Optimal. Leaf size=18 \[ \left (3+\log \left (-\log (x)+\log \left (4+50 x^3\right )\right )\right )^2 \]
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Rubi [A]
time = 0.15, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {6873, 12, 6818}
\begin {gather*} \left (\log \left (\log \left (50 x^3+4\right )-\log (x)\right )+3\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (1-25 x^3\right ) \left (3+\log \left (-\log (x)+\log \left (4+50 x^3\right )\right )\right )}{x \left (2+25 x^3\right ) \left (\log (x)-\log \left (4+50 x^3\right )\right )} \, dx\\ &=4 \int \frac {\left (1-25 x^3\right ) \left (3+\log \left (-\log (x)+\log \left (4+50 x^3\right )\right )\right )}{x \left (2+25 x^3\right ) \left (\log (x)-\log \left (4+50 x^3\right )\right )} \, dx\\ &=\left (3+\log \left (-\log (x)+\log \left (4+50 x^3\right )\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} \left (3+\log \left (-\log (x)+\log \left (4+50 x^3\right )\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.91, size = 34, normalized size = 1.89
method | result | size |
risch | \(\ln \left (\ln \left (50 x^{3}+4\right )-\ln \left (x \right )\right )^{2}+6 \ln \left (\ln \left (50 x^{3}+4\right )-\ln \left (x \right )\right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 37 vs.
\(2 (18) = 36\).
time = 0.51, size = 37, normalized size = 2.06 \begin {gather*} \log \left (\log \left (2\right ) + \log \left (25 \, x^{3} + 2\right ) - \log \left (x\right )\right )^{2} + 6 \, \log \left (\log \left (2\right ) + \log \left (25 \, x^{3} + 2\right ) - \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 33, normalized size = 1.83 \begin {gather*} \log \left (\log \left (50 \, x^{3} + 4\right ) - \log \left (x\right )\right )^{2} + 6 \, \log \left (\log \left (50 \, x^{3} + 4\right ) - \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.47, size = 29, normalized size = 1.61 \begin {gather*} \log {\left (- \log {\left (x \right )} + \log {\left (50 x^{3} + 4 \right )} \right )}^{2} + 6 \log {\left (- \log {\left (x \right )} + \log {\left (50 x^{3} + 4 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 33, normalized size = 1.83 \begin {gather*} \log \left (\log \left (50 \, x^{3} + 4\right ) - \log \left (x\right )\right )^{2} + 6 \, \log \left (\log \left (50 \, x^{3} + 4\right ) - \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.44, size = 31, normalized size = 1.72 \begin {gather*} \ln \left (\ln \left (50\,x^3+4\right )-\ln \left (x\right )\right )\,\left (\ln \left (\ln \left (50\,x^3+4\right )-\ln \left (x\right )\right )+6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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