Optimal. Leaf size=16 \[ \frac {1}{25} (-4+5 (e-x)) x^2 \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.25, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {6, 12} \begin {gather*} -\frac {x^3}{5}-\frac {1}{25} (4-5 e) x^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}{25} \left ((-8+10 e) x-15 x^2\right ) \, dx\\ &=\frac {1}{25} \int \left ((-8+10 e) x-15 x^2\right ) \, dx\\ &=-\frac {1}{25} (4-5 e) x^2-\frac {x^3}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} \frac {1}{25} (-4+5 e-5 x) x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 18, normalized size = 1.12 \begin {gather*} -\frac {1}{5} \, x^{3} + \frac {1}{5} \, x^{2} e - \frac {4}{25} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 18, normalized size = 1.12 \begin {gather*} -\frac {1}{5} \, x^{3} + \frac {1}{5} \, x^{2} e - \frac {4}{25} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 0.94
method | result | size |
gosper | \(\frac {x^{2} \left (-5 x +5 \,{\mathrm e}-4\right )}{25}\) | \(15\) |
norman | \(\left (\frac {{\mathrm e}}{5}-\frac {4}{25}\right ) x^{2}-\frac {x^{3}}{5}\) | \(17\) |
default | \(\frac {x^{2} {\mathrm e}}{5}-\frac {x^{3}}{5}-\frac {4 x^{2}}{25}\) | \(19\) |
risch | \(\frac {x^{2} {\mathrm e}}{5}-\frac {x^{3}}{5}-\frac {4 x^{2}}{25}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 18, normalized size = 1.12 \begin {gather*} -\frac {1}{5} \, x^{3} + \frac {1}{5} \, x^{2} e - \frac {4}{25} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 14, normalized size = 0.88 \begin {gather*} -\frac {x^2\,\left (5\,x-5\,\mathrm {e}+4\right )}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 15, normalized size = 0.94 \begin {gather*} - \frac {x^{3}}{5} + x^{2} \left (- \frac {4}{25} + \frac {e}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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