∫ x2−2x3−log(2)+e2+x(9x2−6x3+7x4−2x5+x6+(−6x+2x2−2x3) log(2)+log2(2))_________________________________________________________ 9x2−6x3+7x4−2x5+x6+(−6x+2x2−2x3) log(2)+log2(2) dx [6980]

Optimal. Leaf size=28 \[ e^{2+x}+\frac {x}{3 x-x \left (x-x^2\right )-\log (2)} \]

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Rubi [F]
time = 0.00, 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*} \text {\$Aborted} \end {gather*}

Int[(x^2 - 2*x^3 - Log[2] + E^(2 + x)*(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + L

og[2]^2))/(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + Log[2]^2),x]

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Mathematica [F]
time = 1.22, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^2-2 x^3-\log (2)+e^{2+x} \left (9 x^2-6 x^3+7 x^4-2 x^5+x^6+\left (-6 x+2 x^2-2 x^3\right ) \log (2)+\log ^2(2)\right )}{9 x^2-6 x^3+7 x^4-2 x^5+x^6+\left (-6 x+2 x^2-2 x^3\right ) \log (2)+\log ^2(2)} \, dx \end {gather*}

Integrate[(x^2 - 2*x^3 - Log[2] + E^(2 + x)*(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[

2] + Log[2]^2))/(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + Log[2]^2),x]

Integrate[(x^2 - 2*x^3 - Log[2] + E^(2 + x)*(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[

2] + Log[2]^2))/(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + Log[2]^2), x]

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 1.32, size = 3011, normalized size = 107.54


method	result	size

risch	$-\frac {x}{-x^{3}+x^{2}+\ln \left (2\right )-3 x}+{\mathrm e}^{2+x}$	$25$
norman	$\frac {x^{2} {\mathrm e}^{2+x}-x +\ln \left (2\right ) {\mathrm e}^{2+x}-3 x \,{\mathrm e}^{2+x}-{\mathrm e}^{2+x} x^{3}}{-x^{3}+x^{2}+\ln \left (2\right )-3 x}$	$53$
derivativedivides	$\text {Expression too large to display}$	$3011$
default	$\text {Expression too large to display}$	$3011$

int(((ln(2)^2+(-2*x^3+2*x^2-6*x)*ln(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-ln(2)-2*x^3+x^2)/(ln(2)^2+(-2*x^3

-14*exp(2+x)*(105*ln(2)^2*(2+x)^2+9*ln(2)^3-32*(2+x)*ln(2)^2+711*ln(2)*(2+x)^2+528*ln(2)^2-4477*(2+x)*ln(2)-10

06*(2+x)^2+6289*ln(2)+5080+5231*x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)+87*exp(2+x)*(9*

ln(2)^2*(2+x)^2+42*(2+x)*ln(2)^2+366*ln(2)*(2+x)^2+139*ln(2)^2-1851*(2+x)*ln(2)-299*(2+x)^2+2477*ln(2)+1724+10

87*x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)-302*exp(2+x)*(9*(2+x)*ln(2)^2+139*ln(2)*(2+x

)^2+42*ln(2)^2-607*(2+x)*ln(2)-25*(2+x)^2+790*ln(2)+364-124*x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln

(2)-20-19*x)+613*exp(2+x)*(42*ln(2)*(2+x)^2+9*ln(2)^2-155*(2+x)*ln(2)+34*(2+x)^2+191*ln(2)-4-263*x)/(27*ln(2)^

2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)-684*exp(2+x)*(9*ln(2)*(2+x)^2-21*(2+x)*ln(2)+29*(2+x)^2+16*l

n(2)-50-169*x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)-16*ln(2)/(-(2+x)^3+7*(2+x)^2+ln(2)-

20-19*x)/(27*ln(2)^2-50*ln(2)+99)*(2+x)^2+83/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)/(27*ln(2)^2-50*ln(2)+99)*(2+x)

*ln(2)-9/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)/(27*ln(2)^2-50*ln(2)+99)*(2+x)*ln(2)^2-135*ln(2)^2*exp(2+x)/(27*ln

