3.93.34 \(\int \frac {80+460 x+540 x^2+120 x^3+e^x (-270-630 x-270 x^2-30 x^3)-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9)+(768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9) \log (2)+(-384 x^3-1104 x^4-864 x^5-144 x^6) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+(8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7) \log (2))+e^x (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+(-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8) \log (2)+(1296 x^3+864 x^4+144 x^5) \log ^2(2))} \, dx\)

Optimal. Leaf size=34 \[ \frac {5}{16 x^2 \left (2-x+\frac {3}{4} (3+x)^2 \left (-e^x+x\right )-\log (2)\right )^2} \]

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Rubi [F]  time = 7.69, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(80 + 460*x + 540*x^2 + 120*x^3 + E^x*(-270 - 630*x - 270*x^2 - 30*x^3) - 40*Log[2])/(-512*x^3 - 4416*x^4
- 16152*x^5 - 32615*x^6 - 39654*x^7 - 29709*x^8 - 13500*x^9 - 3537*x^10 - 486*x^11 - 27*x^12 + E^(3*x)*(19683*
x^3 + 39366*x^4 + 32805*x^5 + 14580*x^6 + 3645*x^7 + 486*x^8 + 27*x^9) + (768*x^3 + 4416*x^4 + 9804*x^5 + 1051
2*x^6 + 5544*x^7 + 1296*x^8 + 108*x^9)*Log[2] + (-384*x^3 - 1104*x^4 - 864*x^5 - 144*x^6)*Log[2]^2 + 64*x^3*Lo
g[2]^3 + E^(2*x)*(-17496*x^3 - 73629*x^4 - 118098*x^5 - 95175*x^6 - 42660*x^7 - 10827*x^8 - 1458*x^9 - 81*x^10
+ (8748*x^3 + 11664*x^4 + 5832*x^5 + 1296*x^6 + 108*x^7)*Log[2]) + E^x*(5184*x^3 + 33264*x^4 + 86625*x^5 + 11
8386*x^6 + 92079*x^7 + 41580*x^8 + 10719*x^9 + 1458*x^10 + 81*x^11 + (-5184*x^3 - 18360*x^4 - 22176*x^5 - 1137
6*x^6 - 2592*x^7 - 216*x^8)*Log[2] + (1296*x^3 + 864*x^4 + 144*x^5)*Log[2]^2)),x]

[Out]

