3.63.13 \(\int \frac {x+2 x^3 \log (\frac {2}{x})+((-x^3+x \log (5)) \log (\frac {2}{x})+x \log (\frac {2}{x}) \log (\log (\frac {2}{x}))) \log (-x^2+\log (5)+\log (\log (\frac {2}{x})))+((-x^2+x^3+(1-x) \log (5)) \log (\frac {2}{x})+(1-x) \log (\frac {2}{x}) \log (\log (\frac {2}{x}))) \log ^2(-x^2+\log (5)+\log (\log (\frac {2}{x})))}{((-x^4+x^2 \log (5)) \log (\frac {2}{x})+x^2 \log (\frac {2}{x}) \log (\log (\frac {2}{x}))) \log (-x^2+\log (5)+\log (\log (\frac {2}{x})))+((-5 x^3+x^4+(5 x-x^2) \log (5)) \log (\frac {2}{x})+(-x^3+x \log (5)) \log (\frac {2}{x}) \log (x)+((5 x-x^2) \log (\frac {2}{x})+x \log (\frac {2}{x}) \log (x)) \log (\log (\frac {2}{x}))) \log ^2(-x^2+\log (5)+\log (\log (\frac {2}{x})))} \, dx\)

Optimal. Leaf size=28 \[ \log \left (5-x+\log (x)+\frac {x}{\log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}\right ) \]

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Rubi [F]  time = 22.63, 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+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x + 2*x^3*Log[2/x] + ((-x^3 + x*Log[5])*Log[2/x] + x*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[
2/x]]] + ((-x^2 + x^3 + (1 - x)*Log[5])*Log[2/x] + (1 - x)*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log
[2/x]]]^2)/(((-x^4 + x^2*Log[5])*Log[2/x] + x^2*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]] + (
(-5*x^3 + x^4 + (5*x - x^2)*Log[5])*Log[2/x] + (-x^3 + x*Log[5])*Log[2/x]*Log[x] + ((5*x - x^2)*Log[2/x] + x*L
og[2/x]*Log[x])*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]^2),x]

[Out]

