Optimal. Leaf size=20 \[ 2 x-16 x^4+x \left (-e^3+3 x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} -16 x^4+3 x^2+\left (2-e^3\right ) x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (2-e^3\right ) x+3 x^2-16 x^4\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} 2 x-e^3 x+3 x^2-16 x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 20, normalized size = 1.00
method | result | size |
gosper | \(-x \left (16 x^{3}+{\mathrm e}^{3}-3 x -2\right )\) | \(16\) |
default | \(-x \,{\mathrm e}^{3}-16 x^{4}+3 x^{2}+2 x\) | \(20\) |
norman | \(\left (2-{\mathrm e}^{3}\right ) x +3 x^{2}-16 x^{4}\) | \(20\) |
risch | \(-x \,{\mathrm e}^{3}-16 x^{4}+3 x^{2}+2 x\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 0.95 \begin {gather*} -16 \, x^{4} + 3 \, x^{2} - x e^{3} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 19, normalized size = 0.95 \begin {gather*} -16 \, x^{4} + 3 \, x^{2} - x e^{3} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 15, normalized size = 0.75 \begin {gather*} - 16 x^{4} + 3 x^{2} + x \left (2 - e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 19, normalized size = 0.95 \begin {gather*} -16 \, x^{4} + 3 \, x^{2} - x e^{3} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.58, size = 18, normalized size = 0.90 \begin {gather*} -16\,x^4+3\,x^2+\left (2-{\mathrm {e}}^3\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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