Optimal. Leaf size=25 \[ \frac {5 x}{e^2 \left (6+6 e^4+e^{e-x^2}+x\right )} \]
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Rubi [F] time = 3.72, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {30+30 e^4+e^{e-x^2} \left (5+10 x^2\right )}{36 e^{10}+e^{2+2 e-2 x^2}+e^6 (72+12 x)+e^2 \left (36+12 x+x^2\right )+e^{e-x^2} \left (12 e^6+e^2 (12+2 x)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 e^{-2+x^2} \left (6 e^{x^2} \left (1+e^4\right )+e^e \left (1+2 x^2\right )\right )}{\left (e^e+6 e^{4+x^2}+e^{x^2} (6+x)\right )^2} \, dx\\ &=5 \int \frac {e^{-2+x^2} \left (6 e^{x^2} \left (1+e^4\right )+e^e \left (1+2 x^2\right )\right )}{\left (e^e+6 e^{4+x^2}+e^{x^2} (6+x)\right )^2} \, dx\\ &=5 \int \left (\frac {6 e^{-2+x^2} \left (1+e^4\right )}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )}+\frac {e^{-2+e+x^2} x \left (1+12 \left (1+e^4\right ) x+2 x^2\right )}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2}\right ) \, dx\\ &=5 \int \frac {e^{-2+e+x^2} x \left (1+12 \left (1+e^4\right ) x+2 x^2\right )}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2} \, dx+\left (30 \left (1+e^4\right )\right ) \int \frac {e^{-2+x^2}}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )} \, dx\\ &=5 \int \left (\frac {e^{-2+e+x^2}}{\left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2}+\frac {2 e^{-2+e+x^2} x^2}{\left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2}+\frac {6 e^{-2+e+x^2} \left (-1-e^4\right )}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2}\right ) \, dx+\left (30 \left (1+e^4\right )\right ) \int \frac {e^{-2+x^2}}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )} \, dx\\ &=5 \int \frac {e^{-2+e+x^2}}{\left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2} \, dx+10 \int \frac {e^{-2+e+x^2} x^2}{\left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2} \, dx-\left (30 \left (1+e^4\right )\right ) \int \frac {e^{-2+e+x^2}}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )^2} \, dx+\left (30 \left (1+e^4\right )\right ) \int \frac {e^{-2+x^2}}{\left (6+6 e^4+x\right ) \left (e^e+6 e^{x^2} \left (1+e^4\right )+e^{x^2} x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.96, size = 49, normalized size = 1.96 \begin {gather*} -\frac {5 \left (e^e+6 e^{x^2}+6 e^{4+x^2}\right )}{e^2 \left (e^e+6 e^{4+x^2}+e^{x^2} (6+x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 26, normalized size = 1.04 \begin {gather*} \frac {5 \, x}{{\left (x + 6\right )} e^{2} + 6 \, e^{6} + e^{\left (-x^{2} + e + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.34, size = 501, normalized size = 20.04 \begin {gather*} -\frac {5 \, {\left (12 \, x^{3} e^{\left (x^{2} + 6\right )} + 12 \, x^{3} e^{\left (x^{2} + 2\right )} + 2 \, x^{3} e^{\left (e + 2\right )} + 144 \, x^{2} e^{\left (x^{2} + 10\right )} + 288 \, x^{2} e^{\left (x^{2} + 6\right )} + 144 \, x^{2} e^{\left (x^{2} + 2\right )} + 2 \, x^{2} e^{\left (-x^{2} + 2 \, e + 2\right )} + 36 \, x^{2} e^{\left (e + 6\right )} + 36 \, x^{2} e^{\left (e + 2\right )} + 432 \, x e^{\left (x^{2} + 14\right )} + 1296 \, x e^{\left (x^{2} + 10\right )} + 1302 \, x e^{\left (x^{2} + 6\right )} + 438 \, x e^{\left (x^{2} + 2\right )} + 12 \, x e^{\left (-x^{2} + 2 \, e + 6\right )} + 12 \, x e^{\left (-x^{2} + 2 \, e + 2\right )} + 144 \, x e^{\left (e + 10\right )} + 288 \, x e^{\left (e + 6\right )} + 145 \, x e^{\left (e + 2\right )} + 36 \, e^{\left (x^{2} + 10\right )} + 72 \, e^{\left (x^{2} + 6\right )} + 36 \, e^{\left (x^{2} + 2\right )} + e^{\left (-x^{2} + 2 \, e + 2\right )} + 12 \, e^{\left (e + 6\right )} + 12 \, e^{\left (e + 2\right )}\right )}}{2 \, x^{4} e^{\left (x^{2} + 4\right )} + 36 \, x^{3} e^{\left (x^{2} + 8\right )} + 36 \, x^{3} e^{\left (x^{2} + 4\right )} + 4 \, x^{3} e^{\left (e + 4\right )} + 216 \, x^{2} e^{\left (x^{2} + 12\right )} + 432 \, x^{2} e^{\left (x^{2} + 8\right )} + 217 \, x^{2} e^{\left (x^{2} + 4\right )} + 2 \, x^{2} e^{\left (-x^{2} + 2 \, e + 4\right )} + 48 \, x^{2} e^{\left (e + 8\right )} + 48 \, x^{2} e^{\left (e + 4\right )} + 432 \, x e^{\left (x^{2} + 16\right )} + 1296 \, x e^{\left (x^{2} + 12\right )} + 1308 \, x e^{\left (x^{2} + 8\right )} + 444 \, x e^{\left (x^{2} + 4\right )} + 12 \, x e^{\left (-x^{2} + 2 \, e + 8\right )} + 12 \, x e^{\left (-x^{2} + 2 \, e + 4\right )} + 144 \, x e^{\left (e + 12\right )} + 288 \, x e^{\left (e + 8\right )} + 146 \, x e^{\left (e + 4\right )} + 36 \, e^{\left (x^{2} + 12\right )} + 72 \, e^{\left (x^{2} + 8\right )} + 36 \, e^{\left (x^{2} + 4\right )} + e^{\left (-x^{2} + 2 \, e + 4\right )} + 12 \, e^{\left (e + 8\right )} + 12 \, e^{\left (e + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 24, normalized size = 0.96
method | result | size |
risch | \(\frac {5 x \,{\mathrm e}^{-2}}{{\mathrm e}^{{\mathrm e}-x^{2}}+6+x +6 \,{\mathrm e}^{4}}\) | \(24\) |
norman | \(\frac {5 x \,{\mathrm e}^{-2}}{{\mathrm e}^{{\mathrm e}-x^{2}}+6+x +6 \,{\mathrm e}^{4}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 42, normalized size = 1.68 \begin {gather*} -\frac {5 \, {\left (6 \, {\left (e^{4} + 1\right )} e^{\left (x^{2}\right )} + e^{e}\right )}}{{\left (x e^{2} + 6 \, e^{6} + 6 \, e^{2}\right )} e^{\left (x^{2}\right )} + e^{\left (e + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.77, size = 40, normalized size = 1.60 \begin {gather*} \frac {x\,\left (30\,{\mathrm {e}}^4+30\right )}{6\,\left ({\mathrm {e}}^4+1\right )\,\left ({\mathrm {e}}^{-x^2+\mathrm {e}+2}+6\,{\mathrm {e}}^2+6\,{\mathrm {e}}^6+x\,{\mathrm {e}}^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 29, normalized size = 1.16 \begin {gather*} \frac {5 x}{x e^{2} + e^{2} e^{e - x^{2}} + 6 e^{2} + 6 e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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