Optimal. Leaf size=29 \[ e^{\frac {-1+\log (5)}{\log \left (-e^{x+\frac {25 (3+x)}{3+\log (x)}}+x\right )}} \]
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Rubi [F] time = 66.67, 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 {\exp \left (\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+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 {\exp \left (\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \left (x (-9+9 \log (5))+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=\int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} (1-\log (5)) \left (9 x+6 x \log (x)+x \log ^2(x)-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )\right )}{x \left (x-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (9 x+6 x \log (x)+x \log ^2(x)-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )\right )}{x \left (x-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=(1-\log (5)) \int \left (\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-84+59 x-6 \log (x)+31 x \log (x)-\log ^2(x)+x \log ^2(x)\right )}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \, dx\\ &=(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-84+59 x-6 \log (x)+31 x \log (x)-\log ^2(x)+x \log ^2(x)\right )}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.37, size = 31, normalized size = 1.07 \begin {gather*} \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 30, normalized size = 1.03 \begin {gather*} e^{\left (\frac {\log \relax (5) - 1}{\log \left (x - e^{\left (\frac {x \log \relax (x) + 28 \, x + 75}{\log \relax (x) + 3}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 31, normalized size = 1.07
method | result | size |
risch | \({\mathrm e}^{\frac {\ln \relax (5)-1}{\ln \left (-{\mathrm e}^{\frac {x \ln \relax (x )+28 x +75}{3+\ln \relax (x )}}+x \right )}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.17, size = 79, normalized size = 2.72 \begin {gather*} e^{\left (\frac {\log \relax (5)}{\log \left (x - e^{\left (\frac {x \log \relax (x)}{\log \relax (x) + 3} + \frac {28 \, x}{\log \relax (x) + 3} + \frac {75}{\log \relax (x) + 3}\right )}\right )} - \frac {1}{\log \left (x - e^{\left (\frac {x \log \relax (x)}{\log \relax (x) + 3} + \frac {28 \, x}{\log \relax (x) + 3} + \frac {75}{\log \relax (x) + 3}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.46, size = 78, normalized size = 2.69 \begin {gather*} 5^{\frac {1}{\ln \left (x-x^{\frac {x}{\ln \relax (x)+3}}\,{\mathrm {e}}^{\frac {75}{\ln \relax (x)+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \relax (x)+3}}\right )}}\,{\mathrm {e}}^{-\frac {1}{\ln \left (x-x^{\frac {x}{\ln \relax (x)+3}}\,{\mathrm {e}}^{\frac {75}{\ln \relax (x)+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \relax (x)+3}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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