Optimal. Leaf size=19 \[ \log \left (\frac {1}{40} e^{x^2} x \log (x (1+x) \log (4))\right ) \]
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Rubi [F]
time = 0.39, 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 {1+2 x+\left (1+x+2 x^2+2 x^3\right ) \log \left (\left (x+x^2\right ) \log (4)\right )}{\left (x+x^2\right ) \log \left (\left (x+x^2\right ) \log (4)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1+2 x+\left (1+x+2 x^2+2 x^3\right ) \log \left (\left (x+x^2\right ) \log (4)\right )}{x (1+x) \log \left (\left (x+x^2\right ) \log (4)\right )} \, dx\\ &=\int \frac {1+2 x+\left (1+x+2 x^2+2 x^3\right ) \log \left (\left (x+x^2\right ) \log (4)\right )}{x (1+x) \log (x (1+x) \log (4))} \, dx\\ &=\int \left (\frac {1+2 x^2}{x}+\frac {1+2 x}{x (1+x) \log (x (1+x) \log (4))}\right ) \, dx\\ &=\int \frac {1+2 x^2}{x} \, dx+\int \frac {1+2 x}{x (1+x) \log (x (1+x) \log (4))} \, dx\\ &=\int \left (\frac {1}{x}+2 x\right ) \, dx+\int \frac {1+2 x}{x (1+x) \log (x (1+x) \log (4))} \, dx\\ &=x^2+\log (x)+\int \frac {1+2 x}{x (1+x) \log (x (1+x) \log (4))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 15, normalized size = 0.79 \begin {gather*} x^2+\log (x)+\log (\log (x (1+x) \log (4))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.21, size = 18, normalized size = 0.95
method | result | size |
norman | \(x^{2}+\ln \left (x \right )+\ln \left (\ln \left (2 \left (x^{2}+x \right ) \ln \left (2\right )\right )\right )\) | \(18\) |
risch | \(x^{2}+\ln \left (x \right )+\ln \left (\ln \left (2 \left (x^{2}+x \right ) \ln \left (2\right )\right )\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 19, normalized size = 1.00 \begin {gather*} x^{2} + \log \left (x\right ) + \log \left (\log \left (2\right ) + \log \left (x + 1\right ) + \log \left (x\right ) + \log \left (\log \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 17, normalized size = 0.89 \begin {gather*} x^{2} + \log \left (x\right ) + \log \left (\log \left (2 \, {\left (x^{2} + x\right )} \log \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 20, normalized size = 1.05 \begin {gather*} x^{2} + \log {\left (x \right )} + \log {\left (\log {\left (\left (2 x^{2} + 2 x\right ) \log {\left (2 \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 22, normalized size = 1.16 \begin {gather*} x^{2} + \log \left (x\right ) + \log \left (\log \left (2\right ) + \log \left (x^{2} \log \left (2\right ) + x \log \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.90, size = 17, normalized size = 0.89 \begin {gather*} \ln \left (\ln \left (2\,\ln \left (2\right )\,\left (x^2+x\right )\right )\right )+\ln \left (x\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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