Optimal. Leaf size=24 \[ 4 x^3 \left (-x^4+3 \left (5-x+\frac {\log (2)}{8}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {6, 12} \begin {gather*} -4 x^7-12 x^4+\frac {3}{2} x^3 (40+\log (2)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{2} \left (-96 x^3-56 x^6+x^2 (360+9 \log (2))\right ) \, dx\\ &=\frac {1}{2} \int \left (-96 x^3-56 x^6+x^2 (360+9 \log (2))\right ) \, dx\\ &=-12 x^4-4 x^7+\frac {3}{2} x^3 (40+\log (2))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.79 \begin {gather*} \frac {1}{2} x^3 \left (120-24 x-8 x^4+\log (8)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 23, normalized size = 0.96 \begin {gather*} -4 \, x^{7} - 12 \, x^{4} + \frac {3}{2} \, x^{3} \log \relax (2) + 60 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 23, normalized size = 0.96 \begin {gather*} -4 \, x^{7} - 12 \, x^{4} + \frac {3}{2} \, x^{3} \log \relax (2) + 60 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 20, normalized size = 0.83
method | result | size |
gosper | \(\frac {x^{3} \left (-8 x^{4}+3 \ln \relax (2)-24 x +120\right )}{2}\) | \(20\) |
norman | \(\left (\frac {3 \ln \relax (2)}{2}+60\right ) x^{3}-12 x^{4}-4 x^{7}\) | \(22\) |
default | \(\frac {3 x^{3} \ln \relax (2)}{2}-4 x^{7}-12 x^{4}+60 x^{3}\) | \(24\) |
risch | \(\frac {3 x^{3} \ln \relax (2)}{2}-4 x^{7}-12 x^{4}+60 x^{3}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 23, normalized size = 0.96 \begin {gather*} -4 \, x^{7} - 12 \, x^{4} + \frac {3}{2} \, x^{3} \log \relax (2) + 60 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 19, normalized size = 0.79 \begin {gather*} -\frac {x^3\,\left (24\,x^4+72\,x-\ln \left (512\right )-360\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 20, normalized size = 0.83 \begin {gather*} - 4 x^{7} - 12 x^{4} + x^{3} \left (\frac {3 \log {\relax (2 )}}{2} + 60\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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