\(\int \frac {e^{\frac {-87-26 x-2 x^2-x^3+(29-x+x^2) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} (-12+11 x+11 x^2+2 x^3+(7-10 x-4 x^2) \log (3)+(-1+2 x) \log ^2(3)+e^x (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3))+(-3+\log (3)) \log (x))}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx\) [7984]

Optimal result

Integrand size = 145, antiderivative size = 27 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}} \]

[Out]

exp(exp(x)-x-x*ln(x)/(x-ln(3)+3)+x^2+29)

Rubi [F]

\[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx \]

[In]

Int[(E^((-87 - 26*x - 2*x^2 - x^3 + (29 - x + x^2)*Log[3] + E^x*(-3 - x + Log[3]) + x*Log[x])/(-3 - x + Log[3]
))*(-12 + 11*x + 11*x^2 + 2*x^3 + (7 - 10*x - 4*x^2)*Log[3] + (-1 + 2*x)*Log[3]^2 + E^x*(9 + 6*x + x^2 + (-6 -
2*x)*Log[3] + Log[3]^2) + (-3 + Log[3])*Log[x]))/(9 + 6*x + x^2 + (-6 - 2*x)*Log[3] + Log[3]^2),x]

[Out]

Defer[Int][E^(29 + E^x + x^2 - (x*Log[x])/(3 + x - Log[3])), x] - 4*Log[3]*Defer[Int][E^(29 + E^x - x + x^2)/x
^(x/(3 + x - Log[3])), x] - 11*(3 - Log[3])*Defer[Int][E^(29 + E^x - x + x^2 - (x*Log[x])/(3 + x - Log[3]))/(3
+ x - Log[3])^2, x] + 11*Defer[Int][(E^(29 + E^x - x + x^2)*x^(2 - x/(3 + x - Log[3])))/(3 + x - Log[3])^2, x
] + 2*Defer[Int][(E^(29 + E^x - x + x^2)*x^(3 - x/(3 + x - Log[3])))/(3 + x - Log[3])^2, x] - 12*Defer[Int][E^
(29 + E^x - x + x^2)/(x^(x/(3 + x - Log[3]))*(3 + x - Log[3])^2), x] + Log[3]*(1 + 14*Log[3] - 4*Log[3]^2)*Def
er[Int][E^(29 + E^x - x + x^2)/(x^(x/(3 + x - Log[3]))*(3 + x - Log[3])^2), x] - Log[3]^2*(7 - Log[9])*Defer[I
nt][E^(29 + E^x - x + x^2)/(x^(x/(3 + x - Log[3]))*(3 + x - Log[3])^2), x] - (3 - Log[3])*Log[x]*Defer[Int][E^
(29 + E^x - x + x^2)/(x^(x/(3 + x - Log[3]))*(3 + x - Log[3])^2), x] + 11*Defer[Int][E^(29 + E^x - x + x^2 - (
x*Log[x])/(3 + x - Log[3]))/(3 + x - Log[3]), x] + 2*Log[3]^2*Defer[Int][E^(29 + E^x - x + x^2)/(x^(x/(3 + x -
Log[3]))*(3 + x - Log[3])), x] + 2*Log[3]*(7 - Log[81])*Defer[Int][E^(29 + E^x - x + x^2)/(x^(x/(3 + x - Log[
3]))*(3 + x - Log[3])), x] + (3 - Log[3])*Defer[Int][Defer[Int][E^(29 + E^x - x + x^2)/(x^(x/(3 + x - Log[3]))
*(3 + x - Log[3])^2), x]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{x^2+2 x (3-\log (3))+(-3+\log (3))^2} \, dx \\ & = \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{(3+x-\log (3))^2} \, dx \\ & = \int \left (\exp \left (x+\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right )-\frac {12 \exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right )}{(3+x-\log (3))^2}+\frac {11 \exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) x}{(3+x-\log (3))^2}+\frac {11 \exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) x^2}{(3+x-\log (3))^2}+\frac {2 \exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) x^3}{(3+x-\log (3))^2}-\frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \left (-7+10 x+4 x^2\right ) \log (3)}{(3+x-\log (3))^2}+\frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) (-1+2 x) \log ^2(3)}{(3+x-\log (3))^2}+\frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) (-3+\log (3)) \log (x)}{(3+x-\log (3))^2}\right ) \, dx \\ & = 2 \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) x^3}{(3+x-\log (3))^2} \, dx+11 \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) x}{(3+x-\log (3))^2} \, dx+11 \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) x^2}{(3+x-\log (3))^2} \, dx-12 \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right )}{(3+x-\log (3))^2} \, dx+(-3+\log (3)) \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \log (x)}{(3+x-\log (3))^2} \, dx-\log (3) \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \left (-7+10 x+4 x^2\right )}{(3+x-\log (3))^2} \, dx+\log ^2(3) \int \frac {\exp \left (\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) (-1+2 x)}{(3+x-\log (3))^2} \, dx+\int \exp \left (x+\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}\right ) \, dx \\ & = 2 \int \frac {e^{29+e^x-x+x^2} x^{3-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+11 \int \frac {e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}} x}{(3+x-\log (3))^2} \, dx+11 \int \frac {e^{29+e^x-x+x^2} x^{2-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx-12 \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+(3-\log (3)) \int \frac {\int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx}{x} \, dx-\log (3) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}} \left (-7+10 x+4 x^2\right )}{(3+x-\log (3))^2} \, dx+\log ^2(3) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}} (-1+2 x)}{(3+x-\log (3))^2} \, dx+((-3+\log (3)) \log (x)) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+\int e^{29+e^x+x^2-\frac {x \log (x)}{3+x-\log (3)}} \, dx \\ & = 2 \int \frac {e^{29+e^x-x+x^2} x^{3-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+11 \int \left (\frac {e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}}}{3+x-\log (3)}+\frac {e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}} (-3+\log (3))}{(3+x-\log (3))^2}\right ) \, dx+11 \int \frac {e^{29+e^x-x+x^2} x^{2-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx-12 \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+(3-\log (3)) \int \frac {\int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx}{x} \, dx-\log (3) \int \left (4 e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}+\frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}} \left (-1-14 \log (3)+4 \log ^2(3)\right )}{(3+x-\log (3))^2}+\frac {2 e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}} (-7+\log (81))}{3+x-\log (3)}\right ) \, dx+\log ^2(3) \int \left (\frac {2 e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{3+x-\log (3)}+\frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}} (-7+\log (9))}{(3+x-\log (3))^2}\right ) \, dx+((-3+\log (3)) \log (x)) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+\int e^{29+e^x+x^2-\frac {x \log (x)}{3+x-\log (3)}} \, dx \\ & = 2 \int \frac {e^{29+e^x-x+x^2} x^{3-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+11 \int \frac {e^{29+e^x-x+x^2} x^{2-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+11 \int \frac {e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}}}{3+x-\log (3)} \, dx-12 \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+(3-\log (3)) \int \frac {\int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx}{x} \, dx-(11 (3-\log (3))) \int \frac {e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx-(4 \log (3)) \int e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}} \, dx+\left (2 \log ^2(3)\right ) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{3+x-\log (3)} \, dx+\left (\log (3) \left (1+14 \log (3)-4 \log ^2(3)\right )\right ) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx-\left (\log ^2(3) (7-\log (9))\right ) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+(2 \log (3) (7-\log (81))) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{3+x-\log (3)} \, dx+((-3+\log (3)) \log (x)) \int \frac {e^{29+e^x-x+x^2} x^{-\frac {x}{3+x-\log (3)}}}{(3+x-\log (3))^2} \, dx+\int e^{29+e^x+x^2-\frac {x \log (x)}{3+x-\log (3)}} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx \]

[In]

Integrate[(E^((-87 - 26*x - 2*x^2 - x^3 + (29 - x + x^2)*Log[3] + E^x*(-3 - x + Log[3]) + x*Log[x])/(-3 - x +
Log[3]))*(-12 + 11*x + 11*x^2 + 2*x^3 + (7 - 10*x - 4*x^2)*Log[3] + (-1 + 2*x)*Log[3]^2 + E^x*(9 + 6*x + x^2 +
(-6 - 2*x)*Log[3] + Log[3]^2) + (-3 + Log[3])*Log[x]))/(9 + 6*x + x^2 + (-6 - 2*x)*Log[3] + Log[3]^2),x]

[Out]

Integrate[(E^((-87 - 26*x - 2*x^2 - x^3 + (29 - x + x^2)*Log[3] + E^x*(-3 - x + Log[3]) + x*Log[x])/(-3 - x +
Log[3]))*(-12 + 11*x + 11*x^2 + 2*x^3 + (7 - 10*x - 4*x^2)*Log[3] + (-1 + 2*x)*Log[3]^2 + E^x*(9 + 6*x + x^2 +
(-6 - 2*x)*Log[3] + Log[3]^2) + (-3 + Log[3])*Log[x]))/(9 + 6*x + x^2 + (-6 - 2*x)*Log[3] + Log[3]^2), x]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(51\) vs. \(2(25)=50\).

