Optimal. Leaf size=28 \[ \frac {1875}{4}+\frac {3}{x}-\log (2)-\log \left (1+\frac {1}{5} \left (x+\log ^2(4)\right )\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 16, normalized size of antiderivative = 0.57, number of steps
used = 4, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {6, 1607, 907}
\begin {gather*} \frac {3}{x}-\log \left (x+5+\log ^2(4)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 907
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-15-3 x-x^2-3 \log ^2(4)}{x^3+x^2 \left (5+\log ^2(4)\right )} \, dx\\ &=\int \frac {-15-3 x-x^2-3 \log ^2(4)}{x^2 \left (5+x+\log ^2(4)\right )} \, dx\\ &=\int \left (-\frac {3}{x^2}+\frac {1}{-5-x-\log ^2(4)}\right ) \, dx\\ &=\frac {3}{x}-\log \left (5+x+\log ^2(4)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.57 \begin {gather*} \frac {3}{x}-\log \left (5+x+\log ^2(4)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.65, size = 19, normalized size = 0.68
method | result | size |
default | \(-\ln \left (4 \ln \left (2\right )^{2}+x +5\right )+\frac {3}{x}\) | \(19\) |
norman | \(-\ln \left (4 \ln \left (2\right )^{2}+x +5\right )+\frac {3}{x}\) | \(19\) |
risch | \(-\ln \left (4 \ln \left (2\right )^{2}+x +5\right )+\frac {3}{x}\) | \(19\) |
meijerg | \(-\frac {12 \ln \left (2\right )^{2} \left (\ln \left (1+\frac {x}{4 \ln \left (2\right )^{2}+5}\right )-\ln \left (x \right )+\ln \left (4 \ln \left (2\right )^{2}+5\right )-\frac {4 \ln \left (2\right )^{2}+5}{x}\right )}{\left (4 \ln \left (2\right )^{2}+5\right )^{2}}-\ln \left (1+\frac {x}{4 \ln \left (2\right )^{2}+5}\right )-\frac {3 \left (-\ln \left (1+\frac {x}{4 \ln \left (2\right )^{2}+5}\right )+\ln \left (x \right )-\ln \left (4 \ln \left (2\right )^{2}+5\right )\right )}{4 \ln \left (2\right )^{2}+5}-\frac {15 \left (\ln \left (1+\frac {x}{4 \ln \left (2\right )^{2}+5}\right )-\ln \left (x \right )+\ln \left (4 \ln \left (2\right )^{2}+5\right )-\frac {4 \ln \left (2\right )^{2}+5}{x}\right )}{\left (4 \ln \left (2\right )^{2}+5\right )^{2}}\) | \(174\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.64 \begin {gather*} \frac {3}{x} - \log \left (4 \, \log \left (2\right )^{2} + x + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 19, normalized size = 0.68 \begin {gather*} -\frac {x \log \left (4 \, \log \left (2\right )^{2} + x + 5\right ) - 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 14, normalized size = 0.50 \begin {gather*} - \log {\left (x + 4 \log {\left (2 \right )}^{2} + 5 \right )} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 0.68 \begin {gather*} \frac {3}{x} - \log \left ({\left | 4 \, \log \left (2\right )^{2} + x + 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.82, size = 18, normalized size = 0.64 \begin {gather*} \frac {3}{x}-\ln \left (x+4\,{\ln \left (2\right )}^2+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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