Optimal. Leaf size=20 \[ \frac {x^3 (-4+i \pi +\log (3))}{180 \log ^2(5)} \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {6, 12, 30} \begin {gather*} -\frac {x^3 (4-i \pi -\log (3))}{180 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2 (-4+i \pi +\log (3))}{60 \log ^2(5)} \, dx\\ &=-\frac {(4-i \pi -\log (3)) \int x^2 \, dx}{60 \log ^2(5)}\\ &=-\frac {x^3 (4-i \pi -\log (3))}{180 \log ^2(5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} \frac {x^3 (-4+i \pi +\log (3))}{180 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 22, normalized size = 1.10 \begin {gather*} \frac {{\left (i \, \pi - 4\right )} x^{3} + x^{3} \log \relax (3)}{180 \, \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 22, normalized size = 1.10 \begin {gather*} \frac {{\left (i \, \pi + \log \relax (3)\right )} x^{3} - 4 \, x^{3}}{180 \, \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.90
method | result | size |
gosper | \(\frac {x^{3} \left (\ln \relax (3)+i \pi -4\right )}{180 \ln \relax (5)^{2}}\) | \(18\) |
norman | \(\frac {x^{3} \left (\ln \relax (3)+i \pi -4\right )}{180 \ln \relax (5)^{2}}\) | \(18\) |
default | \(\frac {\frac {x^{3} \left (\ln \relax (3)+i \pi \right )}{3}-\frac {4 x^{3}}{3}}{60 \ln \relax (5)^{2}}\) | \(25\) |
risch | \(\frac {i x^{3} \pi }{180 \ln \relax (5)^{2}}+\frac {x^{3} \ln \relax (3)}{180 \ln \relax (5)^{2}}-\frac {x^{3}}{45 \ln \relax (5)^{2}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 24, normalized size = 1.20 \begin {gather*} -\frac {{\left (-i \, \pi - \log \relax (3)\right )} x^{3} + 4 \, x^{3}}{180 \, \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.17, size = 19, normalized size = 0.95 \begin {gather*} \frac {x^3\,\left (\Pi -\ln \relax (3)\,1{}\mathrm {i}+4{}\mathrm {i}\right )\,1{}\mathrm {i}}{180\,{\ln \relax (5)}^2} \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 = 0.85 \begin {gather*} \frac {x^{3} \left (-4 + \log {\relax (3 )} + i \pi \right )}{180 \log {\relax (5 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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