Optimal. Leaf size=21 \[ -\log \left (-\frac {x^2}{25}+5 (x+\log (x))+\log (3+x)\right ) \]
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Rubi [A] time = 0.23, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6688, 6684} \begin {gather*} -\log ((125-x) x+125 \log (x)+25 \log (x+3)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {375+525 x+119 x^2-2 x^3}{x (3+x) ((-125+x) x-125 \log (x)-25 \log (3+x))} \, dx\\ &=-\log ((125-x) x+125 \log (x)+25 \log (3+x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.98, size = 20, normalized size = 0.95 \begin {gather*} -\log \left (-125 x+x^2-125 \log (x)-25 \log (3+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 22, normalized size = 1.05 \begin {gather*} -\log \left (-x^{2} + 125 \, x + 25 \, \log \left (x + 3\right ) + 125 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 22, normalized size = 1.05 \begin {gather*} -\log \left (-x^{2} + 125 \, x + 25 \, \log \left (x + 3\right ) + 125 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 1.00
method | result | size |
risch | \(-\ln \left (\ln \left (3+x \right )+5 x +5 \ln \relax (x )-\frac {x^{2}}{25}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 20, normalized size = 0.95 \begin {gather*} -\log \left (-\frac {1}{25} \, x^{2} + 5 \, x + \log \left (x + 3\right ) + 5 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.43, size = 20, normalized size = 0.95 \begin {gather*} -\ln \left (5\,x+\ln \left (x+3\right )+5\,\ln \relax (x)-\frac {x^2}{25}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 20, normalized size = 0.95 \begin {gather*} - \log {\left (- \frac {x^{2}}{25} + 5 x + 5 \log {\relax (x )} + \log {\left (x + 3 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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