\(\int \frac {32 x^4-16 x^5+2 x^6+(-16 x^3+4 x^4) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} (10 x^2+2 x^4-56 x^5+6 x^6+(-10 x^2+24 x^4+16 x^5-2 x^6) \log (x)-6 x^4 \log ^2(x))+e^{\frac {2 (-5 x+4 x^3-x^3 \log (x))}{-4 x+x^2+\log (x)}} (10 x-16 x^2+10 x^3-57 x^4+6 x^5+(-2 x-2 x^2+24 x^3+16 x^4-2 x^5) \log (x)+(-1-6 x^3) \log ^2(x))}{16 x^4-8 x^5+x^6+(-8 x^3+2 x^4) \log (x)+x^2 \log ^2(x)} \, dx\) [987]

Optimal result

Integrand size = 258, antiderivative size = 36 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=x+\frac {\left (e^{\frac {-5+x^2 (4-\log (x))}{-4+x+\frac {\log (x)}{x}}}+x\right )^2}{x} \]

[Out]

x+(x+exp((x^2*(-ln(x)+4)-5)/(x+ln(x)/x-4)))^2/x

Rubi [F]

\[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=\int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+\exp \left (\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}\right ) \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+\exp \left (\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}\right ) \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx \]

[In]

Int[(32*x^4 - 16*x^5 + 2*x^6 + (-16*x^3 + 4*x^4)*Log[x] + 2*x^2*Log[x]^2 + E^((-5*x + 4*x^3 - x^3*Log[x])/(-4*
x + x^2 + Log[x]))*(10*x^2 + 2*x^4 - 56*x^5 + 6*x^6 + (-10*x^2 + 24*x^4 + 16*x^5 - 2*x^6)*Log[x] - 6*x^4*Log[x
]^2) + E^((2*(-5*x + 4*x^3 - x^3*Log[x]))/(-4*x + x^2 + Log[x]))*(10*x - 16*x^2 + 10*x^3 - 57*x^4 + 6*x^5 + (-
2*x - 2*x^2 + 24*x^3 + 16*x^4 - 2*x^5)*Log[x] + (-1 - 6*x^3)*Log[x]^2))/(16*x^4 - 8*x^5 + x^6 + (-8*x^3 + 2*x^
4)*Log[x] + x^2*Log[x]^2),x]

[Out]

