3.72.95 \(\int \frac {-6 e^5-6 x+(-6 x-6 x^2-2 x^6+e^5 (-6 x-2 x^5)) \log (\frac {2}{x})+(6 e^5 x^4+6 x^5) \log (\frac {2}{x}) \log (\frac {5 \log (\frac {2}{x})}{e^5+x})+(-6 e^5 x^3-6 x^4) \log (\frac {2}{x}) \log ^2(\frac {5 \log (\frac {2}{x})}{e^5+x})+(2 e^5 x^2+2 x^3) \log (\frac {2}{x}) \log ^3(\frac {5 \log (\frac {2}{x})}{e^5+x})}{(-e^5 x^4-x^5) \log (\frac {2}{x})+(3 e^5 x^3+3 x^4) \log (\frac {2}{x}) \log (\frac {5 \log (\frac {2}{x})}{e^5+x})+(-3 e^5 x^2-3 x^3) \log (\frac {2}{x}) \log ^2(\frac {5 \log (\frac {2}{x})}{e^5+x})+(e^5 x+x^2) \log (\frac {2}{x}) \log ^3(\frac {5 \log (\frac {2}{x})}{e^5+x})} \, dx\)

Optimal. Leaf size=28 \[ x^2-\frac {3}{\left (-x+\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^2} \]

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Rubi [F]  time = 4.86, 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 {-6 e^5-6 x+\left (-6 x-6 x^2-2 x^6+e^5 \left (-6 x-2 x^5\right )\right ) \log \left (\frac {2}{x}\right )+\left (6 e^5 x^4+6 x^5\right ) \log \left (\frac {2}{x}\right ) \log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (-6 e^5 x^3-6 x^4\right ) \log \left (\frac {2}{x}\right ) \log ^2\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (2 e^5 x^2+2 x^3\right ) \log \left (\frac {2}{x}\right ) \log ^3\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )}{\left (-e^5 x^4-x^5\right ) \log \left (\frac {2}{x}\right )+\left (3 e^5 x^3+3 x^4\right ) \log \left (\frac {2}{x}\right ) \log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (-3 e^5 x^2-3 x^3\right ) \log \left (\frac {2}{x}\right ) \log ^2\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (e^5 x+x^2\right ) \log \left (\frac {2}{x}\right ) \log ^3\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-6*E^5 - 6*x + (-6*x - 6*x^2 - 2*x^6 + E^5*(-6*x - 2*x^5))*Log[2/x] + (6*E^5*x^4 + 6*x^5)*Log[2/x]*Log[(5
*Log[2/x])/(E^5 + x)] + (-6*E^5*x^3 - 6*x^4)*Log[2/x]*Log[(5*Log[2/x])/(E^5 + x)]^2 + (2*E^5*x^2 + 2*x^3)*Log[
2/x]*Log[(5*Log[2/x])/(E^5 + x)]^3)/((-(E^5*x^4) - x^5)*Log[2/x] + (3*E^5*x^3 + 3*x^4)*Log[2/x]*Log[(5*Log[2/x
])/(E^5 + x)] + (-3*E^5*x^2 - 3*x^3)*Log[2/x]*Log[(5*Log[2/x])/(E^5 + x)]^2 + (E^5*x + x^2)*Log[2/x]*Log[(5*Lo
g[2/x])/(E^5 + x)]^3),x]

[Out]

