Optimal. Leaf size=28 \[ -1+e^{1+x}-\left (4-\frac {e^{3 x}}{\log \left (\frac {x}{3}\right )}\right )^2 \]
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Rubi [A]
time = 0.96, antiderivative size = 36, normalized size of antiderivative = 1.29, number of steps
used = 5, number of rules used = 3, integrand size = 81, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {6874, 2225,
2233} \begin {gather*} e^{x+1}-\frac {e^{6 x}}{\log ^2\left (\frac {x}{3}\right )}+\frac {8 e^{3 x}}{\log \left (\frac {x}{3}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2233
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{1+x}-\frac {2 e^{6 x} \left (-1+3 x \log \left (\frac {x}{3}\right )\right )}{x \log ^3\left (\frac {x}{3}\right )}+\frac {8 e^{3 x} \left (-1+3 x \log \left (\frac {x}{3}\right )\right )}{x \log ^2\left (\frac {x}{3}\right )}\right ) \, dx\\ &=-\left (2 \int \frac {e^{6 x} \left (-1+3 x \log \left (\frac {x}{3}\right )\right )}{x \log ^3\left (\frac {x}{3}\right )} \, dx\right )+8 \int \frac {e^{3 x} \left (-1+3 x \log \left (\frac {x}{3}\right )\right )}{x \log ^2\left (\frac {x}{3}\right )} \, dx+\int e^{1+x} \, dx\\ &=e^{1+x}-\frac {e^{6 x}}{\log ^2\left (\frac {x}{3}\right )}+\frac {8 e^{3 x}}{\log \left (\frac {x}{3}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.72, size = 36, normalized size = 1.29 \begin {gather*} e^{1+x}-\frac {e^{6 x}}{\log ^2\left (\frac {x}{3}\right )}+\frac {8 e^{3 x}}{\log \left (\frac {x}{3}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.42, size = 29, normalized size = 1.04
method | result | size |
risch | \({\mathrm e}^{x +1}-\frac {{\mathrm e}^{3 x} \left ({\mathrm e}^{3 x}-8 \ln \left (\frac {x}{3}\right )\right )}{\ln \left (\frac {x}{3}\right )^{2}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs.
\(2 (23) = 46\).
time = 0.54, size = 64, normalized size = 2.29 \begin {gather*} -\frac {8 \, {\left (\log \left (3\right ) - \log \left (x\right )\right )} e^{\left (3 \, x\right )} - {\left (e \log \left (3\right )^{2} - 2 \, e \log \left (3\right ) \log \left (x\right ) + e \log \left (x\right )^{2}\right )} e^{x} + e^{\left (6 \, x\right )}}{\log \left (3\right )^{2} - 2 \, \log \left (3\right ) \log \left (x\right ) + \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 36, normalized size = 1.29 \begin {gather*} \frac {{\left (e^{\left (-5 \, x + 1\right )} \log \left (\frac {1}{3} \, x\right )^{2} + 8 \, e^{\left (-3 \, x\right )} \log \left (\frac {1}{3} \, x\right ) - 1\right )} e^{\left (6 \, x\right )}}{\log \left (\frac {1}{3} \, x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 42 vs.
\(2 (19) = 38\).
time = 0.16, size = 42, normalized size = 1.50 \begin {gather*} \frac {- e^{6 x} \log {\left (\frac {x}{3} \right )} + 8 e^{3 x} \log {\left (\frac {x}{3} \right )}^{2} + e e^{x} \log {\left (\frac {x}{3} \right )}^{3}}{\log {\left (\frac {x}{3} \right )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 35, normalized size = 1.25 \begin {gather*} \frac {e^{\left (x + 1\right )} \log \left (\frac {1}{3} \, x\right )^{2} + 8 \, e^{\left (3 \, x\right )} \log \left (\frac {1}{3} \, x\right ) - e^{\left (6 \, x\right )}}{\log \left (\frac {1}{3} \, x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.47, size = 192, normalized size = 6.86 \begin {gather*} {\mathrm {e}}^{x+1}+24\,x\,{\mathrm {e}}^{3\,x}-\frac {12\,x\,{\mathrm {e}}^{3\,x}\,{\ln \left (\frac {x}{3}\right )}^2-{\mathrm {e}}^{-6}\,\left (4\,{\mathrm {e}}^{3\,x+6}+3\,x\,{\mathrm {e}}^{6\,x+6}\right )\,\ln \left (\frac {x}{3}\right )+{\mathrm {e}}^{6\,x}}{{\ln \left (\frac {x}{3}\right )}^2}+\frac {-12\,x\,{\mathrm {e}}^{-3}\,\left ({\mathrm {e}}^{3\,x+3}+3\,x\,{\mathrm {e}}^{3\,x+3}\right )\,{\ln \left (\frac {x}{3}\right )}^2+3\,x\,{\mathrm {e}}^{-6}\,\left ({\mathrm {e}}^{6\,x+6}-4\,{\mathrm {e}}^{3\,x+6}+6\,x\,{\mathrm {e}}^{6\,x+6}\right )\,\ln \left (\frac {x}{3}\right )+{\mathrm {e}}^{-6}\,\left (4\,{\mathrm {e}}^{3\,x+6}-3\,x\,{\mathrm {e}}^{6\,x+6}\right )}{\ln \left (\frac {x}{3}\right )}-{\mathrm {e}}^{6\,x+6}\,\left (18\,{\mathrm {e}}^{-6}\,x^2+3\,{\mathrm {e}}^{-6}\,x\right )+\ln \left (\frac {x}{3}\right )\,{\mathrm {e}}^{3\,x}\,\left (36\,x^2+12\,x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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