2*x - Defer[Int][E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(-2 - (2*x^3)/((-4 + x)*x + Log[x])), x] - 6*D
efer[Int][E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(1 - (2*x^3)/((-4 + x)*x + Log[x])), x] - 6*Defer[Int
][E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(2 - x^3/((-4 + x)*x + Log[x])), x] - 40*Defer[Int][E^((2*x*(-5
+ 4*x^2))/((-4 + x)*x + Log[x]))/(x^((2*x^3)/((-4 + x)*x + Log[x]))*(-4*x + x^2 + Log[x])^2), x] + 10*Defer[I
nt][E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))/(x^(x^3/((-4 + x)*x + Log[x]))*(-4*x + x^2 + Log[x])^2), x] + 1
0*Defer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(-1 - (2*x^3)/((-4 + x)*x + Log[x])))/(-4*x + x^2
+ Log[x])^2, x] + 12*Defer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(1 - (2*x^3)/((-4 + x)*x + Lo
g[x])))/(-4*x + x^2 + Log[x])^2, x] + 40*Defer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(2 - (2*x^
3)/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x] - 50*Defer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Lo
g[x]))*x^(3 - (2*x^3)/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x] + 24*Defer[Int][(E^((2*x*(-5 + 4*x^2
))/((-4 + x)*x + Log[x]))*x^(4 - (2*x^3)/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x] - 4*Defer[Int][(E
^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(5 - (2*x^3)/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x]
- 40*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(1 - x^3/((-4 + x)*x + Log[x])))/(-4*x + x^2 +
Log[x])^2, x] + 12*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(2 - x^3/((-4 + x)*x + Log[x])))/(
-4*x + x^2 + Log[x])^2, x] + 40*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(3 - x^3/((-4 + x)*x
+ Log[x])))/(-4*x + x^2 + Log[x])^2, x] - 50*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(4 - x^3
/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x] + 24*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]
))*x^(5 - x^3/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x] - 4*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x
)*x + Log[x]))*x^(6 - x^3/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x])^2, x] - 10*Defer[Int][E^((x*(-5 + 4*x^
2))/((-4 + x)*x + Log[x]))/(x^(x^3/((-4 + x)*x + Log[x]))*(-4*x + x^2 + Log[x])), x] - 10*Defer[Int][(E^((2*x*
(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(-1 - (2*x^3)/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x]), x] + 24*De
fer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(1 - (2*x^3)/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Lo
g[x]), x] - 32*Defer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(2 - (2*x^3)/((-4 + x)*x + Log[x])))
/(-4*x + x^2 + Log[x]), x] + 10*Defer[Int][(E^((2*x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(3 - (2*x^3)/((-4 +
x)*x + Log[x])))/(-4*x + x^2 + Log[x]), x] + 24*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[x]))*x^(2 -
x^3/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x]), x] - 32*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 + x)*x + Log[
x]))*x^(3 - x^3/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x]), x] + 10*Defer[Int][(E^((x*(-5 + 4*x^2))/((-4 +
x)*x + Log[x]))*x^(4 - x^3/((-4 + x)*x + Log[x])))/(-4*x + x^2 + Log[x]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+\exp \left (\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}\right ) \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+\exp \left (\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}\right ) \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{x^2 \left (4 x-x^2-\log (x)\right )^2} \, dx \\ & = \int \left (\frac {32 x^2}{\left (-4 x+x^2+\log (x)\right )^2}-\frac {16 x^3}{\left (-4 x+x^2+\log (x)\right )^2}+\frac {2 x^4}{\left (-4 x+x^2+\log (x)\right )^2}+\frac {4 (-4+x) x \log (x)}{\left (-4 x+x^2+\log (x)\right )^2}+\frac {2 \log ^2(x)}{\left (-4 x+x^2+\log (x)\right )^2}-\frac {2 e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-\frac {x^3}{(-4+x) x+\log (x)}} \left (-5-x^2+28 x^3-3 x^4+5 \log (x)-12 x^2 \log (x)-8 x^3 \log (x)+x^4 \log (x)+3 x^2 \log ^2(x)\right )}{\left (-4 x+x^2+\log (x)\right )^2}-\frac {e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-2-\frac {2 x^3}{(-4+x) x+\log (x)}} \left (-10 x+16 x^2-10 x^3+57 x^4-6 x^5+2 x \log (x)+2 x^2 \log (x)-24 x^3 \log (x)-16 x^4 \log (x)+2 x^5 \log (x)+\log ^2(x)+6 x^3 \log ^2(x)\right )}{\left (-4 x+x^2+\log (x)\right )^2}\right ) \, dx \\ & = 2 \int \frac {x^4}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+2 \int \frac {\log ^2(x)}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-\frac {x^3}{(-4+x) x+\log (x)}} \left (-5-x^2+28 x^3-3 x^4+5 \log (x)-12 x^2 \log (x)-8 x^3 \log (x)+x^4 \log (x)+3 x^2 \log ^2(x)\right )}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+4 \int \frac {(-4+x) x \log (x)}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-16 \int \frac {x^3}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+32 \int \frac {x^2}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-\int \frac {e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-2-\frac {2 x^3}{(-4+x) x+\log (x)}} \left (-10 x+16 x^2-10 x^3+57 x^4-6 x^5+2 x \log (x)+2 x^2 \log (x)-24 x^3 \log (x)-16 x^4 \log (x)+2 x^5 \log (x)+\log ^2(x)+6 x^3 \log ^2(x)\right )}{\left (-4 x+x^2+\log (x)\right )^2} \, dx \\ & = 2 \int \frac {x^4}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+2 \int \left (1+\frac {(-4+x)^2 x^2}{\left (-4 x+x^2+\log (x)\right )^2}-\frac {2 (-4+x) x}{-4 x+x^2+\log (x)}\right ) \, dx-2 \int \left (3 e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{2-\frac {x^3}{(-4+x) x+\log (x)}}+\frac {e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-\frac {x^3}{(-4+x) x+\log (x)}} \left (-5+20 x-6 x^2-20 x^3+25 x^4-12 x^5+2 x^6\right )}{\left (-4 x+x^2+\log (x)\right )^2}+\frac {e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-\frac {x^3}{(-4+x) x+\log (x)}} \left (5-12 x^2+16 x^3-5 x^4\right )}{-4 x+x^2+\log (x)}\right ) \, dx+4 \int \left (-\frac {(-4+x)^2 x^2}{\left (-4 x+x^2+\log (x)\right )^2}+\frac {(-4+x) x}{-4 x+x^2+\log (x)}\right ) \, dx-16 \int \frac {x^3}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+32 \int \frac {x^2}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-\int \left (e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-2-\frac {2 x^3}{(-4+x) x+\log (x)}}+6 e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{1-\frac {2 x^3}{(-4+x) x+\log (x)}}+\frac {2 e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-1-\frac {2 x^3}{(-4+x) x+\log (x)}} \left (-5+20 x-6 x^2-20 x^3+25 x^4-12 x^5+2 x^6\right )}{\left (-4 x+x^2+\log (x)\right )^2}-\frac {2 e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-1-\frac {2 x^3}{(-4+x) x+\log (x)}} \left (-5+12 x^2-16 x^3+5 x^4\right )}{-4 x+x^2+\log (x)}\right ) \, dx \\ & = 2 x+2 \int \frac {(-4+x)^2 x^2}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+2 \int \frac {x^4}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-\frac {x^3}{(-4+x) x+\log (x)}} \left (-5+20 x-6 x^2-20 x^3+25 x^4-12 x^5+2 x^6\right )}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-1-\frac {2 x^3}{(-4+x) x+\log (x)}} \left (-5+20 x-6 x^2-20 x^3+25 x^4-12 x^5+2 x^6\right )}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-\frac {x^3}{(-4+x) x+\log (x)}} \left (5-12 x^2+16 x^3-5 x^4\right )}{-4 x+x^2+\log (x)} \, dx+2 \int \frac {e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-1-\frac {2 x^3}{(-4+x) x+\log (x)}} \left (-5+12 x^2-16 x^3+5 x^4\right )}{-4 x+x^2+\log (x)} \, dx-4 \int \frac {(-4+x)^2 x^2}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-6 \int e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{1-\frac {2 x^3}{(-4+x) x+\log (x)}} \, dx-6 \int e^{\frac {x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{2-\frac {x^3}{(-4+x) x+\log (x)}} \, dx-16 \int \frac {x^3}{\left (-4 x+x^2+\log (x)\right )^2} \, dx+32 \int \frac {x^2}{\left (-4 x+x^2+\log (x)\right )^2} \, dx-\int e^{\frac {2 x \left (-5+4 x^2\right )}{(-4+x) x+\log (x)}} x^{-2-\frac {2 x^3}{(-4+x) x+\log (x)}} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.34 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.83 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=2 e^{-\frac {x \left (5-4 x^2+x^2 \log (x)\right )}{(-4+x) x+\log (x)}}+\frac {e^{-\frac {2 x \left (5-4 x^2+x^2 \log (x)\right )}{(-4+x) x+\log (x)}}}{x}+2 x \]

