Optimal. Leaf size=15 \[ -2 e^x+e^x (3+2 x) \]
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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 = {2207, 2225}
\begin {gather*} e^x (2 x+3)-2 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
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 \begin {gather*} e^x (1+2 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 9, normalized size = 0.60
method | result | size |
gosper | \(\left (1+2 x \right ) {\mathrm e}^{x}\) | \(9\) |
default | \(2 \,{\mathrm e}^{x} x +{\mathrm e}^{x}\) | \(9\) |
norman | \(2 \,{\mathrm e}^{x} x +{\mathrm e}^{x}\) | \(9\) |
risch | \(\left (1+2 x \right ) {\mathrm e}^{x}\) | \(9\) |
meijerg | \(-1+3 \,{\mathrm e}^{x}-\left (-2 x +2\right ) {\mathrm e}^{x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.39, size = 12, normalized size = 0.80 \begin {gather*} 2 \, {\left (x - 1\right )} e^{x} + 3 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 8, normalized size = 0.53 \begin {gather*} {\left (2 \, x + 1\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.47 \begin {gather*} \left (2 x + 1\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.97, size = 8, normalized size = 0.53 \begin {gather*} {\left (2 \, x + 1\right )} e^{x} \end {gather*}
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 \begin {gather*} {\mathrm {e}}^x\,\left (2\,x+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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