Optimal. Leaf size=24 \[ 1+e^{x^2+\frac {3}{-x+\log (1+5 (2+x))}} \]
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Rubi [F] time = 3.37, 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 {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} \left (18+15 x+22 x^3+10 x^4+\left (-44 x^2-20 x^3\right ) \log (11+5 x)+\left (22 x+10 x^2\right ) \log ^2(11+5 x)\right )}{11 x^2+5 x^3+\left (-22 x-10 x^2\right ) \log (11+5 x)+(11+5 x) \log ^2(11+5 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 {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} \left (18+15 x+22 x^3+10 x^4+\left (-44 x^2-20 x^3\right ) \log (11+5 x)+\left (22 x+10 x^2\right ) \log ^2(11+5 x)\right )}{(11+5 x) (x-\log (11+5 x))^2} \, dx\\ &=\int \left (2 e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} x+\frac {3 e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} (6+5 x)}{(11+5 x) (x-\log (11+5 x))^2}\right ) \, dx\\ &=2 \int e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} x \, dx+3 \int \frac {e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} (6+5 x)}{(11+5 x) (x-\log (11+5 x))^2} \, dx\\ &=2 \int e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} x \, dx+3 \int \left (\frac {e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}}}{(x-\log (11+5 x))^2}-\frac {5 e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}}}{(11+5 x) (x-\log (11+5 x))^2}\right ) \, dx\\ &=2 \int e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}} x \, dx+3 \int \frac {e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}}}{(x-\log (11+5 x))^2} \, dx-15 \int \frac {e^{\frac {3-x^3+x^2 \log (11+5 x)}{-x+\log (11+5 x)}}}{(11+5 x) (x-\log (11+5 x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 44, normalized size = 1.83 \begin {gather*} e^{\frac {-3+x^3}{x-\log (11+5 x)}} (11+5 x)^{-\frac {x^2}{x-\log (11+5 x)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 30, normalized size = 1.25 \begin {gather*} e^{\left (\frac {x^{3} - x^{2} \log \left (5 \, x + 11\right ) - 3}{x - \log \left (5 \, x + 11\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.91, size = 55, normalized size = 2.29 \begin {gather*} e^{\left (\frac {x^{3}}{x - \log \left (5 \, x + 11\right )} - \frac {x^{2} \log \left (5 \, x + 11\right )}{x - \log \left (5 \, x + 11\right )} - \frac {3}{x - \log \left (5 \, x + 11\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 31, normalized size = 1.29
method | result | size |
risch | \({\mathrm e}^{\frac {-x^{2} \ln \left (5 x +11\right )+x^{3}-3}{-\ln \left (5 x +11\right )+x}}\) | \(31\) |
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*} \int \frac {{\left (10 \, x^{4} + 22 \, x^{3} + 2 \, {\left (5 \, x^{2} + 11 \, x\right )} \log \left (5 \, x + 11\right )^{2} - 4 \, {\left (5 \, x^{3} + 11 \, x^{2}\right )} \log \left (5 \, x + 11\right ) + 15 \, x + 18\right )} e^{\left (\frac {x^{3} - x^{2} \log \left (5 \, x + 11\right ) - 3}{x - \log \left (5 \, x + 11\right )}\right )}}{5 \, x^{3} + {\left (5 \, x + 11\right )} \log \left (5 \, x + 11\right )^{2} + 11 \, x^{2} - 2 \, {\left (5 \, x^{2} + 11 \, x\right )} \log \left (5 \, x + 11\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.64, size = 44, normalized size = 1.83 \begin {gather*} \frac {{\mathrm {e}}^{\frac {x^3-3}{x-\ln \left (5\,x+11\right )}}}{{\left (5\,x+11\right )}^{\frac {x^2}{x-\ln \left (5\,x+11\right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.60, size = 24, normalized size = 1.00 \begin {gather*} e^{\frac {- x^{3} + x^{2} \log {\left (5 x + 11 \right )} + 3}{- x + \log {\left (5 x + 11 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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