\right ) + 625\right )} e^{\left (2 \, x^{2}\right )} - 4 \, {\left (\log \left (2\right )^{6} + 30 \, \log \left (2\right )^{5} + 375 \, \log \left (2\right )^{4} + 12 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2} + 8 \, x^{3} + 2500 \, \log \left (2\right )^{3} + 6 \, {\left (\log \left (2\right )^{4} + 20 \, \log \left (2\right )^{3} + 150 \, \log \left (2\right )^{2} + 500 \, \log \left (2\right ) + 625\right )} x + 9375 \, \log \left (2\right )^{2} + 18750 \, \log \left (2\right ) + 15625\right )} e^{\left (x^{2}\right )} + 80 \, {\left (4 \, x^{3} + 150 \, x^{2} + 1875 \, x\right )} \log \left (2\right ) + 125000 \, x + e^{\left (4 \, x^{2}\right )} \end {dmath*}
integrate(8*x*exp(x^2)^4+(-24*x*log(2)^2-240*x*log(2)-48*x^2-600*x-8)*exp( x^2)^3+(24*x*log(2)^4+480*x*log(2)^3+(96*x^2+3600*x+24)*log(2)^2+(960*x^2+ 12000*x+240)*log(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*log(2)^6 -240*x*log(2)^5+(-48*x^2-3000*x-24)*log(2)^4+(-960*x^2-20000*x-480)*log(2) ^3+(-96*x^3-7200*x^2-75096*x-3600)*log(2)^2+(-960*x^3-24000*x^2-150960*x-1 2000)*log(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*log(2)^6 +240*log(2)^5+(48*x+3000)*log(2)^4+(960*x+20000)*log(2)^3+(96*x^2+7200*x+7 5000)*log(2)^2+(960*x^2+24000*x+150000)*log(2)+64*x^3+2400*x^2+30000*x+125 000,x, algorithm=\
8*x*log(2)^6 + 240*x*log(2)^5 + 24*(x^2 + 125*x)*log(2)^4 + 16*x^4 + 160*( 3*x^2 + 125*x)*log(2)^3 + 800*x^3 + 8*(4*x^3 + 450*x^2 + 9375*x)*log(2)^2 + 15000*x^2 - 4*(log(2)^2 + 2*x + 10*log(2) + 25)*e^(3*x^2) + 6*(log(2)^4 + 20*log(2)^3 + 4*(log(2)^2 + 10*log(2) + 25)*x + 4*x^2 + 150*log(2)^2 + 5 00*log(2) + 625)*e^(2*x^2) - 4*(log(2)^6 + 30*log(2)^5 + 375*log(2)^4 + 12 *(log(2)^2 + 10*log(2) + 25)*x^2 + 8*x^3 + 2500*log(2)^3 + 6*(log(2)^4 + 2 0*log(2)^3 + 150*log(2)^2 + 500*log(2) + 625)*x + 9375*log(2)^2 + 18750*lo g(2) + 15625)*e^(x^2) + 80*(4*x^3 + 150*x^2 + 1875*x)*log(2) + 125000*x + e^(4*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 271 vs. \(2 (18) = 36\).
