Optimal. Leaf size=21 \[ \frac {2 \left (x-x^4+4 x^{1+2 x}\right )}{x} \]
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Rubi [A] time = 0.06, antiderivative size = 13, normalized size of antiderivative = 0.62, number of steps used = 6, number of rules used = 4, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {6741, 12, 6742, 2553} \begin {gather*} 8 x^{2 x}-2 x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2553
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-2 x^3+\int x^{2 x} (16+16 \log (x)) \, dx\\ &=-2 x^3+\int 16 x^{2 x} (1+\log (x)) \, dx\\ &=-2 x^3+16 \int x^{2 x} (1+\log (x)) \, dx\\ &=-2 x^3+16 \int \left (x^{2 x}+x^{2 x} \log (x)\right ) \, dx\\ &=-2 x^3+16 \int x^{2 x} \, dx+16 \int x^{2 x} \log (x) \, dx\\ &=-2 x^3+8 x^{2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 13, normalized size = 0.62 \begin {gather*} -2 x^3+8 x^{2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 13, normalized size = 0.62 \begin {gather*} -2 \, x^{3} + 8 \, x^{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 13, normalized size = 0.62 \begin {gather*} -2 \, x^{3} + 8 \, x^{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.67
method | result | size |
risch | \(8 x^{2 x}-2 x^{3}\) | \(14\) |
default | \(8 \,{\mathrm e}^{2 x \ln \relax (x )}-2 x^{3}\) | \(16\) |
norman | \(8 \,{\mathrm e}^{2 x \ln \relax (x )}-2 x^{3}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 13, normalized size = 0.62 \begin {gather*} -2 \, x^{3} + 8 \, x^{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.96, size = 13, normalized size = 0.62 \begin {gather*} 8\,x^{2\,x}-2\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 14, normalized size = 0.67 \begin {gather*} - 2 x^{3} + 8 e^{2 x \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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