Optimal. Leaf size=25 \[ \frac {e^{\frac {x^2}{22+e^x}}}{-5+\frac {e^5}{3}} \]
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Rubi [A] time = 0.64, antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 3, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {6688, 12, 6706} \begin {gather*} -\frac {3 e^{\frac {x^2}{e^x+22}}}{15-e^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 e^{\frac {x^2}{22+e^x}} \left (-44+e^x (-2+x)\right ) x}{\left (15-e^5\right ) \left (22+e^x\right )^2} \, dx\\ &=\frac {3 \int \frac {e^{\frac {x^2}{22+e^x}} \left (-44+e^x (-2+x)\right ) x}{\left (22+e^x\right )^2} \, dx}{15-e^5}\\ &=-\frac {3 e^{\frac {x^2}{22+e^x}}}{15-e^5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 22, normalized size = 0.88 \begin {gather*} \frac {3 e^{\frac {x^2}{22+e^x}}}{-15+e^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 19, normalized size = 0.76 \begin {gather*} \frac {3 \, e^{\left (\frac {x^{2}}{e^{x} + 22}\right )}}{e^{5} - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 19, normalized size = 0.76 \begin {gather*} \frac {3 \, e^{\left (\frac {x^{2}}{e^{x} + 22}\right )}}{e^{5} - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 20, normalized size = 0.80
method | result | size |
risch | \(\frac {3 \,{\mathrm e}^{\frac {x^{2}}{{\mathrm e}^{x}+22}}}{{\mathrm e}^{5}-15}\) | \(20\) |
norman | \(\frac {\frac {66 \,{\mathrm e}^{\frac {x^{2}}{{\mathrm e}^{x}+22}}}{{\mathrm e}^{5}-15}+\frac {3 \,{\mathrm e}^{x} {\mathrm e}^{\frac {x^{2}}{{\mathrm e}^{x}+22}}}{{\mathrm e}^{5}-15}}{{\mathrm e}^{x}+22}\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 19, normalized size = 0.76 \begin {gather*} \frac {3 \, e^{\left (\frac {x^{2}}{e^{x} + 22}\right )}}{e^{5} - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.30, size = 19, normalized size = 0.76 \begin {gather*} \frac {3\,{\mathrm {e}}^{\frac {x^2}{{\mathrm {e}}^x+22}}}{{\mathrm {e}}^5-15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 15, normalized size = 0.60 \begin {gather*} \frac {3 e^{\frac {x^{2}}{e^{x} + 22}}}{-15 + e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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