Optimal. Leaf size=22 \[ 2 e^{-\frac {1}{400 x^4 (x-(5+x) \log (x))}} \]
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Rubi [F] time = 5.22, 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 {1}{-400 x^5+\left (2000 x^4+400 x^5\right ) \log (x)}} (-5+4 x+(-20-5 x) \log (x))}{200 x^7+\left (-2000 x^6-400 x^7\right ) \log (x)+\left (5000 x^5+2000 x^6+200 x^7\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 {1}{400 x^4 (-x+(5+x) \log (x))}} (-5+4 x-5 (4+x) \log (x))}{200 x^5 (x-(5+x) \log (x))^2} \, dx\\ &=\frac {1}{200} \int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}} (-5+4 x-5 (4+x) \log (x))}{x^5 (x-(5+x) \log (x))^2} \, dx\\ &=\frac {1}{200} \int \left (\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}} \left (-25-5 x-x^2\right )}{x^5 (5+x) (-x+5 \log (x)+x \log (x))^2}-\frac {5 e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}} (4+x)}{x^5 (5+x) (-x+5 \log (x)+x \log (x))}\right ) \, dx\\ &=\frac {1}{200} \int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}} \left (-25-5 x-x^2\right )}{x^5 (5+x) (-x+5 \log (x)+x \log (x))^2} \, dx-\frac {1}{40} \int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}} (4+x)}{x^5 (5+x) (-x+5 \log (x)+x \log (x))} \, dx\\ &=\frac {1}{200} \int \left (-\frac {5 e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^5 (-x+5 \log (x)+x \log (x))^2}-\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{5 x^3 (-x+5 \log (x)+x \log (x))^2}+\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{25 x^2 (-x+5 \log (x)+x \log (x))^2}-\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{125 x (-x+5 \log (x)+x \log (x))^2}+\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{125 (5+x) (-x+5 \log (x)+x \log (x))^2}\right ) \, dx-\frac {1}{40} \int \left (\frac {4 e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{5 x^5 (-x+5 \log (x)+x \log (x))}+\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{25 x^4 (-x+5 \log (x)+x \log (x))}-\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{125 x^3 (-x+5 \log (x)+x \log (x))}+\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{625 x^2 (-x+5 \log (x)+x \log (x))}-\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{3125 x (-x+5 \log (x)+x \log (x))}+\frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{3125 (5+x) (-x+5 \log (x)+x \log (x))}\right ) \, dx\\ &=\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x (-x+5 \log (x)+x \log (x))} \, dx}{125000}-\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{(5+x) (-x+5 \log (x)+x \log (x))} \, dx}{125000}-\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x (-x+5 \log (x)+x \log (x))^2} \, dx}{25000}+\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{(5+x) (-x+5 \log (x)+x \log (x))^2} \, dx}{25000}-\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^2 (-x+5 \log (x)+x \log (x))} \, dx}{25000}+\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^2 (-x+5 \log (x)+x \log (x))^2} \, dx}{5000}+\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^3 (-x+5 \log (x)+x \log (x))} \, dx}{5000}-\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^3 (-x+5 \log (x)+x \log (x))^2} \, dx}{1000}-\frac {\int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^4 (-x+5 \log (x)+x \log (x))} \, dx}{1000}-\frac {1}{50} \int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^5 (-x+5 \log (x)+x \log (x))} \, dx-\frac {1}{40} \int \frac {e^{\frac {1}{400 x^4 (-x+(5+x) \log (x))}}}{x^5 (-x+5 \log (x)+x \log (x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.34, size = 25, normalized size = 1.14 \begin {gather*} 2 e^{\frac {1}{400 x^4 (-x+5 \log (x)+x \log (x))}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 24, normalized size = 1.09 \begin {gather*} 2 \, e^{\left (-\frac {1}{400 \, {\left (x^{5} - {\left (x^{5} + 5 \, x^{4}\right )} \log \relax (x)\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (5 \, {\left (x + 4\right )} \log \relax (x) - 4 \, x + 5\right )} e^{\left (-\frac {1}{400 \, {\left (x^{5} - {\left (x^{5} + 5 \, x^{4}\right )} \log \relax (x)\right )}}\right )}}{200 \, {\left (x^{7} + {\left (x^{7} + 10 \, x^{6} + 25 \, x^{5}\right )} \log \relax (x)^{2} - 2 \, {\left (x^{7} + 5 \, x^{6}\right )} \log \relax (x)\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 23, normalized size = 1.05
method | result | size |
risch | \(2 \,{\mathrm e}^{\frac {1}{400 x^{4} \left (x \ln \relax (x )+5 \ln \relax (x )-x \right )}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.72, size = 25, normalized size = 1.14 \begin {gather*} 2\,{\mathrm {e}}^{\frac {1}{2000\,x^4\,\ln \relax (x)+400\,x^5\,\ln \relax (x)-400\,x^5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.63, size = 22, normalized size = 1.00 \begin {gather*} 2 e^{\frac {1}{- 400 x^{5} + \left (400 x^{5} + 2000 x^{4}\right ) \log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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