Optimal. Leaf size=19 \[ \frac {1}{\left (e^{\frac {25+x}{x^2}}+x\right ) \log (\log (16))} \]
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Rubi [A] time = 0.34, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {12, 6688, 6686} \begin {gather*} \frac {1}{\left (e^{\frac {x+25}{x^2}}+x\right ) \log (\log (16))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-x^3+e^{\frac {25+x}{x^2}} (50+x)}{e^{\frac {2 (25+x)}{x^2}} x^3+2 e^{\frac {25+x}{x^2}} x^4+x^5} \, dx}{\log (\log (16))}\\ &=\frac {\int \frac {-x^3+e^{\frac {25+x}{x^2}} (50+x)}{x^3 \left (e^{\frac {25+x}{x^2}}+x\right )^2} \, dx}{\log (\log (16))}\\ &=\frac {1}{\left (e^{\frac {25+x}{x^2}}+x\right ) \log (\log (16))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{\left (e^{\frac {25+x}{x^2}}+x\right ) \log (\log (16))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 20, normalized size = 1.05 \begin {gather*} \frac {1}{{\left (x + e^{\left (\frac {x + 25}{x^{2}}\right )}\right )} \log \left (4 \, \log \relax (2)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 20, normalized size = 1.05 \begin {gather*} \frac {1}{{\left (x + e^{\left (\frac {x + 25}{x^{2}}\right )}\right )} \log \left (4 \, \log \relax (2)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 24, normalized size = 1.26
method | result | size |
norman | \(\frac {1}{\left (2 \ln \relax (2)+\ln \left (\ln \relax (2)\right )\right ) \left (x +{\mathrm e}^{\frac {x +25}{x^{2}}}\right )}\) | \(24\) |
risch | \(\frac {1}{\left (2 \ln \relax (2)+\ln \left (\ln \relax (2)\right )\right ) \left (x +{\mathrm e}^{\frac {x +25}{x^{2}}}\right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 22, normalized size = 1.16 \begin {gather*} \frac {1}{{\left (x + e^{\left (\frac {1}{x} + \frac {25}{x^{2}}\right )}\right )} \log \left (4 \, \log \relax (2)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.36, size = 20, normalized size = 1.05 \begin {gather*} \frac {1}{{\mathrm {e}}^{\frac {x+25}{x^2}}\,\ln \left (\ln \left (16\right )\right )+x\,\ln \left (\ln \left (16\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 32, normalized size = 1.68 \begin {gather*} \frac {1}{x \log {\left (\log {\relax (2 )} \right )} + 2 x \log {\relax (2 )} + \left (\log {\left (\log {\relax (2 )} \right )} + 2 \log {\relax (2 )}\right ) e^{\frac {x + 25}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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