Optimal. Leaf size=30 \[ (-3+x)^2-x^2+x^2 \left (-\frac {e^3}{5}+x+\log \left (2 x^2\right )\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 36, normalized size of antiderivative = 1.20, number of steps used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6, 12, 2304} \begin {gather*} x^3+\frac {1}{5} \left (5-e^3\right ) x^2-x^2+x^2 \log \left (2 x^2\right )-6 x \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{5} \left (-30+\left (10-2 e^3\right ) x+15 x^2+10 x \log \left (2 x^2\right )\right ) \, dx\\ &=\frac {1}{5} \int \left (-30+\left (10-2 e^3\right ) x+15 x^2+10 x \log \left (2 x^2\right )\right ) \, dx\\ &=-6 x+\frac {1}{5} \left (5-e^3\right ) x^2+x^3+2 \int x \log \left (2 x^2\right ) \, dx\\ &=-6 x-x^2+\frac {1}{5} \left (5-e^3\right ) x^2+x^3+x^2 \log \left (2 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 27, normalized size = 0.90 \begin {gather*} -6 x-\frac {e^3 x^2}{5}+x^3+x^2 \log \left (2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 24, normalized size = 0.80 \begin {gather*} x^{3} - \frac {1}{5} \, x^{2} e^{3} + x^{2} \log \left (2 \, x^{2}\right ) - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 24, normalized size = 0.80 \begin {gather*} x^{3} - \frac {1}{5} \, x^{2} e^{3} + x^{2} \log \left (2 \, x^{2}\right ) - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 25, normalized size = 0.83
method | result | size |
default | \(x^{3}-6 x -\frac {x^{2} {\mathrm e}^{3}}{5}+x^{2} \ln \left (2 x^{2}\right )\) | \(25\) |
norman | \(x^{3}-6 x -\frac {x^{2} {\mathrm e}^{3}}{5}+x^{2} \ln \left (2 x^{2}\right )\) | \(25\) |
risch | \(x^{3}-6 x -\frac {x^{2} {\mathrm e}^{3}}{5}+x^{2} \ln \left (2 x^{2}\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 24, normalized size = 0.80 \begin {gather*} x^{3} - \frac {1}{5} \, x^{2} e^{3} + x^{2} \log \left (2 \, x^{2}\right ) - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.87, size = 28, normalized size = 0.93 \begin {gather*} x^2\,\ln \left (x^2\right )-6\,x-\frac {x^2\,{\mathrm {e}}^3}{5}+x^2\,\ln \relax (2)+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 24, normalized size = 0.80 \begin {gather*} x^{3} + x^{2} \log {\left (2 x^{2} \right )} - \frac {x^{2} e^{3}}{5} - 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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