Optimal. Leaf size=31 \[ 4-e+\frac {e^{\frac {2}{-4-2 x+\frac {3+x}{3}+\log (x)}}}{2+x} \]
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Rubi [F]
time = 4.42, 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 {6}{-9-5 x+3 \log (x)}} \left (-36-39 x-60 x^2-25 x^3+\left (54 x+30 x^2\right ) \log (x)-9 x \log ^2(x)\right )}{324 x+684 x^2+541 x^3+190 x^4+25 x^5+\left (-216 x-336 x^2-174 x^3-30 x^4\right ) \log (x)+\left (36 x+36 x^2+9 x^3\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}} \left (-36-39 x-60 x^2-25 x^3+6 x (9+5 x) \log (x)-9 x \log ^2(x)\right )}{x (2+x)^2 (9+5 x-3 \log (x))^2} \, dx\\ &=\int \left (-\frac {e^{-\frac {6}{9+5 x-3 \log (x)}}}{(2+x)^2}+\frac {6 e^{-\frac {6}{9+5 x-3 \log (x)}} (-3+5 x)}{x (2+x) (9+5 x-3 \log (x))^2}\right ) \, dx\\ &=6 \int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}} (-3+5 x)}{x (2+x) (9+5 x-3 \log (x))^2} \, dx-\int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}}}{(2+x)^2} \, dx\\ &=6 \int \left (-\frac {3 e^{-\frac {6}{9+5 x-3 \log (x)}}}{2 x (9+5 x-3 \log (x))^2}+\frac {13 e^{-\frac {6}{9+5 x-3 \log (x)}}}{2 (2+x) (9+5 x-3 \log (x))^2}\right ) \, dx-\int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}}}{(2+x)^2} \, dx\\ &=-\left (9 \int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}}}{x (9+5 x-3 \log (x))^2} \, dx\right )+39 \int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}}}{(2+x) (9+5 x-3 \log (x))^2} \, dx-\int \frac {e^{-\frac {6}{9+5 x-3 \log (x)}}}{(2+x)^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.21, size = 21, normalized size = 0.68 \begin {gather*} \frac {e^{\frac {6}{-9-5 x+3 \log (x)}}}{2+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 21, normalized size = 0.68
method | result | size |
risch | \(\frac {{\mathrm e}^{\frac {6}{3 \ln \left (x \right )-5 x -9}}}{2+x}\) | \(21\) |
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 = 0.41, size = 20, normalized size = 0.65 \begin {gather*} \frac {e^{\left (-\frac {6}{5 \, x - 3 \, \log \left (x\right ) + 9}\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 15, normalized size = 0.48 \begin {gather*} \frac {e^{\frac {6}{- 5 x + 3 \log {\left (x \right )} - 9}}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 30, normalized size = 0.97 \begin {gather*} \frac {e^{\left (\frac {2 \, {\left (5 \, x - 3 \, \log \left (x\right )\right )}}{3 \, {\left (5 \, x - 3 \, \log \left (x\right ) + 9\right )}} - \frac {2}{3}\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.66, size = 20, normalized size = 0.65 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {6}{5\,x-3\,\ln \left (x\right )+9}}}{x+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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