Optimal. Leaf size=22 \[ 1+3 x \left (e^{1-5 e^4}+x (-3+2 x)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 3, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {12} \begin {gather*} 6 x^3-9 x^2+3 e^{1-5 e^4} x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{1-5 e^4} \int \left (3+e^{-1+5 e^4} \left (-18 x+18 x^2\right )\right ) \, dx\\ &=3 e^{1-5 e^4} x+\int \left (-18 x+18 x^2\right ) \, dx\\ &=3 e^{1-5 e^4} x-9 x^2+6 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 1.09 \begin {gather*} 3 \left (e^{1-5 e^4} x-3 x^2+2 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 30, normalized size = 1.36 \begin {gather*} 3 \, {\left ({\left (2 \, x^{3} - 3 \, x^{2}\right )} e^{\left (5 \, e^{4} - 1\right )} + x\right )} e^{\left (-5 \, e^{4} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 30, normalized size = 1.36 \begin {gather*} 3 \, {\left ({\left (2 \, x^{3} - 3 \, x^{2}\right )} e^{\left (5 \, e^{4} - 1\right )} + x\right )} e^{\left (-5 \, e^{4} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 22, normalized size = 1.00
method | result | size |
risch | \(6 x^{3}-9 x^{2}+3 x \,{\mathrm e}^{1-5 \,{\mathrm e}^{4}}\) | \(22\) |
norman | \(-9 x^{2}+6 x^{3}+3 \,{\mathrm e}^{-5 \,{\mathrm e}^{4}} {\mathrm e} x\) | \(24\) |
default | \({\mathrm e}^{1-5 \,{\mathrm e}^{4}} \left ({\mathrm e}^{5 \,{\mathrm e}^{4}-1} \left (6 x^{3}-9 x^{2}\right )+3 x \right )\) | \(34\) |
gosper | \(3 x \left (2 \,{\mathrm e}^{5 \,{\mathrm e}^{4}-1} x^{2}-3 \,{\mathrm e}^{5 \,{\mathrm e}^{4}-1} x +1\right ) {\mathrm e}^{1-5 \,{\mathrm e}^{4}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 30, normalized size = 1.36 \begin {gather*} 3 \, {\left ({\left (2 \, x^{3} - 3 \, x^{2}\right )} e^{\left (5 \, e^{4} - 1\right )} + x\right )} e^{\left (-5 \, e^{4} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 19, normalized size = 0.86 \begin {gather*} 3\,x\,\left (2\,x^2-3\,x+{\mathrm {e}}^{1-5\,{\mathrm {e}}^4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 22, normalized size = 1.00 \begin {gather*} 6 x^{3} - 9 x^{2} + \frac {3 e x}{e^{5 e^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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