Optimal. Leaf size=11 \[ \left (-e-\frac {x}{2}\right )^2 \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9}
\begin {gather*} \frac {1}{4} (x+2 e)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} (2 e+x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} e x+\frac {x^2}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 11, normalized size = 1.00
method | result | size |
gosper | \(\frac {x \left (x +4 \,{\mathrm e}\right )}{4}\) | \(10\) |
default | \(x \,{\mathrm e}+\frac {x^{2}}{4}\) | \(11\) |
norman | \(x \,{\mathrm e}+\frac {x^{2}}{4}\) | \(11\) |
risch | \(x \,{\mathrm e}+\frac {x^{2}}{4}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{4} \, x^{2} + x e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{4} \, x^{2} + x e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.73 \begin {gather*} \frac {x^{2}}{4} + e x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{4} \, x^{2} + x e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 0.82 \begin {gather*} \frac {x\,\left (x+4\,\mathrm {e}\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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