(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)+21*ln(2)^3*exp(2+x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7

*(2+x)^2+ln(2)-20-19*x)+324*exp(2+x)*(9*(2+x)*ln(2)+16*(2+x)^2-21*ln(2)-31-83*x)/(27*ln(2)^2-50*ln(2)+99)/(-(2

+x)^3+7*(2+x)^2+ln(2)-20-19*x)+exp(2+x)*(9*ln(2)^3*(2+x)+703*ln(2)^2*(2+x)^2+105*ln(2)^3-1467*(2+x)*ln(2)^2+50

0*ln(2)*(2+x)^2+2601*ln(2)^2-7220*(2+x)*ln(2)-1811*(2+x)^2+11792*ln(2)+9356+13732*x)/(27*ln(2)^2-50*ln(2)+99)/

(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)+exp(2+x)+2*ln(2)*sum((9*ln(2)^2*_R1+139*ln(2)*_R1^2+51*ln(2)^2-746*ln(2)*_R

1-25*_R1^2+981*ln(2)-99*_R1+1134)/(27*ln(2)^2-50*ln(2)+99)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2-x+_R1),_R1=Roo

tOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))+20*(16/(27*ln(2)^2-50*ln(2)+99)*(2+x)^2+(-83+9*ln(2))/(27*ln(2)^2-50*ln(2)+99

)*(2+x)-3*(-45+7*ln(2))/(27*ln(2)^2-50*ln(2)+99))/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)+28/(27*ln(2)^2-50*ln(2)+9

9)*sum((9*_R*ln(2)+21*ln(2)+29*_R-135)/(3*_R^2-14*_R+19)*ln(2+x-_R),_R=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-2*(

(139*ln(2)-25)/(27*ln(2)^2-50*ln(2)+99)*(2+x)^2+(9*ln(2)^2-607*ln(2)-124)/(27*ln(2)^2-50*ln(2)+99)*(2+x)+2*(21

*ln(2)^2+395*ln(2)+306)/(27*ln(2)^2-50*ln(2)+99))/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)-40/(27*ln(2)^2-50*ln(2)+9

9)*sum((8*_R-27+9*ln(2))/(3*_R^2-14*_R+19)*ln(2+x-_R),_R=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-26/(27*ln(2)^2-50

*ln(2)+99)*sum((21*_R*ln(2)-8*ln(2)+17*_R-144)/(3*_R^2-14*_R+19)*ln(2+x-_R),_R=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-

18))+13*(2*(17+21*ln(2))/(27*ln(2)^2-50*ln(2)+99)*(2+x)^2-(155*ln(2)+263)/(27*ln(2)^2-50*ln(2)+99)*(2+x)+(9*ln

(2)^2+191*ln(2)+522)/(27*ln(2)^2-50*ln(2)+99))/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)+38*ln(2)*sum((9*ln(2)*_R1^2-

30*ln(2)*_R1+29*_R1^2-5*ln(2)-198*_R1+423)/(27*ln(2)^2-50*ln(2)+99)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2-x+_R1

),_R1=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-87*sum((9*ln(2)^2*_R1^2+60*ln(2)^2*_R1+366*ln(2)*_R1^2+181*ln(2)^2-2

267*ln(2)*_R1-299*_R1^2+3267*ln(2)+1485*_R1+162)/(27*ln(2)^2-50*ln(2)+99)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2

-x+_R1),_R1=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-14*ln(2)*sum((42*ln(2)*_R1^2+9*ln(2)^2-197*ln(2)*_R1+34*_R1^2+

207*ln(2)-297*_R1+810)/(27*ln(2)^2-50*ln(2)+99)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2-x+_R1),_R1=RootOf(_Z^3-7*

_Z^2-ln(2)+19*_Z-18))+684*sum((9*ln(2)*_R1^2-30*ln(2)*_R1+29*_R1^2-5*ln(2)-198*_R1+423)/(27*ln(2)^2-50*ln(2)+9

