Optimal. Leaf size=27 \[ e^{\frac {x \left (2-x^4+\log (x)\right )}{4+2 x+\frac {2+x}{x}}} \]
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Rubi [F]
time = 9.29, 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 {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} \left (10 x+15 x^2+2 x^3-12 x^5-25 x^6-8 x^7+\left (4 x+5 x^2\right ) \log (x)\right )}{4+20 x+33 x^2+20 x^3+4 x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {10 e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x}{(2+x)^2 (1+2 x)^2}+\frac {15 e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^2}{(2+x)^2 (1+2 x)^2}+\frac {2 e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^3}{(2+x)^2 (1+2 x)^2}-\frac {12 e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^5}{(2+x)^2 (1+2 x)^2}-\frac {25 e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^6}{(2+x)^2 (1+2 x)^2}-\frac {8 e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^7}{(2+x)^2 (1+2 x)^2}+\frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x (4+5 x) \log (x)}{(2+x)^2 (1+2 x)^2}\right ) \, dx\\ &=2 \int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^3}{(2+x)^2 (1+2 x)^2} \, dx-8 \int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^7}{(2+x)^2 (1+2 x)^2} \, dx+10 \int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x}{(2+x)^2 (1+2 x)^2} \, dx-12 \int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^5}{(2+x)^2 (1+2 x)^2} \, dx+15 \int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^2}{(2+x)^2 (1+2 x)^2} \, dx-25 \int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x^6}{(2+x)^2 (1+2 x)^2} \, dx+\int \frac {e^{\frac {2 x^2-x^6+x^2 \log (x)}{2+5 x+2 x^2}} x (4+5 x) \log (x)}{(2+x)^2 (1+2 x)^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 43, normalized size = 1.59 \begin {gather*} e^{-\frac {x^2 \left (-2+x^4\right )}{2+5 x+2 x^2}} x^{\frac {x^2}{2+5 x+2 x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 27, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{\frac {x^{2} \left (2-x^{4}+\ln \left (x \right )\right )}{\left (2+x \right ) \left (2 x +1\right )}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 31, normalized size = 1.15 \begin {gather*} e^{\left (-\frac {x^{6} - x^{2} \log \left (x\right ) - 2 \, x^{2}}{2 \, x^{2} + 5 \, x + 2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.27, size = 26, normalized size = 0.96 \begin {gather*} e^{\frac {- x^{6} + x^{2} \log {\left (x \right )} + 2 x^{2}}{2 x^{2} + 5 x + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 54, normalized size = 2.00 \begin {gather*} e^{\left (-\frac {x^{6}}{2 \, x^{2} + 5 \, x + 2} + \frac {x^{2} \log \left (x\right )}{2 \, x^{2} + 5 \, x + 2} + \frac {2 \, x^{2}}{2 \, x^{2} + 5 \, x + 2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.43, size = 44, normalized size = 1.63 \begin {gather*} x^{\frac {x^2}{2\,x^2+5\,x+2}}\,{\mathrm {e}}^{\frac {2\,x^2-x^6}{2\,x^2+5\,x+2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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