Optimal. Leaf size=24 \[ x+x^2-x \left (x+\frac {1}{5} x^2 \left (e+\frac {6 x}{5}\right )\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12} \begin {gather*} -\frac {6 x^4}{25}-\frac {e x^3}{5}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \left (25-15 e x^2-24 x^3\right ) \, dx\\ &=x-\frac {e x^3}{5}-\frac {6 x^4}{25}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.71 \begin {gather*} x-\frac {e x^3}{5}-\frac {6 x^4}{25} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 0.62
method | result | size |
default | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
norman | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
risch | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
gosper | \(-\frac {x \left (5 x^{2} {\mathrm e}+6 x^{3}-25\right )}{25}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6\,x^4}{25}-\frac {\mathrm {e}\,x^3}{5}+x \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 = 0.62 \begin {gather*} - \frac {6 x^{4}}{25} - \frac {e x^{3}}{5} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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