Optimal. Leaf size=25 \[ \frac {3+x}{x-x \left (4+x^2 \log ^2(2)\right )^2+\log (6)} \]
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Rubi [F] time = 0.48, 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*} \int \frac {45+\left (72 x^2+16 x^3\right ) \log ^2(2)+\left (15 x^4+4 x^5\right ) \log ^4(2)+\log (6)}{225 x^2+240 x^4 \log ^2(2)+94 x^6 \log ^4(2)+16 x^8 \log ^6(2)+x^{10} \log ^8(2)+\left (-30 x-16 x^3 \log ^2(2)-2 x^5 \log ^4(2)\right ) \log (6)+\log ^2(6)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)}+\frac {-60 x+72 x^2 \log ^2(2)-16 x^3 \log ^2(2)+15 x^4 \log ^4(2)+5 (9+\log (6))}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2}\right ) \, dx\\ &=4 \int \frac {1}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)} \, dx+\int \frac {-60 x+72 x^2 \log ^2(2)-16 x^3 \log ^2(2)+15 x^4 \log ^4(2)+5 (9+\log (6))}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2} \, dx\\ &=-\frac {3}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)}+4 \int \frac {1}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)} \, dx+\frac {\int \frac {-300 x \log ^4(2)-80 x^3 \log ^6(2)+25 \log ^4(2) \log (6)}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2} \, dx}{5 \log ^4(2)}\\ &=-\frac {3}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)}+4 \int \frac {1}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)} \, dx+\frac {\int \left (-\frac {300 x \log ^4(2)}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2}-\frac {80 x^3 \log ^6(2)}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2}+\frac {25 \log ^4(2) \log (6)}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2}\right ) \, dx}{5 \log ^4(2)}\\ &=-\frac {3}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)}+4 \int \frac {1}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)} \, dx-60 \int \frac {x}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2} \, dx-\left (16 \log ^2(2)\right ) \int \frac {x^3}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2} \, dx+(5 \log (6)) \int \frac {1}{\left (15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 33, normalized size = 1.32 \begin {gather*} \frac {-3-x}{15 x+8 x^3 \log ^2(2)+x^5 \log ^4(2)-\log (6)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x + 3}{x^{5} \log \relax (2)^{4} + 8 \, x^{3} \log \relax (2)^{2} + 15 \, x - \log \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x + 3}{x^{5} \log \relax (2)^{4} + 8 \, x^{3} \log \relax (2)^{2} + 15 \, x - \log \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.21, size = 31, normalized size = 1.24
method | result | size |
gosper | \(\frac {3+x}{-x^{5} \ln \relax (2)^{4}-8 x^{3} \ln \relax (2)^{2}+\ln \relax (6)-15 x}\) | \(31\) |
default | \(\frac {3+x}{-x^{5} \ln \relax (2)^{4}-8 x^{3} \ln \relax (2)^{2}+\ln \relax (6)-15 x}\) | \(31\) |
risch | \(\frac {3+x}{-x^{5} \ln \relax (2)^{4}-8 x^{3} \ln \relax (2)^{2}+\ln \relax (3)+\ln \relax (2)-15 x}\) | \(33\) |
norman | \(\frac {\frac {\left (\ln \relax (6)+45\right ) x}{\ln \relax (6)}+\frac {24 \ln \relax (2)^{2} x^{3}}{\ln \relax (6)}+\frac {3 \ln \relax (2)^{4} x^{5}}{\ln \relax (6)}}{-x^{5} \ln \relax (2)^{4}-8 x^{3} \ln \relax (2)^{2}+\ln \relax (6)-15 x}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x + 3}{x^{5} \log \relax (2)^{4} + 8 \, x^{3} \log \relax (2)^{2} + 15 \, x - \log \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.23, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x+3}{{\ln \relax (2)}^4\,x^5+8\,{\ln \relax (2)}^2\,x^3+15\,x-\ln \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.43, size = 29, normalized size = 1.16 \begin {gather*} \frac {- x - 3}{x^{5} \log {\relax (2 )}^{4} + 8 x^{3} \log {\relax (2 )}^{2} + 15 x - \log {\relax (6 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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