x^2 + 6*Defer[Int][(x - Log[(5*Log[2/x])/(E^5 + x)])^(-3), x] - 6*E^5*Defer[Int][1/((E^5 + x)*(x - Log[(5*Log[
2/x])/(E^5 + x)])^3), x] + 6*(1 + E^5)*Defer[Int][1/((E^5 + x)*(x - Log[(5*Log[2/x])/(E^5 + x)])^3), x] + 6*De
fer[Int][1/(x*Log[2/x]*(x - Log[(5*Log[2/x])/(E^5 + x)])^3), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 \left (e^5+x\right )+2 x \log \left (\frac {2}{x}\right ) \left (3+3 x+x^5+e^5 \left (3+x^4\right )-3 x^3 \left (e^5+x\right ) \log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+3 x^2 \left (e^5+x\right ) \log ^2\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )-x \left (e^5+x\right ) \log ^3\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )}{x \left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx\\ &=\int \left (2 x+\frac {6 \left (e^5+x+\left (1+e^5\right ) x \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right )\right )}{x \left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx\\ &=x^2+6 \int \frac {e^5+x+\left (1+e^5\right ) x \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right )}{x \left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx\\ &=x^2+6 \int \frac {e^5+x+x \left (1+e^5+x\right ) \log \left (\frac {2}{x}\right )}{x \left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx\\ &=x^2+6 \int \left (\frac {-e^5-x-\left (1+e^5\right ) x \log \left (\frac {2}{x}\right )-x^2 \log \left (\frac {2}{x}\right )}{e^5 \left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}+\frac {e^5+x+\left (1+e^5\right ) x \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right )}{e^5 x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx\\ &=x^2+\frac {6 \int \frac {-e^5-x-\left (1+e^5\right ) x \log \left (\frac {2}{x}\right )-x^2 \log \left (\frac {2}{x}\right )}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\frac {6 \int \frac {e^5+x+\left (1+e^5\right ) x \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right )}{x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}\\ &=x^2+\frac {6 \int \frac {-e^5-x-x \left (1+e^5+x\right ) \log \left (\frac {2}{x}\right )}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\frac {6 \int \frac {e^5+x+x \left (1+e^5+x\right ) \log \left (\frac {2}{x}\right )}{x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}\\ &=x^2+\frac {6 \int \left (\frac {1+e^5}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}+\frac {x}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}+\frac {1}{\log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}+\frac {e^5}{x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx}{e^5}+\frac {6 \int \left (-\frac {\left (1+e^5\right ) x}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}-\frac {x^2}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}-\frac {e^5}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}-\frac {x}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx}{e^5}\\ &=x^2+6 \int \frac {1}{x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx-6 \int \frac {1}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx+\left (6 \left (1+\frac {1}{e^5}\right )\right ) \int \frac {1}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx+\frac {6 \int \frac {x}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}-\frac {6 \int \frac {x^2}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\frac {6 \int \frac {1}{\log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}-\frac {6 \int \frac {x}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\frac {\left (6 \left (-1-e^5\right )\right ) \int \frac {x}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}\\ &=x^2+6 \int \frac {1}{x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx-6 \int \frac {1}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx+\left (6 \left (1+\frac {1}{e^5}\right )\right ) \int \frac {1}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx-\frac {6 \int \left (-\frac {e^5}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}+\frac {x}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}+\frac {e^{10}}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx}{e^5}-\frac {6 \int \left (\frac {1}{\log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}-\frac {e^5}{\left (e^5+x\right ) \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx}{e^5}+\frac {6 \int \frac {x}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\frac {6 \int \frac {1}{\log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\frac {\left (6 \left (-1-e^5\right )\right ) \int \left (\frac {1}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}-\frac {e^5}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3}\right ) \, dx}{e^5}\\ &=x^2+6 \int \frac {1}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx+6 \int \frac {1}{x \log \left (\frac {2}{x}\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx+\left (6 \left (1+\frac {1}{e^5}\right )\right ) \int \frac {1}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx-\left (6 e^5\right ) \int \frac {1}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx+\frac {\left (6 \left (-1-e^5\right )\right ) \int \frac {1}{\left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx}{e^5}+\left (6 \left (1+e^5\right )\right ) \int \frac {1}{\left (e^5+x\right ) \left (x-\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 28, normalized size = 1.00 \begin {gather*} x^2-\frac {3}{\left (-x+\log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6*E^5 - 6*x + (-6*x - 6*x^2 - 2*x^6 + E^5*(-6*x - 2*x^5))*Log[2/x] + (6*E^5*x^4 + 6*x^5)*Log[2/x]*
Log[(5*Log[2/x])/(E^5 + x)] + (-6*E^5*x^3 - 6*x^4)*Log[2/x]*Log[(5*Log[2/x])/(E^5 + x)]^2 + (2*E^5*x^2 + 2*x^3
)*Log[2/x]*Log[(5*Log[2/x])/(E^5 + x)]^3)/((-(E^5*x^4) - x^5)*Log[2/x] + (3*E^5*x^3 + 3*x^4)*Log[2/x]*Log[(5*L
og[2/x])/(E^5 + x)] + (-3*E^5*x^2 - 3*x^3)*Log[2/x]*Log[(5*Log[2/x])/(E^5 + x)]^2 + (E^5*x + x^2)*Log[2/x]*Log
[(5*Log[2/x])/(E^5 + x)]^3),x]