(10*(29 + 20*Log[2])*Defer[Int][1/(x^2*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*E^x*x^2 - 3*x^3 - 8*(1 - Log[2]/
2))^3), x])/3 - (10*(5 + Log[256])*Defer[Int][1/(x*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*E^x*x^2 - 3*x^3 - 8*
(1 - Log[2]/2))^3), x])/9 - (80*(5 - Log[2])*Defer[Int][1/((3 + x)*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*E^x*
x^2 - 3*x^3 - 8*(1 - Log[2]/2))^3), x])/9 + (20*Defer[Int][1/((-3 - x)*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*
E^x*x^2 - 3*x^3 - 8*(1 - Log[2]/2))^2), x])/9 - 10*Defer[Int][1/(x^3*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*E^
x*x^2 - 3*x^3 - 8*(1 - Log[2]/2))^2), x] - (50*Defer[Int][1/(x^2*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*E^x*x^
2 - 3*x^3 - 8*(1 - Log[2]/2))^2), x])/3 + (20*Defer[Int][1/(x*(27*E^x - 23*x + 18*E^x*x - 18*x^2 + 3*E^x*x^2 -
3*x^3 - 8*(1 - Log[2]/2))^2), x])/9 + 150*Defer[Int][(-27*E^x + 23*x - 18*E^x*x + 18*x^2 - 3*E^x*x^2 + 3*x^3
+ 8*(1 - Log[2]/2))^(-3), x] + 30*Defer[Int][x/(-27*E^x + 23*x - 18*E^x*x + 18*x^2 - 3*E^x*x^2 + 3*x^3 + 8*(1
- Log[2]/2))^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )+x^3 \left (-512+64 \log ^3(2)\right )} \, dx\\ &=\int \frac {10 \left (-46 x-54 x^2-12 x^3+3 e^x \left (9+21 x+9 x^2+x^3\right )-8 \left (1-\frac {\log (2)}{2}\right )\right )}{x^3 \left (23 x+18 x^2+3 x^3-3 e^x (3+x)^2+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx\\ &=10 \int \frac {-46 x-54 x^2-12 x^3+3 e^x \left (9+21 x+9 x^2+x^3\right )-8 \left (1-\frac {\log (2)}{2}\right )}{x^3 \left (23 x+18 x^2+3 x^3-3 e^x (3+x)^2+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx\\ &=10 \int \left (\frac {-3-6 x-x^2}{x^3 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}+\frac {29-50 x^2-24 x^3-3 x^4+20 \log (2)+4 x (2+\log (2))}{x^2 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}\right ) \, dx\\ &=10 \int \frac {-3-6 x-x^2}{x^3 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx+10 \int \frac {29-50 x^2-24 x^3-3 x^4+20 \log (2)+4 x (2+\log (2))}{x^2 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx\\ &=10 \int \left (\frac {2}{9 (-3-x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}-\frac {1}{x^3 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}-\frac {5}{3 x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}+\frac {2}{9 x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}\right ) \, dx+10 \int \left (\frac {15}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {3 x}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {8 (-5+\log (2))}{9 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {29+20 \log (2)}{3 x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {-5-\log (256)}{9 x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}\right ) \, dx\\ &=\frac {20}{9} \int \frac {1}{(-3-x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx+\frac {20}{9} \int \frac {1}{x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx-10 \int \frac {1}{x^3 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx-\frac {50}{3} \int \frac {1}{x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx+30 \int \frac {x}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx+150 \int \frac {1}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx-\frac {1}{9} (80 (5-\log (2))) \int \frac {1}{(3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx+\frac {1}{3} (10 (29+20 \log (2))) \int \frac {1}{x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx-\frac {1}{9} (10 (5+\log (256))) \int \frac {1}{x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.60, size = 36, normalized size = 1.06 \begin {gather*} \frac {5}{x^2 \left (8+23 x+18 x^2+3 x^3-3 e^x (3+x)^2-\log (16)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(80 + 460*x + 540*x^2 + 120*x^3 + E^x*(-270 - 630*x - 270*x^2 - 30*x^3) - 40*Log[2])/(-512*x^3 - 441
6*x^4 - 16152*x^5 - 32615*x^6 - 39654*x^7 - 29709*x^8 - 13500*x^9 - 3537*x^10 - 486*x^11 - 27*x^12 + E^(3*x)*(
19683*x^3 + 39366*x^4 + 32805*x^5 + 14580*x^6 + 3645*x^7 + 486*x^8 + 27*x^9) + (768*x^3 + 4416*x^4 + 9804*x^5
+ 10512*x^6 + 5544*x^7 + 1296*x^8 + 108*x^9)*Log[2] + (-384*x^3 - 1104*x^4 - 864*x^5 - 144*x^6)*Log[2]^2 + 64*
x^3*Log[2]^3 + E^(2*x)*(-17496*x^3 - 73629*x^4 - 118098*x^5 - 95175*x^6 - 42660*x^7 - 10827*x^8 - 1458*x^9 - 8
1*x^10 + (8748*x^3 + 11664*x^4 + 5832*x^5 + 1296*x^6 + 108*x^7)*Log[2]) + E^x*(5184*x^3 + 33264*x^4 + 86625*x^
5 + 118386*x^6 + 92079*x^7 + 41580*x^8 + 10719*x^9 + 1458*x^10 + 81*x^11 + (-5184*x^3 - 18360*x^4 - 22176*x^5
- 11376*x^6 - 2592*x^7 - 216*x^8)*Log[2] + (1296*x^3 + 864*x^4 + 144*x^5)*Log[2]^2)),x]

