Optimal. Leaf size=15 \[ e^x (2 x+3)-2 e^x \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2176, 2194} \[ e^x (2 x+3)-2 e^x \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {align*} \int e^x (3+2 x) \, dx &=e^x (3+2 x)-2 \int e^x \, dx\\ &=-2 e^x+e^x (3+2 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 0.60 \[ e^x (2 x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 8, normalized size = 0.53 \[ {\left (2 \, x + 1\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.72, size = 8, normalized size = 0.53 \[ {\left (2 \, x + 1\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.60 \[ \left (2 x +1\right ) {\mathrm e}^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 12, normalized size = 0.80 \[ 2 \, {\left (x - 1\right )} e^{x} + 3 \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 8, normalized size = 0.53 \[ {\mathrm {e}}^x\,\left (2\,x+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.47 \[ \left (2 x + 1\right ) e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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