[Out]

x^2 - 3/(-x + Log[(5*Log[2/x])/(E^5 + x)])^2

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fricas [B]  time = 0.90, size = 88, normalized size = 3.14 \begin {gather*} \frac {x^{4} - 2 \, x^{3} \log \left (\frac {5 \, \log \left (\frac {2}{x}\right )}{x + e^{5}}\right ) + x^{2} \log \left (\frac {5 \, \log \left (\frac {2}{x}\right )}{x + e^{5}}\right )^{2} - 3}{x^{2} - 2 \, x \log \left (\frac {5 \, \log \left (\frac {2}{x}\right )}{x + e^{5}}\right ) + \log \left (\frac {5 \, \log \left (\frac {2}{x}\right )}{x + e^{5}}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*exp(5)+2*x^3)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-6*x^3*exp(5)-6*x^4)*log(2/x)*log(5*log
(2/x)/(exp(5)+x))^2+(6*x^4*exp(5)+6*x^5)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+((-2*x^5-6*x)*exp(5)-2*x^6-6*x^2-
6*x)*log(2/x)-6*exp(5)-6*x)/((x*exp(5)+x^2)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-3*x^2*exp(5)-3*x^3)*log(2/
x)*log(5*log(2/x)/(exp(5)+x))^2+(3*x^3*exp(5)+3*x^4)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+(-x^4*exp(5)-x^5)*log
(2/x)),x, algorithm="fricas")

[Out]

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

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giac [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(((2*x^2*exp(5)+2*x^3)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-6*x^3*exp(5)-6*x^4)*log(2/x)*log(5*log
(2/x)/(exp(5)+x))^2+(6*x^4*exp(5)+6*x^5)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+((-2*x^5-6*x)*exp(5)-2*x^6-6*x^2-
6*x)*log(2/x)-6*exp(5)-6*x)/((x*exp(5)+x^2)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-3*x^2*exp(5)-3*x^3)*log(2/
x)*log(5*log(2/x)/(exp(5)+x))^2+(3*x^3*exp(5)+3*x^4)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+(-x^4*exp(5)-x^5)*log
(2/x)),x, algorithm="giac")

[Out]

Timed out

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maple [F]  time = 0.08, size = 0, normalized size = 0.00 \[\int \frac {\left (2 x^{2} {\mathrm e}^{5}+2 x^{3}\right ) \ln \left (\frac {2}{x}\right ) \ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )^{3}+\left (-6 x^{3} {\mathrm e}^{5}-6 x^{4}\right ) \ln \left (\frac {2}{x}\right ) \ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )^{2}+\left (6 x^{4} {\mathrm e}^{5}+6 x^{5}\right ) \ln \left (\frac {2}{x}\right ) \ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )+\left (\left (-2 x^{5}-6 x \right ) {\mathrm e}^{5}-2 x^{6}-6 x^{2}-6 x \right ) \ln \left (\frac {2}{x}\right )-6 \,{\mathrm e}^{5}-6 x}{\left (x \,{\mathrm e}^{5}+x^{2}\right ) \ln \left (\frac {2}{x}\right ) \ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )^{3}+\left (-3 x^{2} {\mathrm e}^{5}-3 x^{3}\right ) \ln \left (\frac {2}{x}\right ) \ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )^{2}+\left (3 x^{3} {\mathrm e}^{5}+3 x^{4}\right ) \ln \left (\frac {2}{x}\right ) \ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )+\left (-x^{4} {\mathrm e}^{5}-x^{5}\right ) \ln \left (\frac {2}{x}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [C]  time = 0.79, size = 215, normalized size = 7.68 \begin {gather*} \frac {2 \, {\left (i \, \pi + \log \relax (5)\right )} x^{3} - x^{4} - x^{2} \log \left (x + e^{5}\right )^{2} - x^{2} \log \left (-\log \relax (2) + \log \relax (x)\right )^{2} + {\left (\pi ^{2} - 2 i \, \pi \log \relax (5) - \log \relax (5)^{2}\right )} x^{2} + 2 \, {\left ({\left (i \, \pi + \log \relax (5)\right )} x^{2} - x^{3}\right )} \log \left (x + e^{5}\right ) + 2 \, {\left ({\left (-i \, \pi - \log \relax (5)\right )} x^{2} + x^{3} + x^{2} \log \left (x + e^{5}\right )\right )} \log \left (-\log \relax (2) + \log \relax (x)\right ) + 3}{\pi ^{2} + 2 \, {\left (i \, \pi + \log \relax (5)\right )} x - x^{2} - 2 i \, \pi \log \relax (5) - \log \relax (5)^{2} + 2 \, {\left (i \, \pi - x + \log \relax (5)\right )} \log \left (x + e^{5}\right ) - \log \left (x + e^{5}\right )^{2} + 2 \, {\left (-i \, \pi + x - \log \relax (5) + \log \left (x + e^{5}\right )\right )} \log \left (-\log \relax (2) + \log \relax (x)\right ) - \log \left (-\log \relax (2) + \log \relax (x)\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*exp(5)+2*x^3)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-6*x^3*exp(5)-6*x^4)*log(2/x)*log(5*log
(2/x)/(exp(5)+x))^2+(6*x^4*exp(5)+6*x^5)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+((-2*x^5-6*x)*exp(5)-2*x^6-6*x^2-
6*x)*log(2/x)-6*exp(5)-6*x)/((x*exp(5)+x^2)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-3*x^2*exp(5)-3*x^3)*log(2/
x)*log(5*log(2/x)/(exp(5)+x))^2+(3*x^3*exp(5)+3*x^4)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+(-x^4*exp(5)-x^5)*log
(2/x)),x, algorithm="maxima")