9)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2-x+_R1),_R1=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))+14*sum((132*ln(2)^2*_R1

^2+9*ln(2)^3+52*ln(2)^2*_R1+661*ln(2)*_R1^2+667*ln(2)^2-5538*ln(2)*_R1-907*_R1^2+8766*ln(2)+6930*_R1-5832)/(27

*ln(2)^2-50*ln(2)+99)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2-x+_R1),_R1=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-16*l

n(2)^2*exp(2+x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)*(2+x)^2+83*ln(2)^2*exp(2+x)/(27*ln

(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)*(2+x)-135/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)/(27*ln(2)^2

-50*ln(2)+99)*ln(2)+21/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)/(27*ln(2)^2-50*ln(2)+99)*ln(2)^2+2*ln(2)/(27*ln(2)^2

-50*ln(2)+99)*sum((8*_R-27+9*ln(2))/(3*_R^2-14*_R+19)*ln(2+x-_R),_R=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-9*ln(2

)^3*exp(2+x)/(27*ln(2)^2-50*ln(2)+99)/(-(2+x)^3+7*(2+x)^2+ln(2)-20-19*x)*(2+x)-324*sum((9*_R2*ln(2)+16*_R2^2-3

9*ln(2)-99*_R2+189)/(27*ln(2)^2-50*ln(2)+99)/(3*_R2^2-14*_R2+19)*exp(_R2)*Ei(1,-2-x+_R2),_R2=RootOf(_Z^3-7*_Z^

2-ln(2)+19*_Z-18))-36*ln(2)*sum((9*_R2*ln(2)+16*_R2^2-39*ln(2)-99*_R2+189)/(27*ln(2)^2-50*ln(2)+99)/(3*_R2^2-1

4*_R2+19)*exp(_R2)*Ei(1,-2-x+_R2),_R2=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18))-ln(2)^2*sum((9*_R2*ln(2)+16*_R2^2-39

*ln(2)-99*_R2+189)/(27*ln(2)^2-50*ln(2)+99)/(3*_R2^2-14*_R2+19)*exp(_R2)*Ei(1,-2-x+_R2),_R2=RootOf(_Z^3-7*_Z^2

-ln(2)+19*_Z-18))+302*sum((9*ln(2)^2*_R1+139*ln(2)*_R1^2+51*ln(2)^2-746*ln(2)*_R1-25*_R1^2+981*ln(2)-99*_R1+11

34)/(27*ln(2)^2-50*ln(2)+99)/(3*_R1^2-14*_R1+19)*exp(_R1)*Ei(1,-2-x+_R1),_R1=RootOf(_Z^3-7*_Z^2-ln(2)+19*_Z-18

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Maxima [A]
time = 0.53, size = 49, normalized size = 1.75 \begin {gather*} \frac {{\left (x^{3} e^{2} - x^{2} e^{2} + 3 \, x e^{2} - e^{2} \log \left (2\right )\right )} e^{x} + x}{x^{3} - x^{2} + 3 \, x - \log \left (2\right )} \end {gather*}

integrate(((log(2)^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-log(2)-2*x^3+x^2)/(log(2)

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Fricas [A]
time = 0.35, size = 42, normalized size = 1.50 \begin {gather*} \frac {{\left (x^{3} - x^{2} + 3 \, x - \log \left (2\right )\right )} e^{\left (x + 2\right )} + x}{x^{3} - x^{2} + 3 \, x - \log \left (2\right )} \end {gather*}

integrate(((log(2)^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-log(2)-2*x^3+x^2)/(log(2)

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Sympy [A]
time = 0.41, size = 19, normalized size = 0.68 \begin {gather*} \frac {x}{x^{3} - x^{2} + 3 x - \log {\left (2 \right )}} + e^{x + 2} \end {gather*}

integrate(((ln(2)**2+(-2*x**3+2*x**2-6*x)*ln(2)+x**6-2*x**5+7*x**4-6*x**3+9*x**2)*exp(2+x)-ln(2)-2*x**3+x**2)/