Log[5 - x + Log[x]] - 2*Defer[Int][x/((x^2 - Log[5*Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]), x] - Defer[
Int][1/(x*Log[2/x]*(x^2 - Log[5*Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]), x] - 5*Log[5]*Defer[Int][1/((5
- x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] + Log[5
]*Defer[Int][x/((5 - x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/
x]]])), x] + 4*Defer[Int][x^2/((5 - x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[
5] + Log[Log[2/x]]])), x] + Defer[Int][(x^2*Log[x])/((5 - x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - L
og[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - 5*Defer[Int][Log[Log[2/x]]/((5 - x + Log[x])*(x^2 - Log[5*Lo
g[2/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] + Defer[Int][(x*Log[Log[2/x]])/((5 -
x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] + Defer[In
t][Log[5*Log[2/x]]/((5 - x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Lo
g[2/x]]])), x] - Defer[Int][(x*Log[5*Log[2/x]])/((5 - x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x - (-5 + x - Log[x
])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - 10*Defer[Int][x/((-x^2 + Log[5*Log[2/x]])*(x - (-5 + x - Log[x])
*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] + 2*Defer[Int][x^2/((-x^2 + Log[5*Log[2/x]])*(x - (-5 + x - Log[x])*
Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] + Defer[Int][1/(Log[2/x]*(-x^2 + Log[5*Log[2/x]])*(x - (-5 + x - Log[
x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - 5*Defer[Int][1/(x*Log[2/x]*(-x^2 + Log[5*Log[2/x]])*(x - (-5 +
x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - 2*Defer[Int][(x*Log[x])/((-x^2 + Log[5*Log[2/x]])*(x -
(-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - Defer[Int][Log[x]/(x*Log[2/x]*(-x^2 + Log[5*Log[2
/x]])*(x - (-5 + x - Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - Log[5]*Defer[Int][Log[x]/((5 - x + Log
[x])*(x^2 - Log[5*Log[2/x]])*(x + (5 - x + Log[x])*Log[-x^2 + Log[5] + Log[Log[2/x]]])), x] - Defer[Int][(Log[
x]*Log[Log[2/x]])/((5 - x + Log[x])*(x^2 - Log[5*Log[2/x]])*(x + (5 - x + Log[x])*Log[-x^2 + Log[5] + Log[Log[
2/x]]])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x-\log \left (\frac {2}{x}\right ) \left (2 x^3+x \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+(-1+x) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right ) \left (x-(-5+x-\log (x)) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )} \, dx\\ &=\int \left (\frac {-1+x}{x (-5+x-\log (x))}+\frac {-1-2 x^2 \log \left (\frac {2}{x}\right )}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}+\frac {\left (1+2 x^2 \log \left (\frac {2}{x}\right )\right ) (-5+x-\log (x))}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (-x-5 \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+x \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )-\log (x) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )}+\frac {4 x^2-5 \log (5)+x \log (5)+x^2 \log (x)-\log (5) \log (x)-5 \log \left (\log \left (\frac {2}{x}\right )\right )+x \log \left (\log \left (\frac {2}{x}\right )\right )-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )}{(-5+x-\log (x)) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (-x-5 \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+x \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )-\log (x) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )}\right ) \, dx\\ &=\int \frac {-1+x}{x (-5+x-\log (x))} \, dx+\int \frac {-1-2 x^2 \log \left (\frac {2}{x}\right )}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx+\int \frac {\left (1+2 x^2 \log \left (\frac {2}{x}\right )\right ) (-5+x-\log (x))}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (-x-5 \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+x \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )-\log (x) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )} \, dx+\int \frac {4 x^2-5 \log (5)+x \log (5)+x^2 \log (x)-\log (5) \log (x)-5 \log \left (\log \left (\frac {2}{x}\right )\right )+x \log \left (\log \left (\frac {2}{x}\right )\right )-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )}{(-5+x-\log (x)) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (-x-5 \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+x \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )-\log (x) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )} \, dx\\ &=\log (5-x+\log (x))+\int \left (-\frac {2 x}{\left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}-\frac {1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}\right ) \, dx+\int \frac {\left (1+2 x^2 \log \left (\frac {2}{x}\right )\right ) (5-x+\log (x))}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x-(-5+x-\log (x)) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )} \, dx+\int \frac {4 x^2-5 \log (5)+x \log (5)+\log (x) \left (x^2-\log (5)-\log \left (\log \left (\frac {2}{x}\right )\right )\right )+(-5+x) \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )}{(5-x+\log (x)) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x-(-5+x-\log (x)) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.37, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(x + 2*x^3*Log[2/x] + ((-x^3 + x*Log[5])*Log[2/x] + x*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Lo
g[Log[2/x]]] + ((-x^2 + x^3 + (1 - x)*Log[5])*Log[2/x] + (1 - x)*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + L
og[Log[2/x]]]^2)/(((-x^4 + x^2*Log[5])*Log[2/x] + x^2*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]
]] + ((-5*x^3 + x^4 + (5*x - x^2)*Log[5])*Log[2/x] + (-x^3 + x*Log[5])*Log[2/x]*Log[x] + ((5*x - x^2)*Log[2/x]
+ x*Log[2/x]*Log[x])*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]^2),x]

[Out]

Integrate[(x + 2*x^3*Log[2/x] + ((-x^3 + x*Log[5])*Log[2/x] + x*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Lo
g[Log[2/x]]] + ((-x^2 + x^3 + (1 - x)*Log[5])*Log[2/x] + (1 - x)*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + L
og[Log[2/x]]]^2)/(((-x^4 + x^2*Log[5])*Log[2/x] + x^2*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]
]] + ((-5*x^3 + x^4 + (5*x - x^2)*Log[5])*Log[2/x] + (-x^3 + x*Log[5])*Log[2/x]*Log[x] + ((5*x - x^2)*Log[2/x]
+ x*Log[2/x]*Log[x])*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]^2), x]

