Optimal. Leaf size=11 \[ e^{\left (1+\frac {x}{21}\right )^2} \]
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Rubi [A] time = 0.03, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 2227, 2209} \begin {gather*} e^{\frac {1}{441} (x+21)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{441} \int e^{\frac {1}{441} \left (441+42 x+x^2\right )} (42+2 x) \, dx\\ &=\frac {1}{441} \int e^{\frac {1}{441} (21+x)^2} (42+2 x) \, dx\\ &=e^{\frac {1}{441} (21+x)^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} e^{\frac {1}{441} (21+x)^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 11, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{441} \, x^{2} + \frac {2}{21} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 11, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{441} \, x^{2} + \frac {2}{21} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 9, normalized size = 0.82
method | result | size |
risch | \({\mathrm e}^{\frac {\left (x +21\right )^{2}}{441}}\) | \(9\) |
gosper | \({\mathrm e}^{\frac {1}{441} x^{2}+\frac {2}{21} x +1}\) | \(12\) |
default | \({\mathrm e}^{\frac {1}{441} x^{2}+\frac {2}{21} x +1}\) | \(12\) |
norman | \({\mathrm e}^{\frac {1}{441} x^{2}+\frac {2}{21} x +1}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 11, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{441} \, x^{2} + \frac {2}{21} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 13, normalized size = 1.18 \begin {gather*} {\mathrm {e}}^{\frac {2\,x}{21}}\,\mathrm {e}\,{\mathrm {e}}^{\frac {x^2}{441}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 1.09 \begin {gather*} e^{\frac {x^{2}}{441} + \frac {2 x}{21} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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