Optimal. Leaf size=19 \[ x+5 x^6 \left (2-\frac {x+\log (\log (x))}{x}\right ) \]
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Rubi [A]
time = 0.16, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps
used = 9, number of rules used = 4, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.129, Rules used = {6874, 2346,
2209, 2602} \begin {gather*} 5 x^6-5 x^5 \log (\log (x))+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2346
Rule 2602
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-5 x^4+\log (x)+30 x^5 \log (x)}{\log (x)}-25 x^4 \log (\log (x))\right ) \, dx\\ &=-\left (25 \int x^4 \log (\log (x)) \, dx\right )+\int \frac {-5 x^4+\log (x)+30 x^5 \log (x)}{\log (x)} \, dx\\ &=-5 x^5 \log (\log (x))+5 \int \frac {x^4}{\log (x)} \, dx+\int \left (1+30 x^5-\frac {5 x^4}{\log (x)}\right ) \, dx\\ &=x+5 x^6-5 x^5 \log (\log (x))-5 \int \frac {x^4}{\log (x)} \, dx+5 \text {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )\\ &=x+5 x^6+5 \text {Ei}(5 \log (x))-5 x^5 \log (\log (x))-5 \text {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )\\ &=x+5 x^6-5 x^5 \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 15, normalized size = 0.79 \begin {gather*} x+5 x^6-5 x^5 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.55, size = 16, normalized size = 0.84
method | result | size |
default | \(5 x^{6}+x -5 x^{5} \ln \left (\ln \left (x \right )\right )\) | \(16\) |
risch | \(5 x^{6}+x -5 x^{5} \ln \left (\ln \left (x \right )\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 15, normalized size = 0.79 \begin {gather*} 5 \, x^{6} - 5 \, x^{5} \log \left (\log \left (x\right )\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 15, normalized size = 0.79 \begin {gather*} 5 \, x^{6} - 5 \, x^{5} \log \left (\log \left (x\right )\right ) + x \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*} 5 x^{6} - 5 x^{5} \log {\left (\log {\left (x \right )} \right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 15, normalized size = 0.79 \begin {gather*} 5 \, x^{6} - 5 \, x^{5} \log \left (\log \left (x\right )\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.77, size = 15, normalized size = 0.79 \begin {gather*} x-5\,x^5\,\ln \left (\ln \left (x\right )\right )+5\,x^6 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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