Optimal. Leaf size=20 \[ \log \left (-4 \left (3+\frac {3}{25} e^{-5+x^2}\right ) x+\log (5)\right ) \]
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Rubi [F] time = 1.05, 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 {-12-300 e^{5-x^2}-24 x^2}{-12 x+25 e^{5-x^2} (-12 x+\log (5))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1+2 x^2}{x}-\frac {25 e^5 \left (24 x^3-\log (5)-2 x^2 \log (5)\right )}{x \left (300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)\right )}\right ) \, dx\\ &=-\left (\left (25 e^5\right ) \int \frac {24 x^3-\log (5)-2 x^2 \log (5)}{x \left (300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)\right )} \, dx\right )+\int \frac {1+2 x^2}{x} \, dx\\ &=-\left (\left (25 e^5\right ) \int \left (\frac {24 x^2}{300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)}-\frac {\log (5)}{x \left (300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)\right )}-\frac {2 x \log (5)}{300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)}\right ) \, dx\right )+\int \left (\frac {1}{x}+2 x\right ) \, dx\\ &=x^2+\log (x)-\left (600 e^5\right ) \int \frac {x^2}{300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)} \, dx+\left (25 e^5 \log (5)\right ) \int \frac {1}{x \left (300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)\right )} \, dx+\left (50 e^5 \log (5)\right ) \int \frac {x}{300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 23, normalized size = 1.15 \begin {gather*} \log \left (300 e^5 x+12 e^{x^2} x-25 e^5 \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.74, size = 51, normalized size = 2.55 \begin {gather*} x^{2} + \log \left (12 \, x - \log \relax (5)\right ) + \log \left (-\frac {{\left (12 \, x - \log \relax (5)\right )} e^{\left (-x^{2} + 2 \, \log \relax (5) + 5\right )} + 12 \, x}{12 \, x - \log \relax (5)}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 32, normalized size = 1.60 \begin {gather*} x^{2} + \log \left (300 \, x e^{\left (-x^{2} + 5\right )} - 25 \, e^{\left (-x^{2} + 5\right )} \log \relax (5) + 12 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 40, normalized size = 2.00
method | result | size |
norman | \(x^{2}+\ln \left ({\mathrm e}^{2 \ln \relax (5)-x^{2}+5} \ln \relax (5)-12 x \,{\mathrm e}^{2 \ln \relax (5)-x^{2}+5}-12 x \right )\) | \(40\) |
risch | \(\ln \left (-\ln \relax (5)+12 x \right )+x^{2}-2 \ln \relax (5)-5+\ln \left (25 \,{\mathrm e}^{-x^{2}+5}-\frac {12 x}{\ln \relax (5)-12 x}\right )\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 28, normalized size = 1.40 \begin {gather*} \log \relax (x) + \log \left (\frac {300 \, x e^{5} + 12 \, x e^{\left (x^{2}\right )} - 25 \, e^{5} \log \relax (5)}{12 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 32, normalized size = 1.60 \begin {gather*} \ln \left (12\,x-25\,{\mathrm {e}}^5\,{\mathrm {e}}^{-x^2}\,\ln \relax (5)+300\,x\,{\mathrm {e}}^5\,{\mathrm {e}}^{-x^2}\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 31, normalized size = 1.55 \begin {gather*} x^{2} + \log {\left (12 x - \log {\relax (5 )} \right )} + \log {\left (\frac {12 x}{300 x - 25 \log {\relax (5 )}} + e^{5 - x^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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