[Out]

5/(x^2*(8 + 23*x + 18*x^2 + 3*x^3 - 3*E^x*(3 + x)^2 - Log[16])^2)

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fricas [B]  time = 0.73, size = 157, normalized size = 4.62 \begin {gather*} \frac {5}{9 \, x^{8} + 108 \, x^{7} + 462 \, x^{6} + 876 \, x^{5} + 817 \, x^{4} + 16 \, x^{2} \log \relax (2)^{2} + 368 \, x^{3} + 64 \, x^{2} + 9 \, {\left (x^{6} + 12 \, x^{5} + 54 \, x^{4} + 108 \, x^{3} + 81 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (3 \, x^{7} + 36 \, x^{6} + 158 \, x^{5} + 308 \, x^{4} + 255 \, x^{3} + 72 \, x^{2} - 4 \, {\left (x^{4} + 6 \, x^{3} + 9 \, x^{2}\right )} \log \relax (2)\right )} e^{x} - 8 \, {\left (3 \, x^{5} + 18 \, x^{4} + 23 \, x^{3} + 8 \, x^{2}\right )} \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-30*x^3-270*x^2-630*x-270)*exp(x)-40*log(2)+120*x^3+540*x^2+460*x+80)/((27*x^9+486*x^8+3645*x^7+14
580*x^6+32805*x^5+39366*x^4+19683*x^3)*exp(x)^3+((108*x^7+1296*x^6+5832*x^5+11664*x^4+8748*x^3)*log(2)-81*x^10
-1458*x^9-10827*x^8-42660*x^7-95175*x^6-118098*x^5-73629*x^4-17496*x^3)*exp(x)^2+((144*x^5+864*x^4+1296*x^3)*l
og(2)^2+(-216*x^8-2592*x^7-11376*x^6-22176*x^5-18360*x^4-5184*x^3)*log(2)+81*x^11+1458*x^10+10719*x^9+41580*x^
8+92079*x^7+118386*x^6+86625*x^5+33264*x^4+5184*x^3)*exp(x)+64*x^3*log(2)^3+(-144*x^6-864*x^5-1104*x^4-384*x^3
)*log(2)^2+(108*x^9+1296*x^8+5544*x^7+10512*x^6+9804*x^5+4416*x^4+768*x^3)*log(2)-27*x^12-486*x^11-3537*x^10-1
3500*x^9-29709*x^8-39654*x^7-32615*x^6-16152*x^5-4416*x^4-512*x^3),x, algorithm="fricas")

[Out]

5/(9*x^8 + 108*x^7 + 462*x^6 + 876*x^5 + 817*x^4 + 16*x^2*log(2)^2 + 368*x^3 + 64*x^2 + 9*(x^6 + 12*x^5 + 54*x
^4 + 108*x^3 + 81*x^2)*e^(2*x) - 6*(3*x^7 + 36*x^6 + 158*x^5 + 308*x^4 + 255*x^3 + 72*x^2 - 4*(x^4 + 6*x^3 + 9
*x^2)*log(2))*e^x - 8*(3*x^5 + 18*x^4 + 23*x^3 + 8*x^2)*log(2))

