Optimal. Leaf size=31 \[ \left (-e^{-1-e^5-e^8+2 x}+x\right ) \log \left (\frac {3 e^x}{x}\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 40, normalized size of antiderivative = 1.29, number of steps
used = 5, number of rules used = 3, integrand size = 66, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {14, 2628, 2326}
\begin {gather*} x \log \left (\frac {3 e^x}{x}\right )-e^{2 x-e^8-e^5-1} \log \left (\frac {3 e^x}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2326
Rule 2628
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+x+\log \left (\frac {3 e^x}{x}\right )-\frac {e^{-1-e^5-e^8+2 x} \left (-1+x+2 x \log \left (\frac {3 e^x}{x}\right )\right )}{x}\right ) \, dx\\ &=-x+\frac {x^2}{2}+\int \log \left (\frac {3 e^x}{x}\right ) \, dx-\int \frac {e^{-1-e^5-e^8+2 x} \left (-1+x+2 x \log \left (\frac {3 e^x}{x}\right )\right )}{x} \, dx\\ &=-x+\frac {x^2}{2}-e^{-1-e^5-e^8+2 x} \log \left (\frac {3 e^x}{x}\right )+x \log \left (\frac {3 e^x}{x}\right )-\int (-1+x) \, dx\\ &=-e^{-1-e^5-e^8+2 x} \log \left (\frac {3 e^x}{x}\right )+x \log \left (\frac {3 e^x}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.17, size = 31, normalized size = 1.00 \begin {gather*} \left (-e^{-1-e^5-e^8+2 x}+x\right ) \log \left (\frac {3 e^x}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs.
\(2(29)=58\).
time = 0.90, size = 80, normalized size = 2.58
method | result | size |
risch | \(\ln \left (\frac {{\mathrm e}^{x}}{x}\right ) \left ({\mathrm e}^{{\mathrm e}^{8}+{\mathrm e}^{5}+1}-\frac {{\mathrm e}^{2 x}}{x}\right ) x \,{\mathrm e}^{-{\mathrm e}^{8}-{\mathrm e}^{5}-1}+\frac {\left (2 \ln \left (3\right ) {\mathrm e}^{{\mathrm e}^{8}+{\mathrm e}^{5}+1}-\frac {2 \ln \left (3\right ) {\mathrm e}^{2 x}}{x}\right ) x \,{\mathrm e}^{-{\mathrm e}^{8}-{\mathrm e}^{5}-1}}{2}\) | \(76\) |
default | \(\ln \left (x \right ) {\mathrm e}^{-{\mathrm e}^{8}-{\mathrm e}^{5}+2 x -1}-x \,{\mathrm e}^{-{\mathrm e}^{8}-{\mathrm e}^{5}+2 x -1}-\left (\ln \left (3 \,{\mathrm e}^{x -\ln \left (x \right )}\right )+\ln \left (x \right )-x \right ) {\mathrm e}^{-{\mathrm e}^{8}-{\mathrm e}^{5}+2 x -1}+\ln \left (3 \,{\mathrm e}^{x -\ln \left (x \right )}\right ) x\) | \(80\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 69 vs.
\(2 (29) = 58\).
time = 0.38, size = 69, normalized size = 2.23 \begin {gather*} -{\left (x e^{\left (e^{8} + e^{5} + 1\right )} \log \left (x\right ) + {\left (x^{3} + x^{2} \log \left (3\right ) - x^{2} \log \left (x\right )\right )} e^{\left (2 \, x - 2 \, \log \left (x\right )\right )} - {\left (x^{2} + x \log \left (3\right )\right )} e^{\left (e^{8} + e^{5} + 1\right )}\right )} e^{\left (-e^{8} - e^{5} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (29) = 58\).
time = 0.40, size = 65, normalized size = 2.10 \begin {gather*} x^{2} - x e^{\left (2 \, x - e^{8} - e^{5} - 1\right )} + x \log \left (3\right ) - e^{\left (2 \, x - e^{8} - e^{5} - 1\right )} \log \left (3\right ) - x \log \left (x\right ) + e^{\left (2 \, x - e^{8} - e^{5} - 1\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.74, size = 36, normalized size = 1.16 \begin {gather*} -{\mathrm {e}}^{-{\mathrm {e}}^5-{\mathrm {e}}^8-1}\,\left ({\mathrm {e}}^{2\,x}-x\,{\mathrm {e}}^{{\mathrm {e}}^5+{\mathrm {e}}^8+1}\right )\,\left (x+\ln \left (\frac {3}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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