[In]

Integrate[(32*x^4 - 16*x^5 + 2*x^6 + (-16*x^3 + 4*x^4)*Log[x] + 2*x^2*Log[x]^2 + E^((-5*x + 4*x^3 - x^3*Log[x]
)/(-4*x + x^2 + Log[x]))*(10*x^2 + 2*x^4 - 56*x^5 + 6*x^6 + (-10*x^2 + 24*x^4 + 16*x^5 - 2*x^6)*Log[x] - 6*x^4
*Log[x]^2) + E^((2*(-5*x + 4*x^3 - x^3*Log[x]))/(-4*x + x^2 + Log[x]))*(10*x - 16*x^2 + 10*x^3 - 57*x^4 + 6*x^
5 + (-2*x - 2*x^2 + 24*x^3 + 16*x^4 - 2*x^5)*Log[x] + (-1 - 6*x^3)*Log[x]^2))/(16*x^4 - 8*x^5 + x^6 + (-8*x^3
+ 2*x^4)*Log[x] + x^2*Log[x]^2),x]

[Out]

2/E^((x*(5 - 4*x^2 + x^2*Log[x]))/((-4 + x)*x + Log[x])) + 1/(E^((2*x*(5 - 4*x^2 + x^2*Log[x]))/((-4 + x)*x +
Log[x]))*x) + 2*x

Maple [A] (verified)

Time = 5.29 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.86

method	result	size
risch	\(2 x +\frac {{\mathrm e}^{-\frac {2 x \left (x^{2} \ln \left (x \right )-4 x^{2}+5\right )}{\ln \left (x \right )+x^{2}-4 x}}}{x}+2 \,{\mathrm e}^{-\frac {x \left (x^{2} \ln \left (x \right )-4 x^{2}+5\right )}{\ln \left (x \right )+x^{2}-4 x}}\)	\(67\)
parallelrisch	\(\frac {32 x^{2}+32 x \,{\mathrm e}^{\frac {-x^{3} \ln \left (x \right )+4 x^{3}-5 x}{\ln \left (x \right )+x^{2}-4 x}}+16 \,{\mathrm e}^{\frac {-2 x^{3} \ln \left (x \right )+8 x^{3}-10 x}{\ln \left (x \right )+x^{2}-4 x}}+80 x}{16 x}\)	\(80\)

[In]

int((((-6*x^3-1)*ln(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*ln(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((-x^3*ln(
x)+4*x^3-5*x)/(ln(x)+x^2-4*x))^2+(-6*x^4*ln(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*ln(x)+6*x^6-56*x^5+2*x^4+10*x^2
)*exp((-x^3*ln(x)+4*x^3-5*x)/(ln(x)+x^2-4*x))+2*x^2*ln(x)^2+(4*x^4-16*x^3)*ln(x)+2*x^6-16*x^5+32*x^4)/(x^2*ln(
x)^2+(2*x^4-8*x^3)*ln(x)+x^6-8*x^5+16*x^4),x,method=_RETURNVERBOSE)

[Out]

2*x+1/x*exp(-2*x*(x^2*ln(x)-4*x^2+5)/(ln(x)+x^2-4*x))+2*exp(-x*(x^2*ln(x)-4*x^2+5)/(ln(x)+x^2-4*x))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (34) = 68\).

Time = 0.25 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.97 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=\frac {2 \, x^{2} + 2 \, x e^{\left (-\frac {x^{3} \log \left (x\right ) - 4 \, x^{3} + 5 \, x}{x^{2} - 4 \, x + \log \left (x\right )}\right )} + e^{\left (-\frac {2 \, {\left (x^{3} \log \left (x\right ) - 4 \, x^{3} + 5 \, x\right )}}{x^{2} - 4 \, x + \log \left (x\right )}\right )}}{x} \]

[In]

integrate((((-6*x^3-1)*log(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*log(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((
-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))^2+(-6*x^4*log(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*log(x)+6*x^6-56*x^5+
2*x^4+10*x^2)*exp((-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))+2*x^2*log(x)^2+(4*x^4-16*x^3)*log(x)+2*x^6-16*x^5+
32*x^4)/(x^2*log(x)^2+(2*x^4-8*x^3)*log(x)+x^6-8*x^5+16*x^4),x, algorithm="fricas")

[Out]

(2*x^2 + 2*x*e^(-(x^3*log(x) - 4*x^3 + 5*x)/(x^2 - 4*x + log(x))) + e^(-2*(x^3*log(x) - 4*x^3 + 5*x)/(x^2 - 4*
x + log(x))))/x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (26) = 52\).

Time = 0.30 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.75 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=2 x + \frac {2 x e^{\frac {- x^{3} \log {\left (x \right )} + 4 x^{3} - 5 x}{x^{2} - 4 x + \log {\left (x \right )}}} + e^{\frac {2 \left (- x^{3} \log {\left (x \right )} + 4 x^{3} - 5 x\right )}{x^{2} - 4 x + \log {\left (x \right )}}}}{x} \]

