Optimal. Leaf size=28 \[ 1+e^{1+9 (4+2 x)^2+\frac {6 \log (2)}{1-e^5}} \]
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Rubi [A] time = 0.25, antiderivative size = 30, normalized size of antiderivative = 1.07, number of steps used = 2, number of rules used = 2, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2244, 2236} \begin {gather*} e^{36 x^2+144 x+\frac {145-145 e^5+\log (64)}{1-e^5}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{144 x+36 x^2+\frac {145-145 e^5+\log (64)}{1-e^5}} (144+72 x) \, dx\\ &=e^{144 x+36 x^2+\frac {145-145 e^5+\log (64)}{1-e^5}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 24, normalized size = 0.86 \begin {gather*} 2^{-\frac {6}{-1+e^5}} e^{145+144 x+36 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 37, normalized size = 1.32 \begin {gather*} e^{\left (-\frac {36 \, x^{2} - {\left (36 \, x^{2} + 144 \, x + 145\right )} e^{5} + 144 \, x + 6 \, \log \relax (2) + 145}{e^{5} - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.46, size = 74, normalized size = 2.64 \begin {gather*} e^{\left (\frac {36 \, x^{2} e^{5}}{e^{5} - 1} - \frac {36 \, x^{2}}{e^{5} - 1} + \frac {144 \, x e^{5}}{e^{5} - 1} - \frac {144 \, x}{e^{5} - 1} + \frac {145 \, e^{5}}{e^{5} - 1} - \frac {6 \, \log \relax (2)}{e^{5} - 1} - \frac {145}{e^{5} - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 21, normalized size = 0.75
method | result | size |
risch | \(\left (\frac {1}{64}\right )^{\frac {1}{{\mathrm e}^{5}-1}} {\mathrm e}^{36 x^{2}+144 x +145}\) | \(21\) |
norman | \({\mathrm e}^{\frac {-6 \ln \relax (2)+\left (36 x^{2}+144 x +145\right ) {\mathrm e}^{5}-36 x^{2}-144 x -145}{{\mathrm e}^{5}-1}}\) | \(36\) |
gosper | \({\mathrm e}^{\frac {36 x^{2} {\mathrm e}^{5}+144 x \,{\mathrm e}^{5}-36 x^{2}+145 \,{\mathrm e}^{5}-6 \ln \relax (2)-144 x -145}{{\mathrm e}^{5}-1}}\) | \(39\) |
default | \(72 \,2^{-\frac {6}{{\mathrm e}^{5}-1}} \left (\frac {{\mathrm e}^{\left (\frac {36 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {36}{{\mathrm e}^{5}-1}\right ) x^{2}+\left (\frac {144 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {144}{{\mathrm e}^{5}-1}\right ) x +\frac {145 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {145}{{\mathrm e}^{5}-1}}}{\frac {72 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {72}{{\mathrm e}^{5}-1}}+\frac {i \left (\frac {144 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {144}{{\mathrm e}^{5}-1}\right ) \sqrt {\pi }\, {\mathrm e}^{\frac {145 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {145}{{\mathrm e}^{5}-1}-\frac {\left (\frac {144 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {144}{{\mathrm e}^{5}-1}\right )^{2}}{4 \left (\frac {36 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {36}{{\mathrm e}^{5}-1}\right )}} \erf \left (6 i \sqrt {\frac {{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {1}{{\mathrm e}^{5}-1}}\, x +\frac {i \left (\frac {144 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {144}{{\mathrm e}^{5}-1}\right )}{12 \sqrt {\frac {{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {1}{{\mathrm e}^{5}-1}}}\right )}{24 \left (\frac {36 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {36}{{\mathrm e}^{5}-1}\right ) \sqrt {\frac {{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {1}{{\mathrm e}^{5}-1}}}\right )-\frac {12 i 2^{-\frac {6}{{\mathrm e}^{5}-1}} \sqrt {\pi }\, {\mathrm e}^{\frac {145 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {145}{{\mathrm e}^{5}-1}-\frac {\left (\frac {144 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {144}{{\mathrm e}^{5}-1}\right )^{2}}{4 \left (\frac {36 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {36}{{\mathrm e}^{5}-1}\right )}} \erf \left (6 i \sqrt {\frac {{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {1}{{\mathrm e}^{5}-1}}\, x +\frac {i \left (\frac {144 \,{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {144}{{\mathrm e}^{5}-1}\right )}{12 \sqrt {\frac {{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {1}{{\mathrm e}^{5}-1}}}\right )}{\sqrt {\frac {{\mathrm e}^{5}}{{\mathrm e}^{5}-1}-\frac {1}{{\mathrm e}^{5}-1}}}\) | \(468\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.59, size = 156, normalized size = 5.57 \begin {gather*} -24 i \, \sqrt {\pi } 2^{-\frac {6}{e^{5} - 1} - 1} \operatorname {erf}\left (6 i \, x + 12 i\right ) e^{\left (\frac {145 \, e^{5}}{e^{5} - 1} - \frac {145}{e^{5} - 1} - 144\right )} - {\left (\frac {12 \, \sqrt {\pi } {\left (x + 2\right )} {\left (\operatorname {erf}\left (6 \, \sqrt {-{\left (x + 2\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (x + 2\right )}^{2}}} - e^{\left (36 \, {\left (x + 2\right )}^{2}\right )}\right )} e^{\left (\frac {145 \, e^{5}}{{\left (e^{4} + e^{3} + e^{2} + e + 1\right )} {\left (e - 1\right )}} - \frac {6 \, \log \relax (2)}{{\left (e^{4} + e^{3} + e^{2} + e + 1\right )} {\left (e - 1\right )}} - \frac {145}{{\left (e^{4} + e^{3} + e^{2} + e + 1\right )} {\left (e - 1\right )}} - 144\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 81, normalized size = 2.89 \begin {gather*} \frac {{\mathrm {e}}^{\frac {36\,x^2\,{\mathrm {e}}^5}{{\mathrm {e}}^5-1}}\,{\mathrm {e}}^{\frac {145\,{\mathrm {e}}^5}{{\mathrm {e}}^5-1}}\,{\mathrm {e}}^{-\frac {144\,x}{{\mathrm {e}}^5-1}}\,{\mathrm {e}}^{-\frac {36\,x^2}{{\mathrm {e}}^5-1}}\,{\mathrm {e}}^{\frac {144\,x\,{\mathrm {e}}^5}{{\mathrm {e}}^5-1}}\,{\mathrm {e}}^{-\frac {145}{{\mathrm {e}}^5-1}}}{2^{\frac {6}{{\mathrm {e}}^5-1}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 34, normalized size = 1.21 \begin {gather*} e^{\frac {- 36 x^{2} - 144 x + \left (36 x^{2} + 144 x + 145\right ) e^{5} - 145 - 6 \log {\relax (2 )}}{-1 + e^{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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