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fricas [B]  time = 0.81, size = 85, normalized size = 3.04 \begin {gather*} \log \left (x - \log \relax (2) + \log \left (\frac {2}{x}\right ) - 5\right ) + \log \left (\frac {{\left (x - \log \relax (2) + \log \left (\frac {2}{x}\right ) - 5\right )} \log \left (-x^{2} + \log \relax (5) + \log \left (\log \left (\frac {2}{x}\right )\right )\right ) - x}{x - \log \relax (2) + \log \left (\frac {2}{x}\right ) - 5}\right ) - \log \left (\log \left (-x^{2} + \log \relax (5) + \log \left (\log \left (\frac {2}{x}\right )\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*log(2/x)*log(log(2/x))+((-x+1)*log(5)+x^3-x^2)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x
*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)
*log(x)+(-x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x^2+5*x)*log(5)+x^4-5*x^3)*log(2/
x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*log(2/x)*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+l
og(5)-x^2)),x, algorithm="fricas")

[Out]

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

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giac [B]  time = 0.65, size = 85, normalized size = 3.04 \begin {gather*} \log \left (x \log \left (-x^{2} + \log \relax (5) + \log \left (\log \relax (2) - \log \relax (x)\right )\right ) - \log \left (-x^{2} + \log \relax (5) + \log \left (\log \relax (2) - \log \relax (x)\right )\right ) \log \relax (x) - x - 5 \, \log \left (-x^{2} + \log \relax (5) + \log \left (\log \relax (2) - \log \relax (x)\right )\right )\right ) - \log \left (\log \left (-x^{2} + \log \relax (5) + \log \left (\log \relax (2) - \log \relax (x)\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*log(2/x)*log(log(2/x))+((-x+1)*log(5)+x^3-x^2)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x
*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)
*log(x)+(-x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x^2+5*x)*log(5)+x^4-5*x^3)*log(2/
x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*log(2/x)*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+l
og(5)-x^2)),x, algorithm="giac")

[Out]

log(x*log(-x^2 + log(5) + log(log(2) - log(x))) - log(-x^2 + log(5) + log(log(2) - log(x)))*log(x) - x - 5*log
(-x^2 + log(5) + log(log(2) - log(x)))) - log(log(-x^2 + log(5) + log(log(2) - log(x))))

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maple [B]  time = 1.63, size = 61, normalized size = 2.18

method	result	size
risch	\(\ln \left (\ln \relax (x )-x +5\right )-\ln \left (\ln \left (\ln \left (\ln \relax (2)-\ln \relax (x )\right )+\ln \relax (5)-x^{2}\right )\right )+\ln \left (-\frac {x}{-\ln \relax (x )+x -5}+\ln \left (\ln \left (\ln \relax (2)-\ln \relax (x )\right )+\ln \relax (5)-x^{2}\right )\right )\)	\(61\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((1-x)*ln(2/x)*ln(ln(2/x))+((1-x)*ln(5)+x^3-x^2)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x^2)^2+(x*ln(2/x)*ln(ln(2/
x))+(x*ln(5)-x^3)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x^2)+2*x^3*ln(2/x)+x)/(((x*ln(2/x)*ln(x)+(-x^2+5*x)*ln(2/x))*l
n(ln(2/x))+(x*ln(5)-x^3)*ln(2/x)*ln(x)+((-x^2+5*x)*ln(5)+x^4-5*x^3)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x^2)^2+(x^2*
ln(2/x)*ln(ln(2/x))+(x^2*ln(5)-x^4)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x^2)),x,method=_RETURNVERBOSE)

[Out]

ln(ln(x)-x+5)-ln(ln(ln(ln(2)-ln(x))+ln(5)-x^2))+ln(-x/(-ln(x)+x-5)+ln(ln(ln(2)-ln(x))+ln(5)-x^2))