[Out]

(2*(I*pi + log(5))*x^3 - x^4 - x^2*log(x + e^5)^2 - x^2*log(-log(2) + log(x))^2 + (pi^2 - 2*I*pi*log(5) - log(
5)^2)*x^2 + 2*((I*pi + log(5))*x^2 - x^3)*log(x + e^5) + 2*((-I*pi - log(5))*x^2 + x^3 + x^2*log(x + e^5))*log
(-log(2) + log(x)) + 3)/(pi^2 + 2*(I*pi + log(5))*x - x^2 - 2*I*pi*log(5) - log(5)^2 + 2*(I*pi - x + log(5))*l
og(x + e^5) - log(x + e^5)^2 + 2*(-I*pi + x - log(5) + log(x + e^5))*log(-log(2) + log(x)) - log(-log(2) + log
(x))^2)

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mupad [B]  time = 5.11, size = 27, normalized size = 0.96 \begin {gather*} x^2-\frac {3}{{\left (x-\ln \left (\frac {5\,\ln \left (\frac {2}{x}\right )}{x+{\mathrm {e}}^5}\right )\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6*x + 6*exp(5) + log(2/x)*(6*x + exp(5)*(6*x + 2*x^5) + 6*x^2 + 2*x^6) - log((5*log(2/x))/(x + exp(5)))*l
og(2/x)*(6*x^4*exp(5) + 6*x^5) - log((5*log(2/x))/(x + exp(5)))^3*log(2/x)*(2*x^2*exp(5) + 2*x^3) + log((5*log
(2/x))/(x + exp(5)))^2*log(2/x)*(6*x^3*exp(5) + 6*x^4))/(log(2/x)*(x^4*exp(5) + x^5) - log((5*log(2/x))/(x + e
xp(5)))*log(2/x)*(3*x^3*exp(5) + 3*x^4) + log((5*log(2/x))/(x + exp(5)))^2*log(2/x)*(3*x^2*exp(5) + 3*x^3) - l
og((5*log(2/x))/(x + exp(5)))^3*log(2/x)*(x*exp(5) + x^2)),x)

[Out]

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

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sympy [A]  time = 1.07, size = 39, normalized size = 1.39 \begin {gather*} x^{2} - \frac {3}{x^{2} - 2 x \log {\left (\frac {5 \log {\left (\frac {2}{x} \right )}}{x + e^{5}} \right )} + \log {\left (\frac {5 \log {\left (\frac {2}{x} \right )}}{x + e^{5}} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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