Optimal. Leaf size=23 \[ e^{-5+e^{3 x}}+3 \left (e^4+(-2+2 x)^2\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps used = 4, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2282, 2194} \begin {gather*} 12 (1-x)^2+e^{e^{3 x}-5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (3 e^{e^{3 x}+3 x}+e^5 (-24+24 x)\right ) \, dx}{e^5}\\ &=12 (1-x)^2+\frac {3 \int e^{e^{3 x}+3 x} \, dx}{e^5}\\ &=12 (1-x)^2+\frac {\operatorname {Subst}\left (\int e^x \, dx,x,e^{3 x}\right )}{e^5}\\ &=e^{-5+e^{3 x}}+12 (1-x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 1.04 \begin {gather*} 3 \left (\frac {1}{3} e^{-5+e^{3 x}}-8 x+4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 32, normalized size = 1.39 \begin {gather*} {\left (12 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x + 5\right )} + e^{\left (3 \, x + e^{\left (3 \, x\right )}\right )}\right )} e^{\left (-3 \, x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.42, size = 20, normalized size = 0.87 \begin {gather*} {\left (12 \, {\left (x^{2} - 2 \, x\right )} e^{5} + e^{\left (e^{\left (3 \, x\right )}\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 17, normalized size = 0.74
method | result | size |
risch | \({\mathrm e}^{-5+{\mathrm e}^{3 x}}-24 x +12 x^{2}\) | \(17\) |
norman | \({\mathrm e}^{-5} {\mathrm e}^{{\mathrm e}^{3 x}}-24 x +12 x^{2}\) | \(20\) |
default | \({\mathrm e}^{-5} \left ({\mathrm e}^{5} \left (12 x^{2}-24 x \right )+{\mathrm e}^{{\mathrm e}^{x} {\mathrm e}^{2 x}}\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 20, normalized size = 0.87 \begin {gather*} {\left (12 \, {\left (x^{2} - 2 \, x\right )} e^{5} + e^{\left (e^{\left (3 \, x\right )}\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 17, normalized size = 0.74 \begin {gather*} {\mathrm {e}}^{-5}\,{\mathrm {e}}^{{\mathrm {e}}^{3\,x}}-24\,x+12\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 17, normalized size = 0.74 \begin {gather*} 12 x^{2} - 24 x + \frac {e^{e^{3 x}}}{e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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