[In]

integrate((((-6*x**3-1)*ln(x)**2+(-2*x**5+16*x**4+24*x**3-2*x**2-2*x)*ln(x)+6*x**5-57*x**4+10*x**3-16*x**2+10*
x)*exp((-x**3*ln(x)+4*x**3-5*x)/(ln(x)+x**2-4*x))**2+(-6*x**4*ln(x)**2+(-2*x**6+16*x**5+24*x**4-10*x**2)*ln(x)
+6*x**6-56*x**5+2*x**4+10*x**2)*exp((-x**3*ln(x)+4*x**3-5*x)/(ln(x)+x**2-4*x))+2*x**2*ln(x)**2+(4*x**4-16*x**3
)*ln(x)+2*x**6-16*x**5+32*x**4)/(x**2*ln(x)**2+(2*x**4-8*x**3)*ln(x)+x**6-8*x**5+16*x**4),x)

[Out]

2*x + (2*x*exp((-x**3*log(x) + 4*x**3 - 5*x)/(x**2 - 4*x + log(x))) + exp(2*(-x**3*log(x) + 4*x**3 - 5*x)/(x**
2 - 4*x + log(x))))/x

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 235 vs. \(2 (34) = 68\).

Time = 0.37 (sec) , antiderivative size = 235, normalized size of antiderivative = 6.53 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=\frac {{\left (2 \, x^{10} e^{\left (2 \, x \log \left (x\right ) + \frac {40 \, x \log \left (x\right )}{x^{2} - 4 \, x + \log \left (x\right )} + \frac {32 \, \log \left (x\right )}{x^{2} - 4 \, x + \log \left (x\right )}\right )} + 2 \, x^{5} e^{\left (x \log \left (x\right ) + \frac {x \log \left (x\right )^{2}}{x^{2} - 4 \, x + \log \left (x\right )} + 4 \, x + \frac {20 \, x \log \left (x\right )}{x^{2} - 4 \, x + \log \left (x\right )} + \frac {4 \, \log \left (x\right )^{2}}{x^{2} - 4 \, x + \log \left (x\right )} + \frac {59 \, x}{x^{2} - 4 \, x + \log \left (x\right )} + \frac {16 \, \log \left (x\right )}{x^{2} - 4 \, x + \log \left (x\right )} + 16\right )} + e^{\left (\frac {2 \, x \log \left (x\right )^{2}}{x^{2} - 4 \, x + \log \left (x\right )} + 8 \, x + \frac {8 \, \log \left (x\right )^{2}}{x^{2} - 4 \, x + \log \left (x\right )} + \frac {118 \, x}{x^{2} - 4 \, x + \log \left (x\right )} + 32\right )}\right )} e^{\left (-2 \, x \log \left (x\right ) - \frac {40 \, x \log \left (x\right )}{x^{2} - 4 \, x + \log \left (x\right )} - \frac {32 \, \log \left (x\right )}{x^{2} - 4 \, x + \log \left (x\right )}\right )}}{x^{9}} \]

[In]

integrate((((-6*x^3-1)*log(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*log(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((
-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))^2+(-6*x^4*log(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*log(x)+6*x^6-56*x^5+
2*x^4+10*x^2)*exp((-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))+2*x^2*log(x)^2+(4*x^4-16*x^3)*log(x)+2*x^6-16*x^5+
32*x^4)/(x^2*log(x)^2+(2*x^4-8*x^3)*log(x)+x^6-8*x^5+16*x^4),x, algorithm="maxima")

[Out]

(2*x^10*e^(2*x*log(x) + 40*x*log(x)/(x^2 - 4*x + log(x)) + 32*log(x)/(x^2 - 4*x + log(x))) + 2*x^5*e^(x*log(x)
+ x*log(x)^2/(x^2 - 4*x + log(x)) + 4*x + 20*x*log(x)/(x^2 - 4*x + log(x)) + 4*log(x)^2/(x^2 - 4*x + log(x))
+ 59*x/(x^2 - 4*x + log(x)) + 16*log(x)/(x^2 - 4*x + log(x)) + 16) + e^(2*x*log(x)^2/(x^2 - 4*x + log(x)) + 8*
x + 8*log(x)^2/(x^2 - 4*x + log(x)) + 118*x/(x^2 - 4*x + log(x)) + 32))*e^(-2*x*log(x) - 40*x*log(x)/(x^2 - 4*
x + log(x)) - 32*log(x)/(x^2 - 4*x + log(x)))/x^9

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (34) = 68\).

