Optimal. Leaf size=19 \[ e^{2 x^2}+e^{16} \left (29-e^x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194, 2209} \begin {gather*} e^{2 x^2}-e^{x+16} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int e^{2 x^2} x \, dx-\int e^{16+x} \, dx\\ &=e^{2 x^2}-e^{16+x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} e^{2 x^2}-e^{16+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 13, normalized size = 0.68 \begin {gather*} e^{\left (2 \, x^{2}\right )} - e^{\left (x + 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 13, normalized size = 0.68 \begin {gather*} e^{\left (2 \, x^{2}\right )} - e^{\left (x + 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.74
method | result | size |
default | \({\mathrm e}^{2 x^{2}}-{\mathrm e}^{16} {\mathrm e}^{x}\) | \(14\) |
norman | \({\mathrm e}^{2 x^{2}}-{\mathrm e}^{16} {\mathrm e}^{x}\) | \(14\) |
risch | \({\mathrm e}^{2 x^{2}}-{\mathrm e}^{x +16}\) | \(14\) |
meijerg | \(-1+{\mathrm e}^{2 x^{2}}+{\mathrm e}^{16} \left (1-{\mathrm e}^{x}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.68 \begin {gather*} e^{\left (2 \, x^{2}\right )} - e^{\left (x + 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.53, size = 13, normalized size = 0.68 \begin {gather*} {\mathrm {e}}^{2\,x^2}-{\mathrm {e}}^{16}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 12, normalized size = 0.63 \begin {gather*} - e^{16} e^{x} + e^{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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