Optimal. Leaf size=29 \[ \left (e^{\frac {1}{4 \log (3)}}-\frac {1}{x}+\frac {5 x}{4}\right ) \left (3-x^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12, 14} \begin {gather*} -\frac {5 x^3}{4}-x^2 e^{\frac {1}{\log (81)}}+\frac {19 x}{4}-\frac {3}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {12+19 x^2-8 e^{\frac {1}{4 \log (3)}} x^3-15 x^4}{x^2} \, dx\\ &=\frac {1}{4} \int \left (19+\frac {12}{x^2}-8 e^{\frac {1}{\log (81)}} x-15 x^2\right ) \, dx\\ &=-\frac {3}{x}+\frac {19 x}{4}-e^{\frac {1}{\log (81)}} x^2-\frac {5 x^3}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \begin {gather*} -\frac {3}{x}+\frac {19 x}{4}-e^{\frac {1}{\log (81)}} x^2-\frac {5 x^3}{4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 29, normalized size = 1.00 \begin {gather*} -\frac {5 \, x^{4} + 4 \, x^{3} e^{\left (\frac {1}{4 \, \log \relax (3)}\right )} - 19 \, x^{2} + 12}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 26, normalized size = 0.90 \begin {gather*} -\frac {5}{4} \, x^{3} - x^{2} e^{\left (\frac {1}{4 \, \log \relax (3)}\right )} + \frac {19}{4} \, x - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 27, normalized size = 0.93
method | result | size |
default | \(\frac {19 x}{4}-\frac {5 x^{3}}{4}-x^{2} {\mathrm e}^{\frac {1}{4 \ln \relax (3)}}-\frac {3}{x}\) | \(27\) |
risch | \(\frac {19 x}{4}-\frac {5 x^{3}}{4}-x^{2} {\mathrm e}^{\frac {1}{4 \ln \relax (3)}}-\frac {3}{x}\) | \(27\) |
norman | \(\frac {-3+\frac {19 x^{2}}{4}-\frac {5 x^{4}}{4}-x^{3} {\mathrm e}^{\frac {1}{4 \ln \relax (3)}}}{x}\) | \(29\) |
gosper | \(-\frac {5 x^{4}+4 x^{3} {\mathrm e}^{\frac {1}{4 \ln \relax (3)}}-19 x^{2}+12}{4 x}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 26, normalized size = 0.90 \begin {gather*} -\frac {5}{4} \, x^{3} - x^{2} e^{\left (\frac {1}{4 \, \log \relax (3)}\right )} + \frac {19}{4} \, x - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.25, size = 26, normalized size = 0.90 \begin {gather*} \frac {19\,x}{4}-x^2\,{\mathrm {e}}^{\frac {1}{4\,\ln \relax (3)}}-\frac {3}{x}-\frac {5\,x^3}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 26, normalized size = 0.90 \begin {gather*} - \frac {5 x^{3}}{4} - x^{2} e^{\frac {1}{4 \log {\relax (3 )}}} + \frac {19 x}{4} - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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