Optimal. Leaf size=27 \[ \frac {77}{16}+x+\frac {3 \left (\frac {1}{5} e^{5+x-x^2}+\log (x)\right )}{x} \]
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Rubi [A] time = 0.11, antiderivative size = 40, normalized size of antiderivative = 1.48, number of steps used = 9, number of rules used = 4, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 14, 2288, 2304} \begin {gather*} \frac {3 e^{-x^2+x+5} \left (x-2 x^2\right )}{5 (1-2 x) x^2}+x+\frac {3 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2288
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {15+5 x^2+e^{5+x-x^2} \left (-3+3 x-6 x^2\right )-15 \log (x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-\frac {3 e^{5+x-x^2} \left (1-x+2 x^2\right )}{x^2}+\frac {5 \left (3+x^2-3 \log (x)\right )}{x^2}\right ) \, dx\\ &=-\left (\frac {3}{5} \int \frac {e^{5+x-x^2} \left (1-x+2 x^2\right )}{x^2} \, dx\right )+\int \frac {3+x^2-3 \log (x)}{x^2} \, dx\\ &=\frac {3 e^{5+x-x^2} \left (x-2 x^2\right )}{5 (1-2 x) x^2}+\int \left (\frac {3+x^2}{x^2}-\frac {3 \log (x)}{x^2}\right ) \, dx\\ &=\frac {3 e^{5+x-x^2} \left (x-2 x^2\right )}{5 (1-2 x) x^2}-3 \int \frac {\log (x)}{x^2} \, dx+\int \frac {3+x^2}{x^2} \, dx\\ &=\frac {3}{x}+\frac {3 e^{5+x-x^2} \left (x-2 x^2\right )}{5 (1-2 x) x^2}+\frac {3 \log (x)}{x}+\int \left (1+\frac {3}{x^2}\right ) \, dx\\ &=x+\frac {3 e^{5+x-x^2} \left (x-2 x^2\right )}{5 (1-2 x) x^2}+\frac {3 \log (x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 29, normalized size = 1.07 \begin {gather*} \frac {3 e^{5+x-x^2}+5 x^2+15 \log (x)}{5 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 26, normalized size = 0.96 \begin {gather*} \frac {5 \, x^{2} + 3 \, e^{\left (-x^{2} + x + 5\right )} + 15 \, \log \relax (x)}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 26, normalized size = 0.96 \begin {gather*} \frac {5 \, x^{2} + 3 \, e^{\left (-x^{2} + x + 5\right )} + 15 \, \log \relax (x)}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 24, normalized size = 0.89
method | result | size |
default | \(x +\frac {3 \ln \relax (x )}{x}+\frac {3 \,{\mathrm e}^{-x^{2}+x +5}}{5 x}\) | \(24\) |
norman | \(\frac {x^{2}+\frac {3 \,{\mathrm e}^{-x^{2}+x +5}}{5}+3 \ln \relax (x )}{x}\) | \(24\) |
risch | \(\frac {3 \ln \relax (x )}{x}+\frac {5 x^{2}+3 \,{\mathrm e}^{-x^{2}+x +5}}{5 x}\) | \(31\) |
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 {3}{5} \, \sqrt {\pi } \operatorname {erf}\left (x - \frac {1}{2}\right ) e^{\frac {21}{4}} + x + \frac {3 \, {\left (\log \relax (x) + 1\right )}}{x} - \frac {3}{x} + \frac {1}{5} \, \int \frac {3 \, {\left (x e^{5} - e^{5}\right )} e^{\left (-x^{2} + x\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.37, size = 24, normalized size = 0.89 \begin {gather*} x+\frac {3\,\ln \relax (x)}{x}+\frac {3\,{\mathrm {e}}^5\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 20, normalized size = 0.74 \begin {gather*} x + \frac {3 e^{- x^{2} + x + 5}}{5 x} + \frac {3 \log {\relax (x )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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