Optimal. Leaf size=24 \[ \log \left (-3-\frac {x}{2}+\log \left ((4-x) \left (\frac {75}{x}-x\right )\right )\right ) \]
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Rubi [A] time = 0.25, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6688, 6684} \begin {gather*} \log \left (-2 \log \left (x^2-4 x+\frac {300}{x}-75\right )+x+6\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {600+300 x-67 x^2-8 x^3+x^4}{x \left (300-75 x-4 x^2+x^3\right ) \left (6+x-2 \log \left (-75+\frac {300}{x}-4 x+x^2\right )\right )} \, dx\\ &=\log \left (6+x-2 \log \left (-75+\frac {300}{x}-4 x+x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.82, size = 20, normalized size = 0.83 \begin {gather*} \log \left (6+x-2 \log \left (-75+\frac {300}{x}-4 x+x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 26, normalized size = 1.08 \begin {gather*} \log \left (-x + 2 \, \log \left (\frac {x^{3} - 4 \, x^{2} - 75 \, x + 300}{x}\right ) - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 24, normalized size = 1.00 \begin {gather*} \log \left (x - 2 \, \log \left (\frac {x^{3} - 4 \, x^{2} - 75 \, x + 300}{x}\right ) + 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 25, normalized size = 1.04
method | result | size |
norman | \(\ln \left (x -2 \ln \left (\frac {x^{3}-4 x^{2}-75 x +300}{x}\right )+6\right )\) | \(25\) |
risch | \(\ln \left (-\frac {x}{2}+\ln \left (\frac {x^{3}-4 x^{2}-75 x +300}{x}\right )-3\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 20, normalized size = 0.83 \begin {gather*} \log \left (-\frac {1}{2} \, x + \log \left (x^{2} - 75\right ) + \log \left (x - 4\right ) - \log \relax (x) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.21, size = 27, normalized size = 1.12 \begin {gather*} \ln \left (\ln \left (-\frac {-x^3+4\,x^2+75\,x-300}{x}\right )-\frac {x}{2}-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 22, normalized size = 0.92 \begin {gather*} \log {\left (- \frac {x}{2} + \log {\left (\frac {x^{3} - 4 x^{2} - 75 x + 300}{x} \right )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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