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maxima [B]  time = 0.61, size = 69, normalized size = 2.46 \begin {gather*} \log \left (-x + \log \relax (x) + 5\right ) + \log \left (\frac {{\left (x - \log \relax (x) - 5\right )} \log \left (-x^{2} + \log \relax (5) + \log \left (\log \relax (2) - \log \relax (x)\right )\right ) - x}{x - \log \relax (x) - 5}\right ) - \log \left (\log \left (-x^{2} + \log \relax (5) + \log \left (\log \relax (2) - \log \relax (x)\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*log(2/x)*log(log(2/x))+((-x+1)*log(5)+x^3-x^2)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x
*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)
*log(x)+(-x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x^2+5*x)*log(5)+x^4-5*x^3)*log(2/
x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*log(2/x)*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+l
og(5)-x^2)),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {x-{\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \relax (5)-x^2\right )}^2\,\left (\ln \left (\frac {2}{x}\right )\,\left (\ln \relax (5)\,\left (x-1\right )+x^2-x^3\right )+\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\frac {2}{x}\right )\,\left (x-1\right )\right )+\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \relax (5)-x^2\right )\,\left (\ln \left (\frac {2}{x}\right )\,\left (x\,\ln \relax (5)-x^3\right )+x\,\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\frac {2}{x}\right )\right )+2\,x^3\,\ln \left (\frac {2}{x}\right )}{\left (\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\left (\ln \left (\frac {2}{x}\right )\,\left (5\,x-x^2\right )+x\,\ln \left (\frac {2}{x}\right )\,\ln \relax (x)\right )+\ln \left (\frac {2}{x}\right )\,\left (\ln \relax (5)\,\left (5\,x-x^2\right )-5\,x^3+x^4\right )+\ln \left (\frac {2}{x}\right )\,\ln \relax (x)\,\left (x\,\ln \relax (5)-x^3\right )\right )\,{\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \relax (5)-x^2\right )}^2+\left (\ln \left (\frac {2}{x}\right )\,\left (x^2\,\ln \relax (5)-x^4\right )+x^2\,\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \relax (5)-x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x - log(log(log(2/x)) + log(5) - x^2)^2*(log(2/x)*(log(5)*(x - 1) + x^2 - x^3) + log(log(2/x))*log(2/x)*(
x - 1)) + log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x*log(5) - x^3) + x*log(log(2/x))*log(2/x)) + 2*x^3*log
(2/x))/(log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x^2*log(5) - x^4) + x^2*log(log(2/x))*log(2/x)) + log(log
(log(2/x)) + log(5) - x^2)^2*(log(log(2/x))*(log(2/x)*(5*x - x^2) + x*log(2/x)*log(x)) + log(2/x)*(log(5)*(5*x
- x^2) - 5*x^3 + x^4) + log(2/x)*log(x)*(x*log(5) - x^3))),x)

[Out]

int((x - log(log(log(2/x)) + log(5) - x^2)^2*(log(2/x)*(log(5)*(x - 1) + x^2 - x^3) + log(log(2/x))*log(2/x)*(
x - 1)) + log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x*log(5) - x^3) + x*log(log(2/x))*log(2/x)) + 2*x^3*log
(2/x))/(log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x^2*log(5) - x^4) + x^2*log(log(2/x))*log(2/x)) + log(log
(log(2/x)) + log(5) - x^2)^2*(log(log(2/x))*(log(2/x)*(5*x - x^2) + x*log(2/x)*log(x)) + log(2/x)*(log(5)*(5*x
- x^2) - 5*x^3 + x^4) + log(2/x)*log(x)*(x*log(5) - x^3))), x)

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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+1)*ln(2/x)*ln(ln(2/x))+((-x+1)*ln(5)+x**3-x**2)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x**2)**2+(x*ln(2
/x)*ln(ln(2/x))+(x*ln(5)-x**3)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x**2)+2*x**3*ln(2/x)+x)/(((x*ln(2/x)*ln(x)+(-x**2
+5*x)*ln(2/x))*ln(ln(2/x))+(x*ln(5)-x**3)*ln(2/x)*ln(x)+((-x**2+5*x)*ln(5)+x**4-5*x**3)*ln(2/x))*ln(ln(ln(2/x)
)+ln(5)-x**2)**2+(x**2*ln(2/x)*ln(ln(2/x))+(x**2*ln(5)-x**4)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x**2)),x)

[Out]

Timed out

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