Optimal. Leaf size=19 \[ -x^2 \log (2)+2 x \left (1+x^3 \log (2)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^4 \log (2)-x^2 \log (2)+2 x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+\log (2) \int \left (-2 x+8 x^3\right ) \, dx\\ &=2 x-x^2 \log (2)+2 x^4 \log (2)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.05 \begin {gather*} 2 x+2 x^4 \log (2)-\frac {1}{2} x^2 \log (4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 18, normalized size = 0.95 \begin {gather*} {\left (2 \, x^{4} - x^{2}\right )} \log \relax (2) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 18, normalized size = 0.95 \begin {gather*} {\left (2 \, x^{4} - x^{2}\right )} \log \relax (2) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.89
method | result | size |
gosper | \(x \left (2 x^{3} \ln \relax (2)-x \ln \relax (2)+2\right )\) | \(17\) |
default | \(\ln \relax (2) \left (2 x^{4}-x^{2}\right )+2 x\) | \(19\) |
norman | \(2 x -x^{2} \ln \relax (2)+2 x^{4} \ln \relax (2)\) | \(19\) |
risch | \(2 x -x^{2} \ln \relax (2)+2 x^{4} \ln \relax (2)\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 18, normalized size = 0.95 \begin {gather*} {\left (2 \, x^{4} - x^{2}\right )} \log \relax (2) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.84 \begin {gather*} x\,\left (2\,\ln \relax (2)\,x^3-\ln \relax (2)\,x+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 0.89 \begin {gather*} 2 x^{4} \log {\relax (2 )} - x^{2} \log {\relax (2 )} + 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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