Time = 0.26 (sec) , antiderivative size = 271, normalized size of antiderivative = 14.26 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx=8 \, x \log \left (2\right )^{6} + 240 \, x \log \left (2\right )^{5} + 24 \, {\left (x^{2} + 125 \, x\right )} \log \left (2\right )^{4} + 16 \, x^{4} + 160 \, {\left (3 \, x^{2} + 125 \, x\right )} \log \left (2\right )^{3} + 800 \, x^{3} + 8 \, {\left (4 \, x^{3} + 450 \, x^{2} + 9375 \, x\right )} \log \left (2\right )^{2} + 15000 \, x^{2} - 4 \, {\left (\log \left (2\right )^{2} + 2 \, x + 10 \, \log \left (2\right ) + 25\right )} e^{\left (3 \, x^{2}\right )} + 6 \, {\left (\log \left (2\right )^{4} + 4 \, x \log \left (2\right )^{2} + 20 \, \log \left (2\right )^{3} + 4 \, x^{2} + 40 \, x \log \left (2\right ) + 150 \, \log \left (2\right )^{2} + 100 \, x + 500 \, \log \left (2\right ) + 625\right )} e^{\left (2 \, x^{2}\right )} - 4 \, {\left (\log \left (2\right )^{6} + 6 \, x \log \left (2\right )^{4} + 30 \, \log \left (2\right )^{5} + 12 \, x^{2} \log \left (2\right )^{2} + 120 \, x \log \left (2\right )^{3} + 375 \, \log \left (2\right )^{4} + 8 \, x^{3} + 120 \, x^{2} \log \left (2\right ) + 900 \, x \log \left (2\right )^{2} + 2500 \, \log \left (2\right )^{3} + 300 \, x^{2} + 3000 \, x \log \left (2\right ) + 9375 \, \log \left (2\right )^{2} + 3750 \, x + 18750 \, \log \left (2\right ) + 15625\right )} e^{\left (x^{2}\right )} + 80 \, {\left (4 \, x^{3} + 150 \, x^{2} + 1875 \, x\right )} \log \left (2\right ) + 125000 \, x + e^{\left (4 \, x^{2}\right )} \end {dmath*}
integrate(8*x*exp(x^2)^4+(-24*x*log(2)^2-240*x*log(2)-48*x^2-600*x-8)*exp( x^2)^3+(24*x*log(2)^4+480*x*log(2)^3+(96*x^2+3600*x+24)*log(2)^2+(960*x^2+ 12000*x+240)*log(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*log(2)^6 -240*x*log(2)^5+(-48*x^2-3000*x-24)*log(2)^4+(-960*x^2-20000*x-480)*log(2) ^3+(-96*x^3-7200*x^2-75096*x-3600)*log(2)^2+(-960*x^3-24000*x^2-150960*x-1 2000)*log(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*log(2)^6 +240*log(2)^5+(48*x+3000)*log(2)^4+(960*x+20000)*log(2)^3+(96*x^2+7200*x+7 5000)*log(2)^2+(960*x^2+24000*x+150000)*log(2)+64*x^3+2400*x^2+30000*x+125 000,x, algorithm=\
8*x*log(2)^6 + 240*x*log(2)^5 + 24*(x^2 + 125*x)*log(2)^4 + 16*x^4 + 160*( 3*x^2 + 125*x)*log(2)^3 + 800*x^3 + 8*(4*x^3 + 450*x^2 + 9375*x)*log(2)^2 + 15000*x^2 - 4*(log(2)^2 + 2*x + 10*log(2) + 25)*e^(3*x^2) + 6*(log(2)^4 + 4*x*log(2)^2 + 20*log(2)^3 + 4*x^2 + 40*x*log(2) + 150*log(2)^2 + 100*x + 500*log(2) + 625)*e^(2*x^2) - 4*(log(2)^6 + 6*x*log(2)^4 + 30*log(2)^5 + 12*x^2*log(2)^2 + 120*x*log(2)^3 + 375*log(2)^4 + 8*x^3 + 120*x^2*log(2) + 900*x*log(2)^2 + 2500*log(2)^3 + 300*x^2 + 3000*x*log(2) + 9375*log(2)^2 + 3750*x + 18750*log(2) + 15625)*e^(x^2) + 80*(4*x^3 + 150*x^2 + 1875*x)* log(2) + 125000*x + e^(4*x^2)
