Optimal. Leaf size=19 \[ \left (5+x+x^2-\log \left (x^4 \log ^4(x)\right )\right )^2 \]
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Rubi [A]
time = 0.20, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 66, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6820, 12, 6818}
\begin {gather*} \left (-\log \left (x^4 \log ^4(x)\right )+x^2+x+5\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (4-\left (-4+x+2 x^2\right ) \log (x)\right ) \left (-5-x-x^2+\log \left (x^4 \log ^4(x)\right )\right )}{x \log (x)} \, dx\\ &=2 \int \frac {\left (4-\left (-4+x+2 x^2\right ) \log (x)\right ) \left (-5-x-x^2+\log \left (x^4 \log ^4(x)\right )\right )}{x \log (x)} \, dx\\ &=\left (5+x+x^2-\log \left (x^4 \log ^4(x)\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} \left (5+x+x^2-\log \left (x^4 \log ^4(x)\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 15.78, size = 13424, normalized size = 706.53
method | result | size |
risch | \(\text {Expression too large to display}\) | \(13424\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 45 vs.
\(2 (19) = 38\).
time = 0.35, size = 45, normalized size = 2.37 \begin {gather*} x^{4} + 2 \, x^{3} + 11 \, x^{2} - 2 \, {\left (x^{2} + x + 5\right )} \log \left (x^{4} \log \left (x\right )^{4}\right ) + \log \left (x^{4} \log \left (x\right )^{4}\right )^{2} + 10 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 60 vs.
\(2 (17) = 34\).
time = 0.15, size = 60, normalized size = 3.16 \begin {gather*} x^{4} + 2 x^{3} + 11 x^{2} + 10 x + \left (- 2 x^{2} - 2 x\right ) \log {\left (x^{4} \log {\left (x \right )}^{4} \right )} - 40 \log {\left (x \right )} + \log {\left (x^{4} \log {\left (x \right )}^{4} \right )}^{2} - 40 \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs.
\(2 (19) = 38\).
time = 0.43, size = 64, normalized size = 3.37 \begin {gather*} x^{4} + 2 \, x^{3} + 11 \, x^{2} - 2 \, {\left (x^{2} + x - 4 \, \log \left (x\right )\right )} \log \left (\log \left (x\right )^{4}\right ) + \log \left (\log \left (x\right )^{4}\right )^{2} - 8 \, {\left (x^{2} + x\right )} \log \left (x\right ) + 16 \, \log \left (x\right )^{2} + 10 \, x - 40 \, \log \left (x\right ) - 40 \, \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.69, size = 57, normalized size = 3.00 \begin {gather*} 10\,x-40\,\ln \left (\ln \left (x\right )\right )-40\,\ln \left (x\right )+{\ln \left (x^4\,{\ln \left (x\right )}^4\right )}^2-\ln \left (x^4\,{\ln \left (x\right )}^4\right )\,\left (2\,x^2+2\,x\right )+11\,x^2+2\,x^3+x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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