Optimal. Leaf size=23 \[ \frac {2}{3} (4+2 (-2+x)) \left (4-\frac {3}{x}\right ) x^2 \log (3) \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.74, number of steps
used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12}
\begin {gather*} \frac {16}{3} x^3 \log (3)-4 x^2 \log (3) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (3) \int \left (-8 x+16 x^2\right ) \, dx\\ &=-4 x^2 \log (3)+\frac {16}{3} x^3 \log (3)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 0.83 \begin {gather*} 8 \left (-\frac {x^2}{2}+\frac {2 x^3}{3}\right ) \log (3) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 15, normalized size = 0.65
method | result | size |
gosper | \(\frac {4 \ln \left (3\right ) \left (4 x -3\right ) x^{2}}{3}\) | \(13\) |
default | \(\ln \left (3\right ) \left (\frac {16}{3} x^{3}-4 x^{2}\right )\) | \(15\) |
norman | \(-4 x^{2} \ln \left (3\right )+\frac {16 x^{3} \ln \left (3\right )}{3}\) | \(16\) |
risch | \(-4 x^{2} \ln \left (3\right )+\frac {16 x^{3} \ln \left (3\right )}{3}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 15, normalized size = 0.65 \begin {gather*} \frac {4}{3} \, {\left (4 \, x^{3} - 3 \, x^{2}\right )} \log \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 15, normalized size = 0.65 \begin {gather*} \frac {4}{3} \, {\left (4 \, x^{3} - 3 \, x^{2}\right )} \log \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 0.74 \begin {gather*} \frac {16 x^{3} \log {\left (3 \right )}}{3} - 4 x^{2} \log {\left (3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.65 \begin {gather*} \frac {4}{3} \, {\left (4 \, x^{3} - 3 \, x^{2}\right )} \log \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 12, normalized size = 0.52 \begin {gather*} \frac {4\,x^2\,\ln \left (3\right )\,\left (4\,x-3\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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