Optimal. Leaf size=14 \[ 4 e^{-3+3 x+25 x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 2236} \begin {gather*} 4 e^{25 x^2+3 x-3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int e^{-3+3 x+25 x^2} (3+50 x) \, dx\\ &=4 e^{-3+3 x+25 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 14, normalized size = 1.00 \begin {gather*} 4 e^{-3+3 x+25 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 15, normalized size = 1.07 \begin {gather*} e^{\left (25 \, x^{2} + 3 \, x + 2 \, \log \relax (2) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 15, normalized size = 1.07 \begin {gather*} e^{\left (25 \, x^{2} + 3 \, x + 2 \, \log \relax (2) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 1.00
method | result | size |
risch | \(4 \,{\mathrm e}^{25 x^{2}+3 x -3}\) | \(14\) |
gosper | \({\mathrm e}^{2 \ln \relax (2)+25 x^{2}+3 x -3}\) | \(16\) |
derivativedivides | \({\mathrm e}^{2 \ln \relax (2)+25 x^{2}+3 x -3}\) | \(16\) |
default | \({\mathrm e}^{2 \ln \relax (2)+25 x^{2}+3 x -3}\) | \(16\) |
norman | \({\mathrm e}^{2 \ln \relax (2)+25 x^{2}+3 x -3}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.93 \begin {gather*} 4 \, e^{\left (25 \, x^{2} + 3 \, x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 14, normalized size = 1.00 \begin {gather*} 4\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{25\,x^2} \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 = 0.86 \begin {gather*} 4 e^{25 x^{2} + 3 x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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