Optimal. Leaf size=24 \[ -x+\left (2+e^5\right ) \left (-5-x+(4-e) x^2\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.62, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6} \begin {gather*} 2 (4-e) x^2-3 x+\frac {e^5 (2 e x-8 x+1)^2}{4 (4-e)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3+(16-4 e) x+e^5 (-1+8 x-2 e x)\right ) \, dx\\ &=-3 x+2 (4-e) x^2+\frac {e^5 (1-8 x+2 e x)^2}{4 (4-e)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 1.38 \begin {gather*} -3 x-e^5 x+8 x^2-2 e x^2+(4-e) e^5 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 35, normalized size = 1.46 \begin {gather*} -x^{2} e^{6} - 2 \, x^{2} e + 8 \, x^{2} + {\left (4 \, x^{2} - x\right )} e^{5} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 33, normalized size = 1.38 \begin {gather*} -2 \, x^{2} e + 8 \, x^{2} - {\left (x^{2} e - 4 \, x^{2} + x\right )} e^{5} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.12
method | result | size |
gosper | \(-x \left (x \,{\mathrm e} \,{\mathrm e}^{5}-4 x \,{\mathrm e}^{5}+2 x \,{\mathrm e}+{\mathrm e}^{5}-8 x +3\right )\) | \(27\) |
norman | \(\left (-3-{\mathrm e}^{5}\right ) x +\left (-{\mathrm e} \,{\mathrm e}^{5}+4 \,{\mathrm e}^{5}-2 \,{\mathrm e}+8\right ) x^{2}\) | \(30\) |
default | \({\mathrm e}^{5} \left (-x^{2} {\mathrm e}+4 x^{2}-x \right )-2 x^{2} {\mathrm e}+8 x^{2}-3 x\) | \(36\) |
risch | \(-x^{2} {\mathrm e}^{6}+4 x^{2} {\mathrm e}^{5}-x \,{\mathrm e}^{5}-2 x^{2} {\mathrm e}+8 x^{2}-3 x\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.78, size = 33, normalized size = 1.38 \begin {gather*} -2 \, x^{2} e + 8 \, x^{2} - {\left (x^{2} e - 4 \, x^{2} + x\right )} e^{5} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 29, normalized size = 1.21 \begin {gather*} \left (8-\frac {{\mathrm {e}}^5\,\left (2\,\mathrm {e}-8\right )}{2}-2\,\mathrm {e}\right )\,x^2+\left (-{\mathrm {e}}^5-3\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 26, normalized size = 1.08 \begin {gather*} x^{2} \left (- e^{6} - 2 e + 8 + 4 e^{5}\right ) + x \left (- e^{5} - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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