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 53 vs. $2 (26) = 52$.
time = 0.42, size = 53, normalized size = 1.89 \begin {gather*} \frac {x^{3} e^{\left (x + 2\right )} - x^{2} e^{\left (x + 2\right )} + 3 \, x e^{\left (x + 2\right )} - e^{\left (x + 2\right )} \log \left (2\right ) + x}{x^{3} - x^{2} + 3 \, x - \log \left (2\right )} \end {gather*}

integrate(((log(2)^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-log(2)-2*x^3+x^2)/(log(2)

(x^3*e^(x + 2) - x^2*e^(x + 2) + 3*x*e^(x + 2) - e^(x + 2)*log(2) + x)/(x^3 - x^2 + 3*x - log(2))

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Mupad [B]
time = 5.06, size = 368, normalized size = 13.14 \begin {gather*} {\mathrm {e}}^{x+2}+\left (\sum _{k=1}^6\ln \left (-1089\,\ln \left (2\right )+\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,\ln \left (2\right )\,6534-\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,x\,19602+1452\,x\,\ln \left (2\right )-\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,{\ln \left (2\right )}^2\,3894+\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,{\ln \left (2\right )}^3\,2082-\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,{\ln \left (2\right )}^4\,162-1832\,x\,{\ln \left (2\right )}^2+108\,x\,{\ln \left (2\right )}^3-250\,{\ln \left (2\right )}^2+567\,{\ln \left (2\right )}^3+\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,x\,\ln \left (2\right )\,15444-\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,x\,{\ln \left (2\right )}^2\,9928+\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,x\,{\ln \left (2\right )}^3\,2412-\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\,x\,{\ln \left (2\right )}^4\,486\right )\,\mathrm {root}\left (9900\,\ln \left (2\right )-7846\,{\ln \left (2\right )}^2+2700\,{\ln \left (2\right )}^3-729\,{\ln \left (2\right )}^4-9801,z,k\right )\right ) \end {gather*}

int(-(log(2) - x^2 + 2*x^3 - exp(x + 2)*(log(2)^2 - log(2)*(6*x - 2*x^2 + 2*x^3) + 9*x^2 - 6*x^3 + 7*x^4 - 2*x

^5 + x^6))/(log(2)^2 - log(2)*(6*x - 2*x^2 + 2*x^3) + 9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6),x)

exp(x + 2) + symsum(log(6534*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log

(2) - 1089*log(2) - 19602*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x + 14

52*x*log(2) - 3894*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log(2)^2 + 20

82*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log(2)^3 - 162*root(9900*log(

2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log(2)^4 - 1832*x*log(2)^2 + 108*x*log(2)^3 -

250*log(2)^2 + 567*log(2)^3 + 15444*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z,

k)*x*log(2) - 9928*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x*log(2)^2 +

2412*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x*log(2)^3 - 486*root(9900

*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x*log(2)^4)*root(9900*log(2) - 7846*log(2

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method	result	size

risch	\(-\frac {x}{-x^{3}+x^{2}+\ln \left (2\right )-3 x}+{\mathrm e}^{2+x}\)	\(25\)
norman	\(\frac {x^{2} {\mathrm e}^{2+x}-x +\ln \left (2\right ) {\mathrm e}^{2+x}-3 x \,{\mathrm e}^{2+x}-{\mathrm e}^{2+x} x^{3}}{-x^{3}+x^{2}+\ln \left (2\right )-3 x}\)	\(53\)
derivativedivides	\(\text {Expression too large to display}\)	\(3011\)
default	\(\text {Expression too large to display}\)	\(3011\)

3.70.80 \(\int \frac {x^2-2 x^3-\log (2)+e^{2+x} (9 x^2-6 x^3+7 x^4-2 x^5+x^6+(-6 x+2 x^2-2 x^3) \log (2)+\log ^2(2))}{9 x^2-6 x^3+7 x^4-2 x^5+x^6+(-6 x+2 x^2-2 x^3) \log (2)+\log ^2(2)} \, dx\) [6980]