Time = 9.50 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.93

method	result	size
parallelrisch	\({\mathrm e}^{\frac {x \ln \left (x \right )+\left (\ln \left (3\right )-3-x \right ) {\mathrm e}^{x}+\left (x^{2}-x +29\right ) \ln \left (3\right )-x^{3}-2 x^{2}-26 x -87}{\ln \left (3\right )-3-x}}\)	\(52\)
risch	\({\mathrm e}^{\frac {x^{2} \ln \left (3\right )-x^{3}+x \ln \left (x \right )+\ln \left (3\right ) {\mathrm e}^{x}-{\mathrm e}^{x} x -x \ln \left (3\right )-2 x^{2}-3 \,{\mathrm e}^{x}+29 \ln \left (3\right )-26 x -87}{\ln \left (3\right )-3-x}}\)	\(60\)

[In]

int(((ln(3)-3)*ln(x)+(ln(3)^2+(-2*x-6)*ln(3)+x^2+6*x+9)*exp(x)+(-1+2*x)*ln(3)^2+(-4*x^2-10*x+7)*ln(3)+2*x^3+11
*x^2+11*x-12)*exp((x*ln(x)+(ln(3)-3-x)*exp(x)+(x^2-x+29)*ln(3)-x^3-2*x^2-26*x-87)/(ln(3)-3-x))/(ln(3)^2+(-2*x-
6)*ln(3)+x^2+6*x+9),x,method=_RETURNVERBOSE)

[Out]

exp((x*ln(x)+(ln(3)-3-x)*exp(x)+(x^2-x+29)*ln(3)-x^3-2*x^2-26*x-87)/(ln(3)-3-x))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (25) = 50\).

Time = 0.28 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.89 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{\left (\frac {x^{3} + 2 \, x^{2} + {\left (x - \log \left (3\right ) + 3\right )} e^{x} - {\left (x^{2} - x + 29\right )} \log \left (3\right ) - x \log \left (x\right ) + 26 \, x + 87}{x - \log \left (3\right ) + 3}\right )} \]

[In]

integrate(((log(3)-3)*log(x)+(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9)*exp(x)+(-1+2*x)*log(3)^2+(-4*x^2-10*x+7)*log
(3)+2*x^3+11*x^2+11*x-12)*exp((x*log(x)+(log(3)-3-x)*exp(x)+(x^2-x+29)*log(3)-x^3-2*x^2-26*x-87)/(log(3)-3-x))
/(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9),x, algorithm="fricas")

[Out]

e^((x^3 + 2*x^2 + (x - log(3) + 3)*e^x - (x^2 - x + 29)*log(3) - x*log(x) + 26*x + 87)/(x - log(3) + 3))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).

Time = 0.75 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.70 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{\frac {- x^{3} - 2 x^{2} + x \log {\left (x \right )} - 26 x + \left (- x - 3 + \log {\left (3 \right )}\right ) e^{x} + \left (x^{2} - x + 29\right ) \log {\left (3 \right )} - 87}{- x - 3 + \log {\left (3 \right )}}} \]

[In]

integrate(((ln(3)-3)*ln(x)+(ln(3)**2+(-2*x-6)*ln(3)+x**2+6*x+9)*exp(x)+(-1+2*x)*ln(3)**2+(-4*x**2-10*x+7)*ln(3
)+2*x**3+11*x**2+11*x-12)*exp((x*ln(x)+(ln(3)-3-x)*exp(x)+(x**2-x+29)*ln(3)-x**3-2*x**2-26*x-87)/(ln(3)-3-x))/
(ln(3)**2+(-2*x-6)*ln(3)+x**2+6*x+9),x)

[Out]

exp((-x**3 - 2*x**2 + x*log(x) - 26*x + (-x - 3 + log(3))*exp(x) + (x**2 - x + 29)*log(3) - 87)/(-x - 3 + log(
3)))

