Optimal. Leaf size=23 \[ \frac {1}{x}-x^2-\log \left (x^2+105 (\log (4)+\log (x))\right ) \]
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Rubi [A]
time = 0.27, antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps
used = 5, number of rules used = 3, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {6874, 14, 6816}
\begin {gather*} -x^2-\log \left (x^2+105 \log (x)+105 \log (4)\right )+\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 6816
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1-2 x^3}{x^2}+\frac {-105-2 x^2}{x \left (x^2+105 \log (4)+105 \log (x)\right )}\right ) \, dx\\ &=\int \frac {-1-2 x^3}{x^2} \, dx+\int \frac {-105-2 x^2}{x \left (x^2+105 \log (4)+105 \log (x)\right )} \, dx\\ &=-\log \left (x^2+105 \log (4)+105 \log (x)\right )+\int \left (-\frac {1}{x^2}-2 x\right ) \, dx\\ &=\frac {1}{x}-x^2-\log \left (x^2+105 \log (4)+105 \log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 24, normalized size = 1.04 \begin {gather*} \frac {1}{x}-x^2-\log \left (x^2+105 \log (4)+105 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.44, size = 27, normalized size = 1.17
method | result | size |
default | \(-\frac {x^{3}-1}{x}-\ln \left (x^{2}+105 \ln \left (x \right )+210 \ln \left (2\right )\right )\) | \(27\) |
risch | \(-\frac {x^{3}-1}{x}-\ln \left (\frac {x^{2}}{105}+2 \ln \left (2\right )+\ln \left (x \right )\right )\) | \(27\) |
norman | \(\frac {-x^{3}+1}{x}-\ln \left (x^{2}+105 \ln \left (x \right )+210 \ln \left (2\right )\right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 26, normalized size = 1.13 \begin {gather*} -\frac {x^{3} - 1}{x} - \log \left (\frac {1}{105} \, x^{2} + 2 \, \log \left (2\right ) + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 25, normalized size = 1.09 \begin {gather*} -\frac {x^{3} + x \log \left (x^{2} + 210 \, \log \left (2\right ) + 105 \, \log \left (x\right )\right ) - 1}{x} \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 = 0.87 \begin {gather*} - x^{2} - \log {\left (\frac {x^{2}}{105} + \log {\left (x \right )} + 2 \log {\left (2 \right )} \right )} + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 24, normalized size = 1.04 \begin {gather*} -x^{2} + \frac {1}{x} - \log \left (x^{2} + 210 \, \log \left (2\right ) + 105 \, \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.30, size = 22, normalized size = 0.96 \begin {gather*} \frac {1}{x}-\ln \left (\ln \left (4\,x\right )+\frac {x^2}{105}\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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