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 = 0.33, 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 = 0.02, 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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Maple [A]
time = 0.28, size = 31, normalized size = 1.24
method | result | size |
gosper | \(\frac {3+x}{-x^{5} \ln \left (2\right )^{4}-8 x^{3} \ln \left (2\right )^{2}+\ln \left (6\right )-15 x}\) | \(31\) |
default | \(\frac {3+x}{-x^{5} \ln \left (2\right )^{4}-8 x^{3} \ln \left (2\right )^{2}+\ln \left (6\right )-15 x}\) | \(31\) |
risch | \(\frac {3+x}{-x^{5} \ln \left (2\right )^{4}-8 x^{3} \ln \left (2\right )^{2}+\ln \left (3\right )+\ln \left (2\right )-15 x}\) | \(33\) |
norman | \(\frac {\frac {\left (\ln \left (6\right )+45\right ) x}{\ln \left (6\right )}+\frac {24 \ln \left (2\right )^{2} x^{3}}{\ln \left (6\right )}+\frac {3 \ln \left (2\right )^{4} x^{5}}{\ln \left (6\right )}}{-x^{5} \ln \left (2\right )^{4}-8 x^{3} \ln \left (2\right )^{2}+\ln \left (6\right )-15 x}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x + 3}{x^{5} \log \left (2\right )^{4} + 8 \, x^{3} \log \left (2\right )^{2} + 15 \, x - \log \left (6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x + 3}{x^{5} \log \left (2\right )^{4} + 8 \, x^{3} \log \left (2\right )^{2} + 15 \, x - \log \left (6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 8.76, size = 29, normalized size = 1.16 \begin {gather*} \frac {- x - 3}{x^{5} \log {\left (2 \right )}^{4} + 8 x^{3} \log {\left (2 \right )}^{2} + 15 x - \log {\left (6 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 32, normalized size = 1.28 \begin {gather*} -\frac {x + 3}{x^{5} \log \left (2\right )^{4} + 8 \, x^{3} \log \left (2\right )^{2} + 15 \, x - \log \left (6\right )} \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 \left (2\right )}^4\,x^5+8\,{\ln \left (2\right )}^2\,x^3+15\,x-\ln \left (6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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