Optimal. Leaf size=24 \[ -2+\frac {e^x}{3}+\frac {(4+3 x)^2}{e^2}-\log (5) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 2194} \begin {gather*} \frac {9 x^2}{e^2}+\frac {24 x}{e^2}+\frac {e^x}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (72+e^{2+x}+54 x\right ) \, dx}{3 e^2}\\ &=\frac {24 x}{e^2}+\frac {9 x^2}{e^2}+\frac {\int e^{2+x} \, dx}{3 e^2}\\ &=\frac {e^x}{3}+\frac {24 x}{e^2}+\frac {9 x^2}{e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 0.88 \begin {gather*} \frac {e^{2+x}+72 x+27 x^2}{3 e^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 17, normalized size = 0.71 \begin {gather*} \frac {1}{3} \, {\left (27 \, x^{2} + 72 \, x + e^{\left (x + 2\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.99, size = 17, normalized size = 0.71 \begin {gather*} \frac {1}{3} \, {\left (27 \, x^{2} + 72 \, x + e^{\left (x + 2\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.75
method | result | size |
risch | \(24 \,{\mathrm e}^{-2} x +9 x^{2} {\mathrm e}^{-2}+\frac {{\mathrm e}^{x}}{3}\) | \(18\) |
default | \(\frac {{\mathrm e}^{-2} \left (72 x +{\mathrm e}^{2} {\mathrm e}^{x}+27 x^{2}\right )}{3}\) | \(21\) |
norman | \(24 \,{\mathrm e}^{-2} x +9 x^{2} {\mathrm e}^{-2}+\frac {{\mathrm e}^{x}}{3}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 17, normalized size = 0.71 \begin {gather*} \frac {1}{3} \, {\left (27 \, x^{2} + 72 \, x + e^{\left (x + 2\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 17, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^x}{3}+24\,x\,{\mathrm {e}}^{-2}+9\,x^2\,{\mathrm {e}}^{-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 19, normalized size = 0.79 \begin {gather*} \frac {9 x^{2}}{e^{2}} + \frac {24 x}{e^{2}} + \frac {e^{x}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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