Optimal. Leaf size=24 \[ \left (e^{x^2}+\left (5+e^{\frac {1}{x^2}-x^2}\right ) x\right ) \log (x) \]
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Rubi [A] time = 0.17, antiderivative size = 45, normalized size of antiderivative = 1.88, number of steps used = 6, number of rules used = 3, integrand size = 77, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {14, 2295, 2288} \begin {gather*} e^{x^2} \log (x)+\frac {e^{\frac {1}{x^2}-x^2} \left (x^4 \log (x)+\log (x)\right )}{x^2 \left (\frac {1}{x^3}+x\right )}+5 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5 (1+\log (x))+\frac {e^{x^2} \left (1+2 x^2 \log (x)\right )}{x}-\frac {e^{\frac {1}{x^2}-x^2} \left (-x^2+2 \log (x)-x^2 \log (x)+2 x^4 \log (x)\right )}{x^2}\right ) \, dx\\ &=5 \int (1+\log (x)) \, dx+\int \frac {e^{x^2} \left (1+2 x^2 \log (x)\right )}{x} \, dx-\int \frac {e^{\frac {1}{x^2}-x^2} \left (-x^2+2 \log (x)-x^2 \log (x)+2 x^4 \log (x)\right )}{x^2} \, dx\\ &=5 x+e^{x^2} \log (x)+\frac {e^{\frac {1}{x^2}-x^2} \left (\log (x)+x^4 \log (x)\right )}{x^2 \left (\frac {1}{x^3}+x\right )}+5 \int \log (x) \, dx\\ &=e^{x^2} \log (x)+5 x \log (x)+\frac {e^{\frac {1}{x^2}-x^2} \left (\log (x)+x^4 \log (x)\right )}{x^2 \left (\frac {1}{x^3}+x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.23, size = 25, normalized size = 1.04 \begin {gather*} \left (e^{x^2}+5 x+e^{\frac {1}{x^2}-x^2} x\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 24, normalized size = 1.00 \begin {gather*} {\left (x e^{\left (-\frac {x^{4} - 1}{x^{2}}\right )} + 5 \, x + e^{\left (x^{2}\right )}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 28, normalized size = 1.17 \begin {gather*} x e^{\left (-\frac {x^{4} - 1}{x^{2}}\right )} \log \relax (x) + 5 \, x \log \relax (x) + e^{\left (x^{2}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 30, normalized size = 1.25
method | result | size |
default | \(x \,{\mathrm e}^{\frac {-x^{4}+1}{x^{2}}} \ln \relax (x )+{\mathrm e}^{x^{2}} \ln \relax (x )+5 x \ln \relax (x )\) | \(30\) |
risch | \(\left (x \,{\mathrm e}^{-\frac {\left (x -1\right ) \left (x +1\right ) \left (x^{2}+1\right )}{x^{2}}}+5 x +{\mathrm e}^{x^{2}}\right ) \ln \relax (x )\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {1}{4} \, \sqrt {\pi } {\left (\operatorname {erfc}\left (x + \frac {i}{x}\right ) e^{\left (4 i\right )} - \operatorname {erfc}\left (-x + \frac {i}{x}\right )\right )} e^{\left (-2 i\right )} + 5 \, x \log \relax (x) + e^{\left (x^{2}\right )} \log \relax (x) + \frac {1}{2} \, {\rm Ei}\left (x^{2}\right ) - \int \frac {{\left (2 \, x^{4} - x^{2} + 2\right )} e^{\left (-x^{2} + \frac {1}{x^{2}}\right )} \log \relax (x)}{x^{2}}\,{d x} - \int \frac {e^{\left (x^{2}\right )}}{x}\,{d x} \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 {x^2\,{\mathrm {e}}^{-\frac {x^4-1}{x^2}}+x\,{\mathrm {e}}^{x^2}+\ln \relax (x)\,\left (2\,x^3\,{\mathrm {e}}^{x^2}+5\,x^2-{\mathrm {e}}^{-\frac {x^4-1}{x^2}}\,\left (2\,x^4-x^2+2\right )\right )+5\,x^2}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.58, size = 29, normalized size = 1.21 \begin {gather*} x e^{\frac {1 - x^{4}}{x^{2}}} \log {\relax (x )} + 5 x \log {\relax (x )} + e^{x^{2}} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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