∫ x x ____________________________________________ x2+(25x2+10x3+11x4+2x5+x6)x log(x) (5x2+x3+x4+(−5x2−x3−x4) log(x)+(25x2+10x3+11x4+2x5+x6)x((5−9x−3x2−6x3) log2(x)+(−5x−x2−x3) log2(x) log(25x2+10x3+11x4+2x5+x6))) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________5x4 +x5+x6+(10x2+2x3+2x4)(25x2+10x3+11x4+2x5+x6)x log(x)+(5+x+x2)(25x2+10x3+11x4+2x5+x6)2x log2(x) dx

3.7.98 \(\int \frac {x^{\frac {x}{x^2+(25 x^2+10 x^3+11 x^4+2 x^5+x^6)^x \log (x)}} (5 x^2+x^3+x^4+(-5 x^2-x^3-x^4) \log (x)+(25 x^2+10 x^3+11 x^4+2 x^5+x^6)^x ((5-9 x-3 x^2-6 x^3) \log ^2(x)+(-5 x-x^2-x^3) \log ^2(x) \log (25 x^2+10 x^3+11 x^4+2 x^5+x^6)))}{5 x^4+x^5+x^6+(10 x^2+2 x^3+2 x^4) (25 x^2+10 x^3+11 x^4+2 x^5+x^6)^x \log (x)+(5+x+x^2) (25 x^2+10 x^3+11 x^4+2 x^5+x^6)^{2 x} \log ^2(x)} \, dx\)

Optimal. Leaf size=29 \[ e^{\frac {x}{\left (\left (x+x \left (4+x+x^2\right )\right )^2\right )^x+\frac {x^2}{\log (x)}}} \]

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Rubi [F] time = 174.24, 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 {x^{\frac {x}{x^2+\left (25 x^2+10 x^3+11 x^4+2 x^5+x^6\right )^x \log (x)}} \left (5 x^2+x^3+x^4+\left (-5 x^2-x^3-x^4\right ) \log (x)+\left (25 x^2+10 x^3+11 x^4+2 x^5+x^6\right )^x \left (\left (5-9 x-3 x^2-6 x^3\right ) \log ^2(x)+\left (-5 x-x^2-x^3\right ) \log ^2(x) \log \left (25 x^2+10 x^3+11 x^4+2 x^5+x^6\right )\right )\right )}{5 x^4+x^5+x^6+\left (10 x^2+2 x^3+2 x^4\right ) \left (25 x^2+10 x^3+11 x^4+2 x^5+x^6\right )^x \log (x)+\left (5+x+x^2\right ) \left (25 x^2+10 x^3+11 x^4+2 x^5+x^6\right )^{2 x} \log ^2(x)} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(x^(x/(x^2 + (25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x*Log[x]))*(5*x^2 + x^3 + x^4 + (-5*x^2 - x^3 - x^4)

*Log[x] + (25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x*((5 - 9*x - 3*x^2 - 6*x^3)*Log[x]^2 + (-5*x - x^2 - x^3)*

Log[x]^2*Log[25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6])))/(5*x^4 + x^5 + x^6 + (10*x^2 + 2*x^3 + 2*x^4)*(25*x^2

+ 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x*Log[x] + (5 + x + x^2)*(25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^(2*x)*Log[x

]^2),x]

[Out]

((10*I)*Defer[Int][x^(2 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 +

x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))/((

-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][x^(4 + x/(x

^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/

Sqrt[19] + ((10*I)*Defer[Int][x^(2 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))/((1 + I*Sqrt[19] + 2*x)*(x^2 +

(x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*L

og[x]))/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][x^

(4 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^

2), x])/Sqrt[19] - ((20*I)*Defer[Int][(x^(2 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[

19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((16*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*

(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sq

rt[19] + ((4*I)*Defer[Int][(x^(4 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19] - 2*x)*

(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((12*I)*Defer[Int][(x^(5 + x/(x^2 + (x^2*(5 + x + x^

2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] - ((

20*I)*Defer[Int][(x^(2 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2

*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((16*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log

