Optimal. Leaf size=13 \[ -5+e^{\left (-1+\frac {9 x}{25}\right )^2} \]
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Rubi [A] time = 0.03, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 2227, 2209} \begin {gather*} e^{\frac {1}{625} (25-9 x)^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}{625} \int e^{\frac {1}{625} \left (625-450 x+81 x^2\right )} (-450+162 x) \, dx\\ &=\frac {1}{625} \int e^{\frac {1}{625} (-25+9 x)^2} (-450+162 x) \, dx\\ &=e^{\frac {1}{625} (25-9 x)^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} e^{\frac {1}{625} (25-9 x)^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 11, normalized size = 0.85 \begin {gather*} e^{\left (\frac {81}{625} \, x^{2} - \frac {18}{25} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 11, normalized size = 0.85 \begin {gather*} e^{\left (\frac {81}{625} \, x^{2} - \frac {18}{25} \, 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 = 11, normalized size = 0.85
method | result | size |
risch | \({\mathrm e}^{\frac {\left (9 x -25\right )^{2}}{625}}\) | \(11\) |
gosper | \({\mathrm e}^{\frac {81}{625} x^{2}-\frac {18}{25} x +1}\) | \(12\) |
default | \({\mathrm e}^{\frac {81}{625} x^{2}-\frac {18}{25} x +1}\) | \(12\) |
norman | \({\mathrm e}^{\frac {81}{625} x^{2}-\frac {18}{25} x +1}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 11, normalized size = 0.85 \begin {gather*} e^{\left (\frac {81}{625} \, x^{2} - \frac {18}{25} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.21, size = 13, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{-\frac {18\,x}{25}}\,\mathrm {e}\,{\mathrm {e}}^{\frac {81\,x^2}{625}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 1.08 \begin {gather*} e^{\frac {81 x^{2}}{625} - \frac {18 x}{25} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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