Optimal. Leaf size=21 \[ x+\frac {5 e^{36 x^4} \log \left (\log \left (4 x^2\right )\right )}{x} \]
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Rubi [A] time = 0.55, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6742, 2288} \begin {gather*} \frac {5 e^{36 x^4} \log \left (\log \left (4 x^2\right )\right )}{x}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {5 e^{36 x^4} \left (2-\log \left (4 x^2\right ) \log \left (\log \left (4 x^2\right )\right )+144 x^4 \log \left (4 x^2\right ) \log \left (\log \left (4 x^2\right )\right )\right )}{x^2 \log \left (4 x^2\right )}\right ) \, dx\\ &=x+5 \int \frac {e^{36 x^4} \left (2-\log \left (4 x^2\right ) \log \left (\log \left (4 x^2\right )\right )+144 x^4 \log \left (4 x^2\right ) \log \left (\log \left (4 x^2\right )\right )\right )}{x^2 \log \left (4 x^2\right )} \, dx\\ &=x+\frac {5 e^{36 x^4} \log \left (\log \left (4 x^2\right )\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 21, normalized size = 1.00 \begin {gather*} x+\frac {5 e^{36 x^4} \log \left (\log \left (4 x^2\right )\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 23, normalized size = 1.10 \begin {gather*} \frac {x^{2} + 5 \, e^{\left (36 \, x^{4}\right )} \log \left (\log \left (4 \, x^{2}\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 23, normalized size = 1.10 \begin {gather*} \frac {x^{2} + 5 \, e^{\left (36 \, x^{4}\right )} \log \left (\log \left (4 \, x^{2}\right )\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.45, size = 52, normalized size = 2.48
method | result | size |
risch | \(\frac {5 \,{\mathrm e}^{36 x^{4}} \ln \left (2 \ln \relax (2)+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )}{x}+x\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 30, normalized size = 1.43 \begin {gather*} x + \frac {5 \, {\left (e^{\left (36 \, x^{4}\right )} \log \relax (2) + e^{\left (36 \, x^{4}\right )} \log \left (\log \relax (2) + \log \relax (x)\right )\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {10\,{\mathrm {e}}^{36\,x^4}+x^2\,\ln \left (4\,x^2\right )+\ln \left (\ln \left (4\,x^2\right )\right )\,{\mathrm {e}}^{36\,x^4}\,\ln \left (4\,x^2\right )\,\left (720\,x^4-5\right )}{x^2\,\ln \left (4\,x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 19, normalized size = 0.90 \begin {gather*} x + \frac {5 e^{36 x^{4}} \log {\left (\log {\left (4 x^{2} \right )} \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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