[x]))*Log[x])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((4*I)*Defer[I

nt][(x^(4 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2

)^2)^x*Log[x])^2), x])/Sqrt[19] + ((12*I)*Defer[Int][(x^(5 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])

/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((10*I)*Defer[Int][(x^(x/(x

^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))

, x])/Sqrt[19] - ((18*I)*Defer[Int][(x^(1 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19

] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((6*I)*Defer[Int][(x^(2 + x/(x^2 + (x^2*(5 +

x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19]

- ((12*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((-1 + I*Sqrt[19] - 2*x)*(x^2 +

(x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] + ((10*I)*Defer[Int][(x^(x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[

x]))*Log[x])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((18*I)*Defer[Int

][(x^(1 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^

2)^x*Log[x])), x])/Sqrt[19] - ((6*I)*Defer[Int][(x^(2 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((1

+ I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((12*I)*Defer[Int][(x^(3 + x/(x^2

+ (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x]

)/Sqrt[19] + ((10*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)

^2])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][(x^(

4 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((-1 + I*Sqrt[19] - 2*x)*(x^2 +

(x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][(x^(5 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x

*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2),

x])/Sqrt[19] + ((10*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x

^2)^2])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][(x

^(4 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((1 + I*Sqrt[19] + 2*x)*(x^2

+ (x^2*(5 + x + x^2)^2)^x*Log[x])^2), x])/Sqrt[19] + ((2*I)*Defer[Int][(x^(5 + x/(x^2 + (x^2*(5 + x + x^2)^2)^

x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])^2),

x])/Sqrt[19] - ((10*I)*Defer[Int][(x^(1 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x

^2)^2])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((2*I)*Defer[Int][(x^

(2 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((-1 + I*Sqrt[19] - 2*x)*(x^2

+ (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((2*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*

Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((-1 + I*Sqrt[19] - 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x]

)/Sqrt[19] - ((10*I)*Defer[Int][(x^(1 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)

^2])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((2*I)*Defer[Int][(x^(2 +

x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^

2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt[19] - ((2*I)*Defer[Int][(x^(3 + x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x

]))*Log[x]*Log[x^2*(5 + x + x^2)^2])/((1 + I*Sqrt[19] + 2*x)*(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x])), x])/Sqrt

[19]

Rubi steps

Aborted

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Mathematica [A] time = 0.26, size = 27, normalized size = 0.93 \begin {gather*} x^{\frac {x}{x^2+\left (x^2 \left (5+x+x^2\right )^2\right )^x \log (x)}} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(x^(x/(x^2 + (25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x*Log[x]))*(5*x^2 + x^3 + x^4 + (-5*x^2 - x^3

- x^4)*Log[x] + (25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x*((5 - 9*x - 3*x^2 - 6*x^3)*Log[x]^2 + (-5*x - x^2 -

x^3)*Log[x]^2*Log[25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6])))/(5*x^4 + x^5 + x^6 + (10*x^2 + 2*x^3 + 2*x^4)*(2

5*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x*Log[x] + (5 + x + x^2)*(25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^(2*x)

*Log[x]^2),x]

[Out]

x^(x/(x^2 + (x^2*(5 + x + x^2)^2)^x*Log[x]))

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fricas [A] time = 0.65, size = 39, normalized size = 1.34 \begin {gather*} x^{\frac {x}{x^{2} + {\left (x^{6} + 2 \, x^{5} + 11 \, x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )}^{x} \log \relax (x)}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-x^2-5*x)*log(x)^2*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2)+(-6*x^3-3*x^2-9*x+5)*log(x)^2)*exp(x*l

og(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+(-x^4-x^3-5*x^2)*log(x)+x^4+x^3+5*x^2)*exp(x*log(x)/(log(x)*exp(x*log(x^6+

2*x^5+11*x^4+10*x^3+25*x^2))+x^2))/((x^2+x+5)*log(x)^2*exp(x*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2))^2+(2*x^4+2*x

^3+10*x^2)*log(x)*exp(x*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+x^6+x^5+5*x^4),x, algorithm="fricas")

[Out]

x^(x/(x^2 + (x^6 + 2*x^5 + 11*x^4 + 10*x^3 + 25*x^2)^x*log(x)))

