Optimal. Leaf size=31 \[ e^{3 x+\frac {2}{3 x+x^2 \left (1+\frac {1}{4 x \log (4)}\right )}} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(31)=62\).
time = 1.21, antiderivative size = 93, normalized size of antiderivative = 3.00, number of steps
used = 3, number of rules used = 3, integrand size = 113, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6873, 27,
2326} \begin {gather*} \frac {e^{3 x} 4^{\frac {8}{x (4 x \log (4)+1+12 \log (4))}} (8 x \log (4)+1+12 \log (4))}{x^2 (4 x \log (4)+1+12 \log (4))^2 \left (\frac {1}{x^2 (4 x \log (4)+1+12 \log (4))}+\frac {4 \log (4)}{x (4 x \log (4)+1+12 \log (4))^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 2326
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4^{\frac {8}{x (1+12 \log (4)+4 x \log (4))}} e^{3 x} \left (-64 x \log ^2(4)+48 x^4 \log ^2(4)-8 \log (4) (1+12 \log (4))+24 x^3 \log (4) (1+12 \log (4))+3 x^2 (1+12 \log (4))^2\right )}{x^2 \left (16 x^2 \log ^2(4)+8 x \log (4) (1+12 \log (4))+(1+12 \log (4))^2\right )} \, dx\\ &=\int \frac {4^{\frac {8}{x (1+12 \log (4)+4 x \log (4))}} e^{3 x} \left (-64 x \log ^2(4)+48 x^4 \log ^2(4)-8 \log (4) (1+12 \log (4))+24 x^3 \log (4) (1+12 \log (4))+3 x^2 (1+12 \log (4))^2\right )}{x^2 (1+12 \log (4)+4 x \log (4))^2} \, dx\\ &=\frac {4^{\frac {8}{x (1+12 \log (4)+4 x \log (4))}} e^{3 x} (1+12 \log (4)+8 x \log (4))}{x^2 (1+12 \log (4)+4 x \log (4))^2 \left (\frac {4 \log (4)}{x (1+12 \log (4)+4 x \log (4))^2}+\frac {1}{x^2 (1+12 \log (4)+4 x \log (4))}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 26, normalized size = 0.84 \begin {gather*} 4^{\frac {8}{x (1+12 \log (4)+4 x \log (4))}} e^{3 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.62, size = 25, normalized size = 0.81
method | result | size |
risch | \({\mathrm e}^{3 x} 65536^{\frac {1}{x \left (8 x \ln \left (2\right )+24 \ln \left (2\right )+1\right )}}\) | \(25\) |
gosper | \({\mathrm e}^{\frac {16 \ln \left (2\right )}{x \left (8 x \ln \left (2\right )+24 \ln \left (2\right )+1\right )}+3 x}\) | \(26\) |
norman | \(\frac {\left (24 \ln \left (2\right )+1\right ) x \,{\mathrm e}^{3 x} {\mathrm e}^{\frac {16 \ln \left (2\right )}{2 \left (4 x^{2}+12 x \right ) \ln \left (2\right )+x}}+8 x^{2} \ln \left (2\right ) {\mathrm e}^{3 x} {\mathrm e}^{\frac {16 \ln \left (2\right )}{2 \left (4 x^{2}+12 x \right ) \ln \left (2\right )+x}}}{x \left (8 x \ln \left (2\right )+24 \ln \left (2\right )+1\right )}\) | \(86\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.60, size = 52, normalized size = 1.68 \begin {gather*} e^{\left (3 \, x - \frac {128 \, \log \left (2\right )^{2}}{8 \, {\left (24 \, \log \left (2\right )^{2} + \log \left (2\right )\right )} x + 576 \, \log \left (2\right )^{2} + 48 \, \log \left (2\right ) + 1} + \frac {16 \, \log \left (2\right )}{x {\left (24 \, \log \left (2\right ) + 1\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 24, normalized size = 0.77 \begin {gather*} 2^{\frac {16}{8 \, {\left (x^{2} + 3 \, x\right )} \log \left (2\right ) + x}} e^{\left (3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 10.12, size = 24, normalized size = 0.77 \begin {gather*} e^{3 x} e^{\frac {16 \log {\left (2 \right )}}{x + \left (8 x^{2} + 24 x\right ) \log {\left (2 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.12, size = 25, normalized size = 0.81 \begin {gather*} 2^{\frac {16}{x+24\,x\,\ln \left (2\right )+8\,x^2\,\ln \left (2\right )}}\,{\mathrm {e}}^{3\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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