Optimal. Leaf size=28 \[ \frac {x}{x+x^4 \left (9+\frac {x}{5}+\frac {5}{3 x^4 \log ^2(x)}\right )} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A] time = 0.30, size = 28, normalized size = 1.00 \begin {gather*} \frac {15 x \log ^2(x)}{25+3 x \left (5+45 x^3+x^4\right ) \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 29, normalized size = 1.04 \begin {gather*} \frac {15 \, x \log \relax (x)^{2}}{3 \, {\left (x^{5} + 45 \, x^{4} + 5 \, x\right )} \log \relax (x)^{2} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 3.34, size = 83, normalized size = 2.96 \begin {gather*} -\frac {125}{3 \, x^{9} \log \relax (x)^{2} + 270 \, x^{8} \log \relax (x)^{2} + 6075 \, x^{7} \log \relax (x)^{2} + 30 \, x^{5} \log \relax (x)^{2} + 1350 \, x^{4} \log \relax (x)^{2} + 25 \, x^{4} + 1125 \, x^{3} + 75 \, x \log \relax (x)^{2} + 125} + \frac {5}{x^{4} + 45 \, x^{3} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 59, normalized size = 2.11
method | result | size |
risch | \(\frac {5}{x^{4}+45 x^{3}+5}-\frac {125}{\left (x^{4}+45 x^{3}+5\right ) \left (3 x^{5} \ln \relax (x )^{2}+135 x^{4} \ln \relax (x )^{2}+15 x \ln \relax (x )^{2}+25\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 29, normalized size = 1.04 \begin {gather*} \frac {15 \, x \log \relax (x)^{2}}{3 \, {\left (x^{5} + 45 \, x^{4} + 5 \, x\right )} \log \relax (x)^{2} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\left (-180\,x^5-6075\,x^4\right )\,{\ln \relax (x)}^4+375\,{\ln \relax (x)}^2+750\,\ln \relax (x)}{\left (9\,x^{10}+810\,x^9+18225\,x^8+90\,x^6+4050\,x^5+225\,x^2\right )\,{\ln \relax (x)}^4+\left (150\,x^5+6750\,x^4+750\,x\right )\,{\ln \relax (x)}^2+625} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.36, size = 58, normalized size = 2.07 \begin {gather*} - \frac {125}{25 x^{4} + 1125 x^{3} + \left (3 x^{9} + 270 x^{8} + 6075 x^{7} + 30 x^{5} + 1350 x^{4} + 75 x\right ) \log {\relax (x )}^{2} + 125} + \frac {5}{x^{4} + 45 x^{3} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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