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giac [B]  time = 0.55, size = 191, normalized size = 5.62 \begin {gather*} \frac {5}{9 \, x^{8} - 18 \, x^{7} e^{x} + 108 \, x^{7} + 9 \, x^{6} e^{\left (2 \, x\right )} - 216 \, x^{6} e^{x} + 462 \, x^{6} + 108 \, x^{5} e^{\left (2 \, x\right )} - 948 \, x^{5} e^{x} - 24 \, x^{5} \log \relax (2) + 24 \, x^{4} e^{x} \log \relax (2) + 876 \, x^{5} + 486 \, x^{4} e^{\left (2 \, x\right )} - 1848 \, x^{4} e^{x} - 144 \, x^{4} \log \relax (2) + 144 \, x^{3} e^{x} \log \relax (2) + 817 \, x^{4} + 972 \, x^{3} e^{\left (2 \, x\right )} - 1530 \, x^{3} e^{x} - 184 \, x^{3} \log \relax (2) + 216 \, x^{2} e^{x} \log \relax (2) + 16 \, x^{2} \log \relax (2)^{2} + 368 \, x^{3} + 729 \, x^{2} e^{\left (2 \, x\right )} - 432 \, x^{2} e^{x} - 64 \, x^{2} \log \relax (2) + 64 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-30*x^3-270*x^2-630*x-270)*exp(x)-40*log(2)+120*x^3+540*x^2+460*x+80)/((27*x^9+486*x^8+3645*x^7+14
580*x^6+32805*x^5+39366*x^4+19683*x^3)*exp(x)^3+((108*x^7+1296*x^6+5832*x^5+11664*x^4+8748*x^3)*log(2)-81*x^10
-1458*x^9-10827*x^8-42660*x^7-95175*x^6-118098*x^5-73629*x^4-17496*x^3)*exp(x)^2+((144*x^5+864*x^4+1296*x^3)*l
og(2)^2+(-216*x^8-2592*x^7-11376*x^6-22176*x^5-18360*x^4-5184*x^3)*log(2)+81*x^11+1458*x^10+10719*x^9+41580*x^
8+92079*x^7+118386*x^6+86625*x^5+33264*x^4+5184*x^3)*exp(x)+64*x^3*log(2)^3+(-144*x^6-864*x^5-1104*x^4-384*x^3
)*log(2)^2+(108*x^9+1296*x^8+5544*x^7+10512*x^6+9804*x^5+4416*x^4+768*x^3)*log(2)-27*x^12-486*x^11-3537*x^10-1
3500*x^9-29709*x^8-39654*x^7-32615*x^6-16152*x^5-4416*x^4-512*x^3),x, algorithm="giac")

[Out]

5/(9*x^8 - 18*x^7*e^x + 108*x^7 + 9*x^6*e^(2*x) - 216*x^6*e^x + 462*x^6 + 108*x^5*e^(2*x) - 948*x^5*e^x - 24*x
^5*log(2) + 24*x^4*e^x*log(2) + 876*x^5 + 486*x^4*e^(2*x) - 1848*x^4*e^x - 144*x^4*log(2) + 144*x^3*e^x*log(2)
+ 817*x^4 + 972*x^3*e^(2*x) - 1530*x^3*e^x - 184*x^3*log(2) + 216*x^2*e^x*log(2) + 16*x^2*log(2)^2 + 368*x^3
+ 729*x^2*e^(2*x) - 432*x^2*e^x - 64*x^2*log(2) + 64*x^2)

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maple [A]  time = 0.10, size = 43, normalized size = 1.26

method	result	size
risch	\(\frac {5}{x^{2} \left (3 \,{\mathrm e}^{x} x^{2}-3 x^{3}+18 \,{\mathrm e}^{x} x -18 x^{2}+4 \ln \relax (2)+27 \,{\mathrm e}^{x}-23 x -8\right )^{2}}\)	\(43\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-30*x^3-270*x^2-630*x-270)*exp(x)-40*ln(2)+120*x^3+540*x^2+460*x+80)/((27*x^9+486*x^8+3645*x^7+14580*x^6
+32805*x^5+39366*x^4+19683*x^3)*exp(x)^3+((108*x^7+1296*x^6+5832*x^5+11664*x^4+8748*x^3)*ln(2)-81*x^10-1458*x^
9-10827*x^8-42660*x^7-95175*x^6-118098*x^5-73629*x^4-17496*x^3)*exp(x)^2+((144*x^5+864*x^4+1296*x^3)*ln(2)^2+(
-216*x^8-2592*x^7-11376*x^6-22176*x^5-18360*x^4-5184*x^3)*ln(2)+81*x^11+1458*x^10+10719*x^9+41580*x^8+92079*x^
7+118386*x^6+86625*x^5+33264*x^4+5184*x^3)*exp(x)+64*x^3*ln(2)^3+(-144*x^6-864*x^5-1104*x^4-384*x^3)*ln(2)^2+(
108*x^9+1296*x^8+5544*x^7+10512*x^6+9804*x^5+4416*x^4+768*x^3)*ln(2)-27*x^12-486*x^11-3537*x^10-13500*x^9-2970
9*x^8-39654*x^7-32615*x^6-16152*x^5-4416*x^4-512*x^3),x,method=_RETURNVERBOSE)

