Optimal. Leaf size=21 \[ x+\left (e^3-x\right ) (-x+(2-2 x) x) \]
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Rubi [A] time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps used = 1, number of rules used = 0, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^3-x^2+x-\frac {1}{8} e^3 (1-4 x)^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{8} e^3 (1-4 x)^2+x-x^2+2 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.19 \begin {gather*} x+e^3 x-x^2-2 e^3 x^2+2 x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 25, normalized size = 1.19 \begin {gather*} 2 \, x^{3} - x^{2} - {\left (2 \, x^{2} - x\right )} e^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 25, normalized size = 1.19 \begin {gather*} 2 \, x^{3} - x^{2} - {\left (2 \, x^{2} - x\right )} e^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 1.00
method | result | size |
gosper | \(-x \left (2 x \,{\mathrm e}^{3}-2 x^{2}-{\mathrm e}^{3}+x -1\right )\) | \(21\) |
default | \({\mathrm e}^{3} \left (-2 x^{2}+x \right )+2 x^{3}-x^{2}+x\) | \(23\) |
norman | \(\left (-2 \,{\mathrm e}^{3}-1\right ) x^{2}+\left ({\mathrm e}^{3}+1\right ) x +2 x^{3}\) | \(23\) |
risch | \(-2 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}+2 x^{3}-x^{2}+x\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 25, normalized size = 1.19 \begin {gather*} 2 \, x^{3} - x^{2} - {\left (2 \, x^{2} - x\right )} e^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.10, size = 23, normalized size = 1.10 \begin {gather*} 2\,x^3+\left (-2\,{\mathrm {e}}^3-1\right )\,x^2+\left ({\mathrm {e}}^3+1\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 22, normalized size = 1.05 \begin {gather*} 2 x^{3} + x^{2} \left (- 2 e^{3} - 1\right ) + x \left (1 + e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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