Optimal. Leaf size=19 \[ \frac {x+625 x^5+\log (2)}{x \log (5 x)} \]
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Rubi [F] time = 0.28, 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-625 x^5-\log (2)+\left (2500 x^5-\log (2)\right ) \log (5 x)}{x^2 \log ^2(5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-x-625 x^5-\log (2)}{x^2 \log ^2(5 x)}+\frac {2500 x^5-\log (2)}{x^2 \log (5 x)}\right ) \, dx\\ &=\int \frac {-x-625 x^5-\log (2)}{x^2 \log ^2(5 x)} \, dx+\int \frac {2500 x^5-\log (2)}{x^2 \log (5 x)} \, dx\\ &=\int \left (\frac {2500 x^3}{\log (5 x)}-\frac {\log (2)}{x^2 \log (5 x)}\right ) \, dx+\int \frac {-x-625 x^5-\log (2)}{x^2 \log ^2(5 x)} \, dx\\ &=2500 \int \frac {x^3}{\log (5 x)} \, dx-\log (2) \int \frac {1}{x^2 \log (5 x)} \, dx+\int \frac {-x-625 x^5-\log (2)}{x^2 \log ^2(5 x)} \, dx\\ &=4 \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (5 x)\right )-(5 \log (2)) \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (5 x)\right )+\int \frac {-x-625 x^5-\log (2)}{x^2 \log ^2(5 x)} \, dx\\ &=4 \text {Ei}(4 \log (5 x))-5 \text {Ei}(-\log (5 x)) \log (2)+\int \frac {-x-625 x^5-\log (2)}{x^2 \log ^2(5 x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 19, normalized size = 1.00 \begin {gather*} \frac {x+625 x^5+\log (2)}{x \log (5 x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 19, normalized size = 1.00 \begin {gather*} \frac {625 \, x^{5} + x + \log \relax (2)}{x \log \left (5 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 19, normalized size = 1.00 \begin {gather*} \frac {625 \, x^{5} + x + \log \relax (2)}{x \log \left (5 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 20, normalized size = 1.05
method | result | size |
norman | \(\frac {x +625 x^{5}+\ln \relax (2)}{x \ln \left (5 x \right )}\) | \(20\) |
risch | \(\frac {x +625 x^{5}+\ln \relax (2)}{x \ln \left (5 x \right )}\) | \(20\) |
derivativedivides | \(\frac {625 x^{4}}{\ln \left (5 x \right )}+5 \ln \relax (2) \expIntegralEi \left (1, \ln \left (5 x \right )\right )-5 \ln \relax (2) \left (-\frac {1}{5 x \ln \left (5 x \right )}+\expIntegralEi \left (1, \ln \left (5 x \right )\right )\right )+\frac {1}{\ln \left (5 x \right )}\) | \(51\) |
default | \(\frac {625 x^{4}}{\ln \left (5 x \right )}+5 \ln \relax (2) \expIntegralEi \left (1, \ln \left (5 x \right )\right )-5 \ln \relax (2) \left (-\frac {1}{5 x \ln \left (5 x \right )}+\expIntegralEi \left (1, \ln \left (5 x \right )\right )\right )+\frac {1}{\ln \left (5 x \right )}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 47, normalized size = 2.47 \begin {gather*} -5 \, {\rm Ei}\left (-\log \left (5 \, x\right )\right ) \log \relax (2) + 5 \, \Gamma \left (-1, \log \left (5 \, x\right )\right ) \log \relax (2) + \frac {1}{\log \left (5 \, x\right )} + 4 \, {\rm Ei}\left (4 \, \log \left (5 \, x\right )\right ) - 4 \, \Gamma \left (-1, -4 \, \log \left (5 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.55, size = 19, normalized size = 1.00 \begin {gather*} \frac {625\,x^5+x+\ln \relax (2)}{x\,\ln \left (5\,x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.79 \begin {gather*} \frac {625 x^{5} + x + \log {\relax (2 )}}{x \log {\left (5 x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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