Optimal. Leaf size=33 \[ -x \left (\frac {4 \left (5+e^{3+x}\right )}{x}+e^{5/4} x\right )+x \left (5+3 x^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 26, normalized size of antiderivative = 0.79, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2194} \begin {gather*} 3 x^3-e^{5/4} x^2+5 x-4 e^{x+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 x-e^{5/4} x^2+3 x^3-4 \int e^{3+x} \, dx\\ &=-4 e^{3+x}+5 x-e^{5/4} x^2+3 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 0.79 \begin {gather*} -4 e^{3+x}+5 x-e^{5/4} x^2+3 x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.20, size = 22, normalized size = 0.67 \begin {gather*} 3 \, x^{3} - x^{2} e^{\frac {5}{4}} + 5 \, x - 4 \, e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 22, normalized size = 0.67 \begin {gather*} 3 \, x^{3} - x^{2} e^{\frac {5}{4}} + 5 \, x - 4 \, e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 0.70
method | result | size |
default | \(3 x^{3}+5 x -x^{2} {\mathrm e}^{\frac {5}{4}}-4 \,{\mathrm e}^{3+x}\) | \(23\) |
norman | \(3 x^{3}+5 x -x^{2} {\mathrm e}^{\frac {5}{4}}-4 \,{\mathrm e}^{3+x}\) | \(23\) |
risch | \(3 x^{3}+5 x -x^{2} {\mathrm e}^{\frac {5}{4}}-4 \,{\mathrm e}^{3+x}\) | \(23\) |
derivativedivides | \(15+5 x +3 x^{3}-2 \,{\mathrm e}^{\frac {5}{4}} \left (\frac {\left (3+x \right )^{2}}{2}-9-3 x \right )-4 \,{\mathrm e}^{3+x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 22, normalized size = 0.67 \begin {gather*} 3 \, x^{3} - x^{2} e^{\frac {5}{4}} + 5 \, x - 4 \, e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.32, size = 22, normalized size = 0.67 \begin {gather*} 5\,x-4\,{\mathrm {e}}^{x+3}-x^2\,{\mathrm {e}}^{5/4}+3\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 22, normalized size = 0.67 \begin {gather*} 3 x^{3} - x^{2} e^{\frac {5}{4}} + 5 x - 4 e^{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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