Optimal. Leaf size=12 \[ e^{a+b x+c x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2236} \[ e^{a+b x+c x^2} \]
Antiderivative was successfully verified.
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Rule 2236
Rubi steps
\begin {align*} \int e^{a+b x+c x^2} (b+2 c x) \, dx &=e^{a+b x+c x^2}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 12, normalized size = 1.00 \[ e^{a+b x+c x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 11, normalized size = 0.92 \[ e^{\left (c x^{2} + b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 11, normalized size = 0.92 \[ e^{\left (c x^{2} + b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 12, normalized size = 1.00 \[ {\mathrm e}^{c \,x^{2}+b x +a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 11, normalized size = 0.92 \[ e^{\left (c x^{2} + b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 13, normalized size = 1.08 \[ {\mathrm {e}}^{b\,x}\,{\mathrm {e}}^a\,{\mathrm {e}}^{c\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 0.83 \[ e^{a + b x + c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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