Optimal. Leaf size=20 \[ \log \left (-\frac {1}{4}+\left (-\frac {21}{4}-\frac {3}{x}\right )^2-\log (x)\right ) \]
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Rubi [F]
time = 0.34, 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 {288+504 x+16 x^2}{-144 x-504 x^2-437 x^3+16 x^3 \log (x)} \, 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 {504}{-144-504 x-437 x^2+16 x^2 \log (x)}+\frac {288}{x \left (-144-504 x-437 x^2+16 x^2 \log (x)\right )}+\frac {16 x}{-144-504 x-437 x^2+16 x^2 \log (x)}\right ) \, dx\\ &=16 \int \frac {x}{-144-504 x-437 x^2+16 x^2 \log (x)} \, dx+288 \int \frac {1}{x \left (-144-504 x-437 x^2+16 x^2 \log (x)\right )} \, dx+504 \int \frac {1}{-144-504 x-437 x^2+16 x^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 31, normalized size = 1.55 \begin {gather*} 8 \left (-\frac {\log (x)}{4}+\frac {1}{8} \log \left (144+504 x+437 x^2-16 x^2 \log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.74, size = 24, normalized size = 1.20
method | result | size |
risch | \(\ln \left (\ln \left (x \right )-\frac {437 x^{2}+504 x +144}{16 x^{2}}\right )\) | \(20\) |
default | \(-2 \ln \left (x \right )+\ln \left (16 x^{2} \ln \left (x \right )-437 x^{2}-504 x -144\right )\) | \(24\) |
norman | \(-2 \ln \left (x \right )+\ln \left (16 x^{2} \ln \left (x \right )-437 x^{2}-504 x -144\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 23, normalized size = 1.15 \begin {gather*} \log \left (\frac {16 \, x^{2} \log \left (x\right ) - 437 \, x^{2} - 504 \, x - 144}{16 \, x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 22, normalized size = 1.10 \begin {gather*} \log \left (\frac {16 \, x^{2} \log \left (x\right ) - 437 \, x^{2} - 504 \, x - 144}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 20, normalized size = 1.00 \begin {gather*} \log {\left (\log {\left (x \right )} + \frac {- 437 x^{2} - 504 x - 144}{16 x^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 23, normalized size = 1.15 \begin {gather*} \log \left (16 \, x^{2} \log \left (x\right ) - 437 \, x^{2} - 504 \, x - 144\right ) - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.21, size = 23, normalized size = 1.15 \begin {gather*} \ln \left (504\,x-16\,x^2\,\ln \left (x\right )+437\,x^2+144\right )-2\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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