Optimal. Leaf size=35 \[ x-\frac {1}{4} \left (5+\frac {7 x}{6}\right )^4+\log \left (\frac {4+\frac {3-x}{5}}{x}-x\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 42, normalized size of antiderivative = 1.20, number of steps used = 4, number of rules used = 3, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules used = {1594, 1628, 628} \begin {gather*} -\frac {2401 x^4}{5184}-\frac {1715 x^3}{216}-\frac {1225 x^2}{24}+\log \left (-5 x^2-x+23\right )-\frac {869 x}{6}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rule 1594
Rule 1628
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {29808+4317192 x+2861676 x^2-360810 x^3-637147 x^4-156751 x^5-12005 x^6}{x \left (-29808+1296 x+6480 x^2\right )} \, dx\\ &=\int \left (-\frac {869}{6}-\frac {1}{x}-\frac {1225 x}{12}-\frac {1715 x^2}{72}-\frac {2401 x^3}{1296}+\frac {1+10 x}{-23+x+5 x^2}\right ) \, dx\\ &=-\frac {869 x}{6}-\frac {1225 x^2}{24}-\frac {1715 x^3}{216}-\frac {2401 x^4}{5184}-\log (x)+\int \frac {1+10 x}{-23+x+5 x^2} \, dx\\ &=-\frac {869 x}{6}-\frac {1225 x^2}{24}-\frac {1715 x^3}{216}-\frac {2401 x^4}{5184}-\log (x)+\log \left (23-x-5 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 42, normalized size = 1.20 \begin {gather*} \frac {-187704 x-66150 x^2-10290 x^3-\frac {2401 x^4}{4}-1296 \log (x)+1296 \log \left (23-x-5 x^2\right )}{1296} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 32, normalized size = 0.91 \begin {gather*} -\frac {2401}{5184} \, x^{4} - \frac {1715}{216} \, x^{3} - \frac {1225}{24} \, x^{2} - \frac {869}{6} \, x + \log \left (5 \, x^{2} + x - 23\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 34, normalized size = 0.97 \begin {gather*} -\frac {2401}{5184} \, x^{4} - \frac {1715}{216} \, x^{3} - \frac {1225}{24} \, x^{2} - \frac {869}{6} \, x + \log \left ({\left | 5 \, x^{2} + x - 23 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 33, normalized size = 0.94
method | result | size |
default | \(-\frac {2401 x^{4}}{5184}-\frac {1715 x^{3}}{216}-\frac {1225 x^{2}}{24}-\frac {869 x}{6}-\ln \relax (x )+\ln \left (5 x^{2}+x -23\right )\) | \(33\) |
norman | \(-\frac {2401 x^{4}}{5184}-\frac {1715 x^{3}}{216}-\frac {1225 x^{2}}{24}-\frac {869 x}{6}-\ln \relax (x )+\ln \left (5 x^{2}+x -23\right )\) | \(33\) |
risch | \(-\frac {2401 x^{4}}{5184}-\frac {1715 x^{3}}{216}-\frac {1225 x^{2}}{24}-\frac {869 x}{6}-\ln \relax (x )+\ln \left (5 x^{2}+x -23\right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 32, normalized size = 0.91 \begin {gather*} -\frac {2401}{5184} \, x^{4} - \frac {1715}{216} \, x^{3} - \frac {1225}{24} \, x^{2} - \frac {869}{6} \, x + \log \left (5 \, x^{2} + x - 23\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 32, normalized size = 0.91 \begin {gather*} \ln \left (5\,x^2+x-23\right )-\frac {869\,x}{6}-\ln \relax (x)-\frac {1225\,x^2}{24}-\frac {1715\,x^3}{216}-\frac {2401\,x^4}{5184} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 37, normalized size = 1.06 \begin {gather*} - \frac {2401 x^{4}}{5184} - \frac {1715 x^{3}}{216} - \frac {1225 x^{2}}{24} - \frac {869 x}{6} - \log {\relax (x )} + \log {\left (5 x^{2} + x - 23 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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