[Out]

5/x^2/(3*exp(x)*x^2-3*x^3+18*exp(x)*x-18*x^2+4*ln(2)+27*exp(x)-23*x-8)^2

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maxima [B]  time = 1.31, size = 145, normalized size = 4.26 \begin {gather*} \frac {5}{9 \, x^{8} + 108 \, x^{7} + 462 \, x^{6} - 12 \, x^{5} {\left (2 \, \log \relax (2) - 73\right )} - x^{4} {\left (144 \, \log \relax (2) - 817\right )} - 184 \, x^{3} {\left (\log \relax (2) - 2\right )} + 16 \, {\left (\log \relax (2)^{2} - 4 \, \log \relax (2) + 4\right )} x^{2} + 9 \, {\left (x^{6} + 12 \, x^{5} + 54 \, x^{4} + 108 \, x^{3} + 81 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (3 \, x^{7} + 36 \, x^{6} + 158 \, x^{5} - 4 \, x^{4} {\left (\log \relax (2) - 77\right )} - 3 \, x^{3} {\left (8 \, \log \relax (2) - 85\right )} - 36 \, x^{2} {\left (\log \relax (2) - 2\right )}\right )} e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-30*x^3-270*x^2-630*x-270)*exp(x)-40*log(2)+120*x^3+540*x^2+460*x+80)/((27*x^9+486*x^8+3645*x^7+14
580*x^6+32805*x^5+39366*x^4+19683*x^3)*exp(x)^3+((108*x^7+1296*x^6+5832*x^5+11664*x^4+8748*x^3)*log(2)-81*x^10
-1458*x^9-10827*x^8-42660*x^7-95175*x^6-118098*x^5-73629*x^4-17496*x^3)*exp(x)^2+((144*x^5+864*x^4+1296*x^3)*l
og(2)^2+(-216*x^8-2592*x^7-11376*x^6-22176*x^5-18360*x^4-5184*x^3)*log(2)+81*x^11+1458*x^10+10719*x^9+41580*x^
8+92079*x^7+118386*x^6+86625*x^5+33264*x^4+5184*x^3)*exp(x)+64*x^3*log(2)^3+(-144*x^6-864*x^5-1104*x^4-384*x^3
)*log(2)^2+(108*x^9+1296*x^8+5544*x^7+10512*x^6+9804*x^5+4416*x^4+768*x^3)*log(2)-27*x^12-486*x^11-3537*x^10-1
3500*x^9-29709*x^8-39654*x^7-32615*x^6-16152*x^5-4416*x^4-512*x^3),x, algorithm="maxima")

[Out]

