Optimal. Leaf size=26 \[ x \left (1+2 x-\sqrt {e} x \left (\frac {3}{2 x}+x\right )^2\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.04, number of steps
used = 2, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} -\sqrt {e} x^4-3 \sqrt {e} x^2+2 x^2+x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+2 x^2+\sqrt {e} \int \left (-6 x-4 x^3\right ) \, dx\\ &=x+2 x^2-3 \sqrt {e} x^2-\sqrt {e} x^4\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.04 \begin {gather*} x+2 x^2-3 \sqrt {e} x^2-\sqrt {e} x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 26, normalized size = 1.00
method | result | size |
gosper | \(-x \left ({\mathrm e}^{\frac {1}{2}} x^{3}+3 x \,{\mathrm e}^{\frac {1}{2}}-2 x -1\right )\) | \(24\) |
norman | \(x +\left (-3 \,{\mathrm e}^{\frac {1}{2}}+2\right ) x^{2}-{\mathrm e}^{\frac {1}{2}} x^{4}\) | \(24\) |
default | \(-{\mathrm e}^{\frac {1}{2}} x^{4}-3 x^{2} {\mathrm e}^{\frac {1}{2}}+2 x^{2}+x\) | \(26\) |
risch | \(-{\mathrm e}^{\frac {1}{2}} x^{4}-3 x^{2} {\mathrm e}^{\frac {1}{2}}-\frac {9 \,{\mathrm e}^{\frac {1}{2}}}{4}+2 x^{2}+x\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 20, normalized size = 0.77 \begin {gather*} 2 \, x^{2} - {\left (x^{4} + 3 \, x^{2}\right )} e^{\frac {1}{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 20, normalized size = 0.77 \begin {gather*} 2 \, x^{2} - {\left (x^{4} + 3 \, x^{2}\right )} e^{\frac {1}{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 20, normalized size = 0.77 \begin {gather*} - x^{4} e^{\frac {1}{2}} + x^{2} \cdot \left (2 - 3 e^{\frac {1}{2}}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 20, normalized size = 0.77 \begin {gather*} 2 \, x^{2} - {\left (x^{4} + 3 \, x^{2}\right )} e^{\frac {1}{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.10, size = 20, normalized size = 0.77 \begin {gather*} -\sqrt {\mathrm {e}}\,x^4+\left (2-3\,\sqrt {\mathrm {e}}\right )\,x^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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