Optimal. Leaf size=28 \[ 5-\frac {3}{-x^2+3 \left (e^{\frac {1}{e^5 x}}-\log (5)\right )} \]
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Rubi [A] time = 0.36, antiderivative size = 25, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 99, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {3}{-x^2+3 e^{\frac {1}{e^5 x}}-\log (125)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (-3 e^{\frac {1}{e^5 x}}-2 e^5 x^3\right )}{e^5 x^2 \left (3 e^{\frac {1}{e^5 x}}-x^2-\log (125)\right )^2} \, dx\\ &=\frac {3 \int \frac {-3 e^{\frac {1}{e^5 x}}-2 e^5 x^3}{x^2 \left (3 e^{\frac {1}{e^5 x}}-x^2-\log (125)\right )^2} \, dx}{e^5}\\ &=-\frac {3}{3 e^{\frac {1}{e^5 x}}-x^2-\log (125)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 21, normalized size = 0.75 \begin {gather*} \frac {3}{-3 e^{\frac {1}{e^5 x}}+x^2+\log (125)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 21, normalized size = 0.75 \begin {gather*} \frac {3}{x^{2} - 3 \, e^{\left (\frac {e^{\left (-5\right )}}{x}\right )} + 3 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 28, normalized size = 1.00 \begin {gather*} -\frac {3}{x^{2} {\left (\frac {3 \, e^{\left (\frac {e^{\left (-5\right )}}{x}\right )}}{x^{2}} - \frac {3 \, \log \relax (5)}{x^{2}} - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.86, size = 22, normalized size = 0.79
method | result | size |
risch | \(\frac {3}{x^{2}+3 \ln \relax (5)-3 \,{\mathrm e}^{\frac {{\mathrm e}^{-5}}{x}}}\) | \(22\) |
norman | \(\frac {3}{x^{2}+3 \ln \relax (5)-3 \,{\mathrm e}^{\frac {{\mathrm e}^{-5}}{x}}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 21, normalized size = 0.75 \begin {gather*} \frac {3}{x^{2} - 3 \, e^{\left (\frac {e^{\left (-5\right )}}{x}\right )} + 3 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {9\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-5}}{x}}+6\,x^3\,{\mathrm {e}}^5}{x^6\,{\mathrm {e}}^5-{\mathrm {e}}^{\frac {{\mathrm {e}}^{-5}}{x}}\,\left (6\,{\mathrm {e}}^5\,x^4+18\,{\mathrm {e}}^5\,\ln \relax (5)\,x^2\right )+6\,x^4\,{\mathrm {e}}^5\,\ln \relax (5)+9\,x^2\,{\mathrm {e}}^5\,{\ln \relax (5)}^2+9\,x^2\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{-5}}{x}}\,{\mathrm {e}}^5} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 20, normalized size = 0.71 \begin {gather*} - \frac {3}{- x^{2} + 3 e^{\frac {1}{x e^{5}}} - 3 \log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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