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{4} + x^{3} - {\left ({\left (x^{3} + x^{2} + 5 \, x\right )} \log \left (x^{6} + 2 \, x^{5} + 11 \, x^{4} + 10 \, x^{3} + 25 \, x^{2}\right ) \log \relax (x)^{2} + {\left (6 \, x^{3} + 3 \, x^{2} + 9 \, x - 5\right )} \log \relax (x)^{2}\right )} {\left (x^{6} + 2 \, x^{5} + 11 \, x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )}^{x} + 5 \, x^{2} - {\left (x^{4} + x^{3} + 5 \, x^{2}\right )} \log \relax (x)\right )} x^{\frac {x}{x^{2} + {\left (x^{6} + 2 \, x^{5} + 11 \, x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )}^{x} \log \relax (x)}}}{x^{6} + x^{5} + 5 \, x^{4} + {\left (x^{2} + x + 5\right )} {\left (x^{6} + 2 \, x^{5} + 11 \, x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )}^{2 \, x} \log \relax (x)^{2} + 2 \, {\left (x^{4} + x^{3} + 5 \, x^{2}\right )} {\left (x^{6} + 2 \, x^{5} + 11 \, x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )}^{x} \log \relax (x)}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-x^2-5*x)*log(x)^2*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2)+(-6*x^3-3*x^2-9*x+5)*log(x)^2)*exp(x*l

og(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+(-x^4-x^3-5*x^2)*log(x)+x^4+x^3+5*x^2)*exp(x*log(x)/(log(x)*exp(x*log(x^6+

2*x^5+11*x^4+10*x^3+25*x^2))+x^2))/((x^2+x+5)*log(x)^2*exp(x*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2))^2+(2*x^4+2*x

^3+10*x^2)*log(x)*exp(x*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+x^6+x^5+5*x^4),x, algorithm="giac")

[Out]

integrate((x^4 + x^3 - ((x^3 + x^2 + 5*x)*log(x^6 + 2*x^5 + 11*x^4 + 10*x^3 + 25*x^2)*log(x)^2 + (6*x^3 + 3*x^

2 + 9*x - 5)*log(x)^2)*(x^6 + 2*x^5 + 11*x^4 + 10*x^3 + 25*x^2)^x + 5*x^2 - (x^4 + x^3 + 5*x^2)*log(x))*x^(x/(

x^2 + (x^6 + 2*x^5 + 11*x^4 + 10*x^3 + 25*x^2)^x*log(x)))/(x^6 + x^5 + 5*x^4 + (x^2 + x + 5)*(x^6 + 2*x^5 + 11

*x^4 + 10*x^3 + 25*x^2)^(2*x)*log(x)^2 + 2*(x^4 + x^3 + 5*x^2)*(x^6 + 2*x^5 + 11*x^4 + 10*x^3 + 25*x^2)^x*log(

x)), x)

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maple [C] time = 0.30, size = 139, normalized size = 4.79


method	result	size

risch	\(x^{\frac {x}{\ln \relax (x ) {\mathrm e}^{-\frac {x \left (i \pi \,\mathrm {csgn}\left (i \left (x^{2}+x +5\right )^{2}\right )-2 i \pi \,\mathrm {csgn}\left (i \left (x^{2}+x +5\right )\right )+i \pi \,\mathrm {csgn}\left (i \left (x^{2}+x +5\right )^{2}\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x^{2}+x +5\right )^{2}\right )+i \pi \,\mathrm {csgn}\left (i x^{2}\right )-2 i \pi \,\mathrm {csgn}\left (i x \right )+i \pi \,\mathrm {csgn}\left (i x^{2} \left (x^{2}+x +5\right )^{2}\right )-4 \ln \relax (x )-4 \ln \left (x^{2}+x +5\right )\right )}{2}}+x^{2}}}\)	\(139\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^3-x^2-5*x)*ln(x)^2*ln(x^6+2*x^5+11*x^4+10*x^3+25*x^2)+(-6*x^3-3*x^2-9*x+5)*ln(x)^2)*exp(x*ln(x^6+2*x