Time = 0.33 (sec) , antiderivative size = 231, normalized size of antiderivative = 12.16 \begin {dmath*} \int \left (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+\left (150000+24000 x+960 x^2\right ) \log (2)+\left (75000+7200 x+96 x^2\right ) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right )+e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right )+e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right )\right ) \, dx={\mathrm {e}}^{4\,x^2}-4\,{\mathrm {e}}^{3\,x^2}\,{\left (\ln \left (2\right )+5\right )}^2+6\,{\mathrm {e}}^{2\,x^2}\,{\left (\ln \left (2\right )+5\right )}^4+32\,x^3\,{\left (\ln \left (2\right )+5\right )}^2-8\,x\,{\mathrm {e}}^{3\,x^2}-32\,x^3\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^{x^2}\,\left (75000\,\ln \left (2\right )+37500\,{\ln \left (2\right )}^2+10000\,{\ln \left (2\right )}^3+1500\,{\ln \left (2\right )}^4+120\,{\ln \left (2\right )}^5+4\,{\ln \left (2\right )}^6+62500\right )+24\,x^2\,{\mathrm {e}}^{2\,x^2}+16\,x^4+x\,\left (150000\,\ln \left (2\right )+75000\,{\ln \left (2\right )}^2+20000\,{\ln \left (2\right )}^3+3000\,{\ln \left (2\right )}^4+240\,{\ln \left (2\right )}^5+8\,{\ln \left (2\right )}^6+125000\right )+x^2\,\left (12000\,\ln \left (2\right )+3600\,{\ln \left (2\right )}^2+480\,{\ln \left (2\right )}^3+24\,{\ln \left (2\right )}^4+15000\right )-24\,x\,{\mathrm {e}}^{x^2}\,{\left (\ln \left (2\right )+5\right )}^4+24\,x\,{\mathrm {e}}^{2\,x^2}\,{\left (\ln \left (2\right )+5\right )}^2-48\,x^2\,{\mathrm {e}}^{x^2}\,{\left (\ln \left (2\right )+5\right )}^2 \end {dmath*}
int(30000*x - exp(x^2)*(127400*x + log(2)*(150960*x + 24000*x^2 + 960*x^3 + 12000) + log(2)^4*(3000*x + 48*x^2 + 24) + log(2)^3*(20000*x + 960*x^2 + 480) + 240*x*log(2)^5 + 8*x*log(2)^6 + log(2)^2*(75096*x + 7200*x^2 + 96* x^3 + 3600) + 30096*x^2 + 2400*x^3 + 64*x^4 + 15000) + log(2)*(24000*x + 9 60*x^2 + 150000) - exp(3*x^2)*(600*x + 240*x*log(2) + 24*x*log(2)^2 + 48*x ^2 + 8) + log(2)^4*(48*x + 3000) + log(2)^3*(960*x + 20000) + 8*x*exp(4*x^ 2) + log(2)^2*(7200*x + 96*x^2 + 75000) + exp(2*x^2)*(15048*x + log(2)*(12 000*x + 960*x^2 + 240) + log(2)^2*(3600*x + 96*x^2 + 24) + 480*x*log(2)^3 + 24*x*log(2)^4 + 2400*x^2 + 96*x^3 + 600) + 240*log(2)^5 + 8*log(2)^6 + 2 400*x^2 + 64*x^3 + 125000,x)
exp(4*x^2) - 4*exp(3*x^2)*(log(2) + 5)^2 + 6*exp(2*x^2)*(log(2) + 5)^4 + 3 2*x^3*(log(2) + 5)^2 - 8*x*exp(3*x^2) - 32*x^3*exp(x^2) - exp(x^2)*(75000* log(2) + 37500*log(2)^2 + 10000*log(2)^3 + 1500*log(2)^4 + 120*log(2)^5 + 4*log(2)^6 + 62500) + 24*x^2*exp(2*x^2) + 16*x^4 + x*(150000*log(2) + 7500 0*log(2)^2 + 20000*log(2)^3 + 3000*log(2)^4 + 240*log(2)^5 + 8*log(2)^6 + 125000) + x^2*(12000*log(2) + 3600*log(2)^2 + 480*log(2)^3 + 24*log(2)^4 + 15000) - 24*x*exp(x^2)*(log(2) + 5)^4 + 24*x*exp(2*x^2)*(log(2) + 5)^2 - 48*x^2*exp(x^2)*(log(2) + 5)^2