Maxima [A] (verification not implemented)

none

Time = 0.55 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.59 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\frac {e^{\left (x^{2} - x - \frac {\log \left (3\right ) \log \left (x\right )}{x - \log \left (3\right ) + 3} + \frac {3 \, \log \left (x\right )}{x - \log \left (3\right ) + 3} + e^{x} + 29\right )}}{x} \]

[In]

integrate(((log(3)-3)*log(x)+(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9)*exp(x)+(-1+2*x)*log(3)^2+(-4*x^2-10*x+7)*log
(3)+2*x^3+11*x^2+11*x-12)*exp((x*log(x)+(log(3)-3-x)*exp(x)+(x^2-x+29)*log(3)-x^3-2*x^2-26*x-87)/(log(3)-3-x))
/(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9),x, algorithm="maxima")

[Out]

e^(x^2 - x - log(3)*log(x)/(x - log(3) + 3) + 3*log(x)/(x - log(3) + 3) + e^x + 29)/x

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 149 vs. \(2 (25) = 50\).

Time = 0.53 (sec) , antiderivative size = 149, normalized size of antiderivative = 5.52 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{\left (\frac {x^{3}}{x - \log \left (3\right ) + 3} - \frac {x^{2} \log \left (3\right )}{x - \log \left (3\right ) + 3} + \frac {2 \, x^{2}}{x - \log \left (3\right ) + 3} + \frac {x e^{x}}{x - \log \left (3\right ) + 3} + \frac {x \log \left (3\right )}{x - \log \left (3\right ) + 3} - \frac {e^{x} \log \left (3\right )}{x - \log \left (3\right ) + 3} - \frac {x \log \left (x\right )}{x - \log \left (3\right ) + 3} + \frac {26 \, x}{x - \log \left (3\right ) + 3} + \frac {3 \, e^{x}}{x - \log \left (3\right ) + 3} - \frac {29 \, \log \left (3\right )}{x - \log \left (3\right ) + 3} + \frac {87}{x - \log \left (3\right ) + 3}\right )} \]

[In]

integrate(((log(3)-3)*log(x)+(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9)*exp(x)+(-1+2*x)*log(3)^2+(-4*x^2-10*x+7)*log
(3)+2*x^3+11*x^2+11*x-12)*exp((x*log(x)+(log(3)-3-x)*exp(x)+(x^2-x+29)*log(3)-x^3-2*x^2-26*x-87)/(log(3)-3-x))
/(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9),x, algorithm="giac")

[Out]

e^(x^3/(x - log(3) + 3) - x^2*log(3)/(x - log(3) + 3) + 2*x^2/(x - log(3) + 3) + x*e^x/(x - log(3) + 3) + x*lo
g(3)/(x - log(3) + 3) - e^x*log(3)/(x - log(3) + 3) - x*log(x)/(x - log(3) + 3) + 26*x/(x - log(3) + 3) + 3*e^
x/(x - log(3) + 3) - 29*log(3)/(x - log(3) + 3) + 87/(x - log(3) + 3))

Mupad [B] (verification not implemented)

Time = 12.98 (sec) , antiderivative size = 120, normalized size of antiderivative = 4.44 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\frac {{\left (\frac {1}{3}\right )}^{\frac {{\mathrm {e}}^x-x+x^2+29}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {26\,x}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {x^3}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {2\,x^2}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^x}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {87}{x-\ln \left (3\right )+3}}}{x^{\frac {x}{x-\ln \left (3\right )+3}}} \]

[In]

int((exp((26*x - x*log(x) + 2*x^2 + x^3 - log(3)*(x^2 - x + 29) + exp(x)*(x - log(3) + 3) + 87)/(x - log(3) +
3))*(11*x + log(x)*(log(3) - 3) + exp(x)*(6*x - log(3)*(2*x + 6) + log(3)^2 + x^2 + 9) - log(3)*(10*x + 4*x^2
- 7) + log(3)^2*(2*x - 1) + 11*x^2 + 2*x^3 - 12))/(6*x - log(3)*(2*x + 6) + log(3)^2 + x^2 + 9),x)

[Out]

((1/3)^((exp(x) - x + x^2 + 29)/(x - log(3) + 3))*exp((x*exp(x))/(x - log(3) + 3))*exp((26*x)/(x - log(3) + 3)
)*exp(x^3/(x - log(3) + 3))*exp((2*x^2)/(x - log(3) + 3))*exp((3*exp(x))/(x - log(3) + 3))*exp(87/(x - log(3)
+ 3)))/x^(x/(x - log(3) + 3))