5/(9*x^8 + 108*x^7 + 462*x^6 - 12*x^5*(2*log(2) - 73) - x^4*(144*log(2) - 817) - 184*x^3*(log(2) - 2) + 16*(lo
g(2)^2 - 4*log(2) + 4)*x^2 + 9*(x^6 + 12*x^5 + 54*x^4 + 108*x^3 + 81*x^2)*e^(2*x) - 6*(3*x^7 + 36*x^6 + 158*x^
5 - 4*x^4*(log(2) - 77) - 3*x^3*(8*log(2) - 85) - 36*x^2*(log(2) - 2))*e^x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {460\,x-40\,\ln \relax (2)+540\,x^2+120\,x^3-{\mathrm {e}}^x\,\left (30\,x^3+270\,x^2+630\,x+270\right )+80}{{\ln \relax (2)}^2\,\left (144\,x^6+864\,x^5+1104\,x^4+384\,x^3\right )-{\mathrm {e}}^x\,\left ({\ln \relax (2)}^2\,\left (144\,x^5+864\,x^4+1296\,x^3\right )-\ln \relax (2)\,\left (216\,x^8+2592\,x^7+11376\,x^6+22176\,x^5+18360\,x^4+5184\,x^3\right )+5184\,x^3+33264\,x^4+86625\,x^5+118386\,x^6+92079\,x^7+41580\,x^8+10719\,x^9+1458\,x^{10}+81\,x^{11}\right )-64\,x^3\,{\ln \relax (2)}^3-{\mathrm {e}}^{3\,x}\,\left (27\,x^9+486\,x^8+3645\,x^7+14580\,x^6+32805\,x^5+39366\,x^4+19683\,x^3\right )-\ln \relax (2)\,\left (108\,x^9+1296\,x^8+5544\,x^7+10512\,x^6+9804\,x^5+4416\,x^4+768\,x^3\right )+512\,x^3+4416\,x^4+16152\,x^5+32615\,x^6+39654\,x^7+29709\,x^8+13500\,x^9+3537\,x^{10}+486\,x^{11}+27\,x^{12}+{\mathrm {e}}^{2\,x}\,\left (17496\,x^3-\ln \relax (2)\,\left (108\,x^7+1296\,x^6+5832\,x^5+11664\,x^4+8748\,x^3\right )+73629\,x^4+118098\,x^5+95175\,x^6+42660\,x^7+10827\,x^8+1458\,x^9+81\,x^{10}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(460*x - 40*log(2) + 540*x^2 + 120*x^3 - exp(x)*(630*x + 270*x^2 + 30*x^3 + 270) + 80)/(log(2)^2*(384*x^3
+ 1104*x^4 + 864*x^5 + 144*x^6) - exp(x)*(log(2)^2*(1296*x^3 + 864*x^4 + 144*x^5) - log(2)*(5184*x^3 + 18360*
x^4 + 22176*x^5 + 11376*x^6 + 2592*x^7 + 216*x^8) + 5184*x^3 + 33264*x^4 + 86625*x^5 + 118386*x^6 + 92079*x^7
+ 41580*x^8 + 10719*x^9 + 1458*x^10 + 81*x^11) - 64*x^3*log(2)^3 - exp(3*x)*(19683*x^3 + 39366*x^4 + 32805*x^5
+ 14580*x^6 + 3645*x^7 + 486*x^8 + 27*x^9) - log(2)*(768*x^3 + 4416*x^4 + 9804*x^5 + 10512*x^6 + 5544*x^7 + 1
296*x^8 + 108*x^9) + 512*x^3 + 4416*x^4 + 16152*x^5 + 32615*x^6 + 39654*x^7 + 29709*x^8 + 13500*x^9 + 3537*x^1
0 + 486*x^11 + 27*x^12 + exp(2*x)*(17496*x^3 - log(2)*(8748*x^3 + 11664*x^4 + 5832*x^5 + 1296*x^6 + 108*x^7) +
73629*x^4 + 118098*x^5 + 95175*x^6 + 42660*x^7 + 10827*x^8 + 1458*x^9 + 81*x^10)),x)

[Out]