Time = 1.46 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.97 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=\frac {2 \, x^{2} + 2 \, x e^{\left (-\frac {x^{3} \log \left (x\right ) - 4 \, x^{3} + 5 \, x}{x^{2} - 4 \, x + \log \left (x\right )}\right )} + e^{\left (-\frac {2 \, {\left (x^{3} \log \left (x\right ) - 4 \, x^{3} + 5 \, x\right )}}{x^{2} - 4 \, x + \log \left (x\right )}\right )}}{x} \]

[In]

integrate((((-6*x^3-1)*log(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*log(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((
-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))^2+(-6*x^4*log(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*log(x)+6*x^6-56*x^5+
2*x^4+10*x^2)*exp((-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))+2*x^2*log(x)^2+(4*x^4-16*x^3)*log(x)+2*x^6-16*x^5+
32*x^4)/(x^2*log(x)^2+(2*x^4-8*x^3)*log(x)+x^6-8*x^5+16*x^4),x, algorithm="giac")

[Out]

(2*x^2 + 2*x*e^(-(x^3*log(x) - 4*x^3 + 5*x)/(x^2 - 4*x + log(x))) + e^(-2*(x^3*log(x) - 4*x^3 + 5*x)/(x^2 - 4*
x + log(x))))/x

Mupad [B] (verification not implemented)

Time = 9.67 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.14 \[ \int \frac {32 x^4-16 x^5+2 x^6+\left (-16 x^3+4 x^4\right ) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} \left (10 x^2+2 x^4-56 x^5+6 x^6+\left (-10 x^2+24 x^4+16 x^5-2 x^6\right ) \log (x)-6 x^4 \log ^2(x)\right )+e^{\frac {2 \left (-5 x+4 x^3-x^3 \log (x)\right )}{-4 x+x^2+\log (x)}} \left (10 x-16 x^2+10 x^3-57 x^4+6 x^5+\left (-2 x-2 x^2+24 x^3+16 x^4-2 x^5\right ) \log (x)+\left (-1-6 x^3\right ) \log ^2(x)\right )}{16 x^4-8 x^5+x^6+\left (-8 x^3+2 x^4\right ) \log (x)+x^2 \log ^2(x)} \, dx=2\,x+\frac {2\,{\mathrm {e}}^{-\frac {5\,x}{\ln \left (x\right )-4\,x+x^2}}\,{\mathrm {e}}^{\frac {4\,x^3}{\ln \left (x\right )-4\,x+x^2}}}{x^{\frac {x^3}{\ln \left (x\right )-4\,x+x^2}}}+\frac {{\mathrm {e}}^{-\frac {10\,x}{\ln \left (x\right )-4\,x+x^2}}\,{\mathrm {e}}^{\frac {8\,x^3}{\ln \left (x\right )-4\,x+x^2}}}{x^{\frac {2\,x^3}{\ln \left (x\right )-4\,x+x^2}}\,x} \]

[In]

int(-(log(x)*(16*x^3 - 4*x^4) + exp(-(5*x + x^3*log(x) - 4*x^3)/(log(x) - 4*x + x^2))*(6*x^4*log(x)^2 + log(x)
*(10*x^2 - 24*x^4 - 16*x^5 + 2*x^6) - 10*x^2 - 2*x^4 + 56*x^5 - 6*x^6) - 2*x^2*log(x)^2 + exp(-(2*(5*x + x^3*l
og(x) - 4*x^3))/(log(x) - 4*x + x^2))*(log(x)^2*(6*x^3 + 1) - 10*x + log(x)*(2*x + 2*x^2 - 24*x^3 - 16*x^4 + 2
*x^5) + 16*x^2 - 10*x^3 + 57*x^4 - 6*x^5) - 32*x^4 + 16*x^5 - 2*x^6)/(x^2*log(x)^2 - log(x)*(8*x^3 - 2*x^4) +
16*x^4 - 8*x^5 + x^6),x)

[Out]

2*x + (2*exp(-(5*x)/(log(x) - 4*x + x^2))*exp((4*x^3)/(log(x) - 4*x + x^2)))/x^(x^3/(log(x) - 4*x + x^2)) + (e
xp(-(10*x)/(log(x) - 4*x + x^2))*exp((8*x^3)/(log(x) - 4*x + x^2)))/(x^((2*x^3)/(log(x) - 4*x + x^2))*x)