Optimal. Leaf size=22 \[ 3+x-\log \left (x \left (1+x^6\right )+\frac {1}{3} \log (2 x)\right ) \]
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Rubi [A] time = 0.17, antiderivative size = 18, normalized size of antiderivative = 0.82, number of steps used = 3, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6742, 6684} \begin {gather*} x-\log \left (3 x^7+3 x+\log (2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {-1-3 x-21 x^7}{x \left (3 x+3 x^7+\log (2 x)\right )}\right ) \, dx\\ &=x+\int \frac {-1-3 x-21 x^7}{x \left (3 x+3 x^7+\log (2 x)\right )} \, dx\\ &=x-\log \left (3 x+3 x^7+\log (2 x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 18, normalized size = 0.82 \begin {gather*} x-\log \left (3 x+3 x^7+\log (2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 18, normalized size = 0.82 \begin {gather*} x - \log \left (3 \, x^{7} + 3 \, x + \log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 20, normalized size = 0.91 \begin {gather*} x - \log \left (-3 \, x^{7} - 3 \, x - \log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 0.86
method | result | size |
norman | \(x -\ln \left (3 x^{7}+\ln \left (2 x \right )+3 x \right )\) | \(19\) |
risch | \(x -\ln \left (3 x^{7}+\ln \left (2 x \right )+3 x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 18, normalized size = 0.82 \begin {gather*} x - \log \left (3 \, x^{7} + 3 \, x + \log \relax (2) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.56, size = 18, normalized size = 0.82 \begin {gather*} x-\ln \left (3\,x+\ln \left (2\,x\right )+3\,x^7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 15, normalized size = 0.68 \begin {gather*} x - \log {\left (3 x^{7} + 3 x + \log {\left (2 x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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