Optimal. Leaf size=22 \[ \frac {1}{4 x^8 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2} \]
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Rubi [F] time = 1.91, 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 {-5 x^3+e^{\frac {4+4 x+x^2}{x^2}} \left (8+4 x-4 x^2\right )}{2 e^{\frac {3 \left (4+4 x+x^2\right )}{x^2}} x^{11}+6 e^{\frac {2 \left (4+4 x+x^2\right )}{x^2}} x^{12}+6 e^{\frac {4+4 x+x^2}{x^2}} x^{13}+2 x^{14}} \, 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 x^3+e^{\frac {(2+x)^2}{x^2}} \left (8+4 x-4 x^2\right )}{2 x^{11} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3} \, dx\\ &=\frac {1}{2} \int \frac {-5 x^3+e^{\frac {(2+x)^2}{x^2}} \left (8+4 x-4 x^2\right )}{x^{11} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3} \, dx\\ &=\frac {1}{2} \int \left (-\frac {4 (-2+x) (1+x)}{x^{11} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2}-\frac {8+4 x+x^2}{x^{10} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {8+4 x+x^2}{x^{10} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3} \, dx\right )-2 \int \frac {(-2+x) (1+x)}{x^{11} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2} \, dx\\ &=-\left (\frac {1}{2} \int \left (\frac {8}{x^{10} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3}+\frac {4}{x^9 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3}+\frac {1}{x^8 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3}\right ) \, dx\right )-2 \int \left (-\frac {2}{x^{11} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2}-\frac {1}{x^{10} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2}+\frac {1}{x^9 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {1}{x^8 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3} \, dx\right )-2 \int \frac {1}{x^9 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3} \, dx+2 \int \frac {1}{x^{10} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2} \, dx-2 \int \frac {1}{x^9 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2} \, dx-4 \int \frac {1}{x^{10} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^3} \, dx+4 \int \frac {1}{x^{11} \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.35, size = 22, normalized size = 1.00 \begin {gather*} \frac {1}{4 x^8 \left (e^{\frac {(2+x)^2}{x^2}}+x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.78, size = 44, normalized size = 2.00 \begin {gather*} \frac {1}{4 \, {\left (x^{10} + 2 \, x^{9} e^{\left (\frac {x^{2} + 4 \, x + 4}{x^{2}}\right )} + x^{8} e^{\left (\frac {2 \, {\left (x^{2} + 4 \, x + 4\right )}}{x^{2}}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.35, size = 44, normalized size = 2.00 \begin {gather*} \frac {1}{4 \, {\left (x^{10} + 2 \, x^{9} e^{\left (\frac {x^{2} + 4 \, x + 4}{x^{2}}\right )} + x^{8} e^{\left (\frac {2 \, {\left (x^{2} + 4 \, x + 4\right )}}{x^{2}}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 20, normalized size = 0.91
method | result | size |
risch | \(\frac {1}{4 \left (x +{\mathrm e}^{\frac {\left (2+x \right )^{2}}{x^{2}}}\right )^{2} x^{8}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.39, size = 43, normalized size = 1.95 \begin {gather*} \frac {1}{4 \, {\left (x^{10} + 2 \, x^{9} e^{\left (\frac {4}{x} + \frac {4}{x^{2}} + 1\right )} + x^{8} e^{\left (\frac {8}{x} + \frac {8}{x^{2}} + 2\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.31, size = 50, normalized size = 2.27 \begin {gather*} \frac {x^3}{2\,\left (2\,x^{13}+4\,x^{12}\,\mathrm {e}\,{\mathrm {e}}^{4/x}\,{\mathrm {e}}^{\frac {4}{x^2}}+2\,x^{11}\,{\mathrm {e}}^2\,{\mathrm {e}}^{8/x}\,{\mathrm {e}}^{\frac {8}{x^2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.18, size = 44, normalized size = 2.00 \begin {gather*} \frac {1}{4 x^{10} + 8 x^{9} e^{\frac {x^{2} + 4 x + 4}{x^{2}}} + 4 x^{8} e^{\frac {2 \left (x^{2} + 4 x + 4\right )}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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