Optimal. Leaf size=23 \[ \left (e+x+\frac {1}{4} e^{15 e^{-3+x^2}} x^2\right )^2 \]
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Rubi [A]
time = 0.31, antiderivative size = 28, normalized size of antiderivative = 1.22, number of steps
used = 4, number of rules used = 3, integrand size = 104, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {12, 6820,
6818} \begin {gather*} \frac {1}{16} \left (e^{15 e^{x^2-3}} x^2+4 x+4 e\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int e^{-3+x^2} \left (e^{3-x^2} (8 e+8 x)+e^{30 e^{-3+x^2}} \left (e^{3-x^2} x^3+15 x^5\right )+e^{15 e^{-3+x^2}} \left (60 e x^3+60 x^4+e^{3-x^2} \left (4 e x+6 x^2\right )\right )\right ) \, dx\\ &=\frac {1}{4} \int \frac {\left (4 e+4 x+e^{15 e^{-3+x^2}} x^2\right ) \left (2 e^3+e^{3+15 e^{-3+x^2}} x+15 e^{15 e^{-3+x^2}+x^2} x^3\right )}{e^3} \, dx\\ &=\frac {\int \left (4 e+4 x+e^{15 e^{-3+x^2}} x^2\right ) \left (2 e^3+e^{3+15 e^{-3+x^2}} x+15 e^{15 e^{-3+x^2}+x^2} x^3\right ) \, dx}{4 e^3}\\ &=\frac {1}{16} \left (4 e+4 x+e^{15 e^{-3+x^2}} x^2\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 28, normalized size = 1.22 \begin {gather*} \frac {1}{16} \left (4 e+4 x+e^{15 e^{-3+x^2}} x^2\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 42, normalized size = 1.83
method | result | size |
risch | \(2 x \,{\mathrm e}+x^{2}+\frac {x^{4} {\mathrm e}^{30 \,{\mathrm e}^{x^{2}-3}}}{16}+\frac {x^{2} \left (x +{\mathrm e}\right ) {\mathrm e}^{15 \,{\mathrm e}^{x^{2}-3}}}{2}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 44, normalized size = 1.91 \begin {gather*} \frac {1}{16} \, x^{4} e^{\left (30 \, e^{\left (x^{2} - 3\right )}\right )} + x^{2} + 2 \, x e + \frac {1}{2} \, {\left (x^{3} + x^{2} e\right )} e^{\left (15 \, e^{\left (x^{2} - 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 44, normalized size = 1.91 \begin {gather*} \frac {1}{16} \, x^{4} e^{\left (30 \, e^{\left (x^{2} - 3\right )}\right )} + x^{2} + 2 \, x e + \frac {1}{2} \, {\left (x^{3} + x^{2} e\right )} e^{\left (15 \, e^{\left (x^{2} - 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 53 vs.
\(2 (25) = 50\).
time = 0.42, size = 53, normalized size = 2.30 \begin {gather*} \frac {1}{16} \, x^{4} e^{\left (30 \, e^{\left (x^{2} - 3\right )}\right )} + \frac {1}{2} \, x^{3} e^{\left (15 \, e^{\left (x^{2} - 3\right )}\right )} + \frac {1}{2} \, x^{2} e^{\left (15 \, e^{\left (x^{2} - 3\right )} + 1\right )} + x^{2} + 2 \, x e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.59, size = 37, normalized size = 1.61 \begin {gather*} \frac {x\,\left (x\,{\mathrm {e}}^{15\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-3}}+4\right )\,\left (4\,x+8\,\mathrm {e}+x^2\,{\mathrm {e}}^{15\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-3}}\right )}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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