Optimal. Leaf size=22 \[ \frac {3 \left (e^{2 e^4}+x\right ) \log \left (x^2\right )}{x \log (8)} \]
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Rubi [A]
time = 0.04, antiderivative size = 29, normalized size of antiderivative = 1.32, number of steps
used = 6, number of rules used = 4, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 14, 45,
2341} \begin {gather*} \frac {3 e^{2 e^4} \log \left (x^2\right )}{x \log (8)}+\frac {6 \log (x)}{\log (8)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 45
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {6 e^{2 e^4}+6 x-3 e^{2 e^4} \log \left (x^2\right )}{x^2} \, dx}{\log (8)}\\ &=\frac {\int \left (\frac {6 \left (e^{2 e^4}+x\right )}{x^2}-\frac {3 e^{2 e^4} \log \left (x^2\right )}{x^2}\right ) \, dx}{\log (8)}\\ &=\frac {6 \int \frac {e^{2 e^4}+x}{x^2} \, dx}{\log (8)}-\frac {\left (3 e^{2 e^4}\right ) \int \frac {\log \left (x^2\right )}{x^2} \, dx}{\log (8)}\\ &=\frac {6 e^{2 e^4}}{x \log (8)}+\frac {3 e^{2 e^4} \log \left (x^2\right )}{x \log (8)}+\frac {6 \int \left (\frac {e^{2 e^4}}{x^2}+\frac {1}{x}\right ) \, dx}{\log (8)}\\ &=\frac {6 \log (x)}{\log (8)}+\frac {3 e^{2 e^4} \log \left (x^2\right )}{x \log (8)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 26, normalized size = 1.18 \begin {gather*} \frac {6 \log (x)+\frac {3 e^{2 e^4} \log \left (x^2\right )}{x}}{\log (8)} \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. \(43\) vs.
\(2(19)=38\).
time = 0.04, size = 44, normalized size = 2.00
method | result | size |
norman | \(\frac {{\mathrm e}^{2 \,{\mathrm e}^{4}} \ln \left (x^{2}\right )}{\ln \left (2\right ) x}+\frac {2 \ln \left (x \right )}{\ln \left (2\right )}\) | \(27\) |
risch | \(\frac {{\mathrm e}^{2 \,{\mathrm e}^{4}} \ln \left (x^{2}\right )}{\ln \left (2\right ) x}+\frac {2 \ln \left (x \right )}{\ln \left (2\right )}\) | \(27\) |
default | \(\frac {2 \ln \left (x \right )+\frac {{\mathrm e}^{2 \,{\mathrm e}^{4}} \ln \left (x^{2}\right )}{x}}{\ln \left (2\right )}\) | \(44\) |
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. 40 vs.
\(2 (19) = 38\).
time = 0.27, size = 40, normalized size = 1.82 \begin {gather*} \frac {{\left (\frac {\log \left (x^{2}\right )}{x} + \frac {2}{x}\right )} e^{\left (2 \, e^{4}\right )} - \frac {2 \, e^{\left (2 \, e^{4}\right )}}{x} + 2 \, \log \left (x\right )}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 19, normalized size = 0.86 \begin {gather*} \frac {{\left (x + e^{\left (2 \, e^{4}\right )}\right )} \log \left (x^{2}\right )}{x \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 24, normalized size = 1.09 \begin {gather*} \frac {2 \log {\left (x \right )}}{\log {\left (2 \right )}} + \frac {e^{2 e^{4}} \log {\left (x^{2} \right )}}{x \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 24, normalized size = 1.09 \begin {gather*} \frac {e^{\left (2 \, e^{4}\right )} \log \left (x^{2}\right ) + 2 \, x \log \left (x\right )}{x \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.91, size = 19, normalized size = 0.86 \begin {gather*} \frac {\ln \left (x^2\right )\,\left (x+{\mathrm {e}}^{2\,{\mathrm {e}}^4}\right )}{x\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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