int(-(460*x - 40*log(2) + 540*x^2 + 120*x^3 - exp(x)*(630*x + 270*x^2 + 30*x^3 + 270) + 80)/(log(2)^2*(384*x^3
+ 1104*x^4 + 864*x^5 + 144*x^6) - exp(x)*(log(2)^2*(1296*x^3 + 864*x^4 + 144*x^5) - log(2)*(5184*x^3 + 18360*
x^4 + 22176*x^5 + 11376*x^6 + 2592*x^7 + 216*x^8) + 5184*x^3 + 33264*x^4 + 86625*x^5 + 118386*x^6 + 92079*x^7
+ 41580*x^8 + 10719*x^9 + 1458*x^10 + 81*x^11) - 64*x^3*log(2)^3 - exp(3*x)*(19683*x^3 + 39366*x^4 + 32805*x^5
+ 14580*x^6 + 3645*x^7 + 486*x^8 + 27*x^9) - log(2)*(768*x^3 + 4416*x^4 + 9804*x^5 + 10512*x^6 + 5544*x^7 + 1
296*x^8 + 108*x^9) + 512*x^3 + 4416*x^4 + 16152*x^5 + 32615*x^6 + 39654*x^7 + 29709*x^8 + 13500*x^9 + 3537*x^1
0 + 486*x^11 + 27*x^12 + exp(2*x)*(17496*x^3 - log(2)*(8748*x^3 + 11664*x^4 + 5832*x^5 + 1296*x^6 + 108*x^7) +
73629*x^4 + 118098*x^5 + 95175*x^6 + 42660*x^7 + 10827*x^8 + 1458*x^9 + 81*x^10)), x)

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sympy [B]  time = 1.86, size = 170, normalized size = 5.00 \begin {gather*} \frac {5}{9 x^{8} + 108 x^{7} + 462 x^{6} - 24 x^{5} \log {\relax (2 )} + 876 x^{5} - 144 x^{4} \log {\relax (2 )} + 817 x^{4} - 184 x^{3} \log {\relax (2 )} + 368 x^{3} - 64 x^{2} \log {\relax (2 )} + 16 x^{2} \log {\relax (2 )}^{2} + 64 x^{2} + \left (9 x^{6} + 108 x^{5} + 486 x^{4} + 972 x^{3} + 729 x^{2}\right ) e^{2 x} + \left (- 18 x^{7} - 216 x^{6} - 948 x^{5} - 1848 x^{4} + 24 x^{4} \log {\relax (2 )} - 1530 x^{3} + 144 x^{3} \log {\relax (2 )} - 432 x^{2} + 216 x^{2} \log {\relax (2 )}\right ) e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-30*x**3-270*x**2-630*x-270)*exp(x)-40*ln(2)+120*x**3+540*x**2+460*x+80)/((27*x**9+486*x**8+3645*x
**7+14580*x**6+32805*x**5+39366*x**4+19683*x**3)*exp(x)**3+((108*x**7+1296*x**6+5832*x**5+11664*x**4+8748*x**3
)*ln(2)-81*x**10-1458*x**9-10827*x**8-42660*x**7-95175*x**6-118098*x**5-73629*x**4-17496*x**3)*exp(x)**2+((144
*x**5+864*x**4+1296*x**3)*ln(2)**2+(-216*x**8-2592*x**7-11376*x**6-22176*x**5-18360*x**4-5184*x**3)*ln(2)+81*x
**11+1458*x**10+10719*x**9+41580*x**8+92079*x**7+118386*x**6+86625*x**5+33264*x**4+5184*x**3)*exp(x)+64*x**3*l
n(2)**3+(-144*x**6-864*x**5-1104*x**4-384*x**3)*ln(2)**2+(108*x**9+1296*x**8+5544*x**7+10512*x**6+9804*x**5+44
16*x**4+768*x**3)*ln(2)-27*x**12-486*x**11-3537*x**10-13500*x**9-29709*x**8-39654*x**7-32615*x**6-16152*x**5-4
416*x**4-512*x**3),x)

[Out]

5/(9*x**8 + 108*x**7 + 462*x**6 - 24*x**5*log(2) + 876*x**5 - 144*x**4*log(2) + 817*x**4 - 184*x**3*log(2) + 3
68*x**3 - 64*x**2*log(2) + 16*x**2*log(2)**2 + 64*x**2 + (9*x**6 + 108*x**5 + 486*x**4 + 972*x**3 + 729*x**2)*
exp(2*x) + (-18*x**7 - 216*x**6 - 948*x**5 - 1848*x**4 + 24*x**4*log(2) - 1530*x**3 + 144*x**3*log(2) - 432*x*
*2 + 216*x**2*log(2))*exp(x))

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