Optimal. Leaf size=22 \[ 2+x^2+\log (x)+\frac {5}{2} e^{-e^5+x} \log (x) \]
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Rubi [A]
time = 0.06, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps
used = 6, number of rules used = 3, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {12, 14, 2326}
\begin {gather*} x^2+\frac {5}{2} e^{x-e^5} \log (x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} e^{-e^5} \int \frac {5 e^x+e^{e^5} \left (2+4 x^2\right )+5 e^x x \log (x)}{x} \, dx\\ &=\frac {1}{2} e^{-e^5} \int \left (\frac {2 e^{e^5} \left (1+2 x^2\right )}{x}+\frac {5 e^x (1+x \log (x))}{x}\right ) \, dx\\ &=\frac {1}{2} \left (5 e^{-e^5}\right ) \int \frac {e^x (1+x \log (x))}{x} \, dx+\int \frac {1+2 x^2}{x} \, dx\\ &=\frac {5}{2} e^{-e^5+x} \log (x)+\int \left (\frac {1}{x}+2 x\right ) \, dx\\ &=x^2+\log (x)+\frac {5}{2} e^{-e^5+x} \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 27, normalized size = 1.23 \begin {gather*} \frac {1}{2} \left (2 x^2+2 \log (x)+5 e^{-e^5+x} \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.44, size = 30, normalized size = 1.36
method | result | size |
norman | \(x^{2}+\ln \left (x \right )+\frac {5 \ln \left (x \right ) {\mathrm e}^{-{\mathrm e}^{5}} {\mathrm e}^{x}}{2}\) | \(18\) |
risch | \(x^{2}+\ln \left (x \right )+\frac {5 \ln \left (x \right ) {\mathrm e}^{-{\mathrm e}^{5}+x}}{2}\) | \(18\) |
default | \(\frac {{\mathrm e}^{-{\mathrm e}^{5}} \left (5 \,{\mathrm e}^{x} \ln \left (x \right )+2 x^{2} {\mathrm e}^{{\mathrm e}^{5}}+2 \,{\mathrm e}^{{\mathrm e}^{5}} \ln \left (x \right )\right )}{2}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 29, normalized size = 1.32 \begin {gather*} \frac {1}{2} \, {\left (2 \, x^{2} e^{\left (e^{5}\right )} + 5 \, e^{x} \log \left (x\right ) + 2 \, e^{\left (e^{5}\right )} \log \left (x\right )\right )} e^{\left (-e^{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 29, normalized size = 1.32 \begin {gather*} \frac {1}{2} \, {\left (2 \, x^{2} e^{\left (e^{5}\right )} + {\left (5 \, e^{x} + 2 \, e^{\left (e^{5}\right )}\right )} \log \left (x\right )\right )} e^{\left (-e^{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 20, normalized size = 0.91 \begin {gather*} x^{2} + \frac {5 e^{x} \log {\left (x \right )}}{2 e^{e^{5}}} + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 29, normalized size = 1.32 \begin {gather*} \frac {1}{2} \, {\left (2 \, x^{2} e^{\left (e^{5}\right )} + 5 \, e^{x} \log \left (x\right ) + 2 \, e^{\left (e^{5}\right )} \log \left (x\right )\right )} e^{\left (-e^{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.25, size = 17, normalized size = 0.77 \begin {gather*} \ln \left (x\right )+x^2+\frac {5\,{\mathrm {e}}^{-{\mathrm {e}}^5}\,{\mathrm {e}}^x\,\ln \left (x\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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