^5+11*x^4+10*x^3+25*x^2))+(-x^4-x^3-5*x^2)*ln(x)+x^4+x^3+5*x^2)*exp(x*ln(x)/(ln(x)*exp(x*ln(x^6+2*x^5+11*x^4+1

0*x^3+25*x^2))+x^2))/((x^2+x+5)*ln(x)^2*exp(x*ln(x^6+2*x^5+11*x^4+10*x^3+25*x^2))^2+(2*x^4+2*x^3+10*x^2)*ln(x)

*exp(x*ln(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+x^6+x^5+5*x^4),x,method=_RETURNVERBOSE)

[Out]

x^(x/(ln(x)*exp(-1/2*x*(I*Pi*csgn(I*(x^2+x+5)^2)-2*I*Pi*csgn(I*(x^2+x+5))+I*Pi*csgn(I*(x^2+x+5)^2)*csgn(I*x^2)

*csgn(I*x^2*(x^2+x+5)^2)+I*Pi*csgn(I*x^2)-2*I*Pi*csgn(I*x)+I*Pi*csgn(I*x^2*(x^2+x+5)^2)-4*ln(x)-4*ln(x^2+x+5))

)+x^2))

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maxima [A] time = 0.92, size = 30, normalized size = 1.03 \begin {gather*} x^{\frac {x}{x^{2} + e^{\left (2 \, x \log \left (x^{2} + x + 5\right ) + 2 \, x \log \relax (x)\right )} \log \relax (x)}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-x^2-5*x)*log(x)^2*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2)+(-6*x^3-3*x^2-9*x+5)*log(x)^2)*exp(x*l

og(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+(-x^4-x^3-5*x^2)*log(x)+x^4+x^3+5*x^2)*exp(x*log(x)/(log(x)*exp(x*log(x^6+

2*x^5+11*x^4+10*x^3+25*x^2))+x^2))/((x^2+x+5)*log(x)^2*exp(x*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2))^2+(2*x^4+2*x

^3+10*x^2)*log(x)*exp(x*log(x^6+2*x^5+11*x^4+10*x^3+25*x^2))+x^6+x^5+5*x^4),x, algorithm="maxima")

[Out]

x^(x/(x^2 + e^(2*x*log(x^2 + x + 5) + 2*x*log(x))*log(x)))

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mupad [B] time = 1.39, size = 39, normalized size = 1.34 \begin {gather*} x^{\frac {x}{\ln \relax (x)\,{\left (x^6+2\,x^5+11\,x^4+10\,x^3+25\,x^2\right )}^x+x^2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp((x*log(x))/(x^2 + exp(x*log(25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6))*log(x)))*(5*x^2 - exp(x*log(25*x

^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6))*(log(x)^2*(9*x + 3*x^2 + 6*x^3 - 5) + log(25*x^2 + 10*x^3 + 11*x^4 + 2*x^

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

(25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6))*log(x)*(10*x^2 + 2*x^3 + 2*x^4) + exp(2*x*log(25*x^2 + 10*x^3 + 11*x

^4 + 2*x^5 + x^6))*log(x)^2*(x + x^2 + 5)),x)

[Out]

x^(x/(log(x)*(25*x^2 + 10*x^3 + 11*x^4 + 2*x^5 + x^6)^x + x^2))

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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**3-x**2-5*x)*ln(x)**2*ln(x**6+2*x**5+11*x**4+10*x**3+25*x**2)+(-6*x**3-3*x**2-9*x+5)*ln(x)**2)

*exp(x*ln(x**6+2*x**5+11*x**4+10*x**3+25*x**2))+(-x**4-x**3-5*x**2)*ln(x)+x**4+x**3+5*x**2)*exp(x*ln(x)/(ln(x)

*exp(x*ln(x**6+2*x**5+11*x**4+10*x**3+25*x**2))+x**2))/((x**2+x+5)*ln(x)**2*exp(x*ln(x**6+2*x**5+11*x**4+10*x*

*3+25*x**2))**2+(2*x**4+2*x**3+10*x**2)*ln(x)*exp(x*ln(x**6+2*x**5+11*x**4+10*x**3+25*x**2))+x**6+x**5+5*x**4)

,x)

[Out]

Timed out

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