Optimal. Leaf size=20 \[ \frac {1}{2} \left (9+\frac {e^{4 (x+\log (4))^2}}{x}\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 39, normalized size of antiderivative = 1.95, number of steps used = 2, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 2288} \begin {gather*} \frac {2^{16 x-1} e^{4 x^2+4 \log ^2(4)} \left (x^2+x \log (4)\right )}{x^2 (x+\log (4))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {e^{4 x^2+8 x \log (4)+4 \log ^2(4)} \left (-1+8 x^2+8 x \log (4)\right )}{x^2} \, dx\\ &=\frac {2^{-1+16 x} e^{4 x^2+4 \log ^2(4)} \left (x^2+x \log (4)\right )}{x^2 (x+\log (4))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 23, normalized size = 1.15 \begin {gather*} \frac {2^{-1+16 x} e^{4 \left (x^2+\log ^2(4)\right )}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 23, normalized size = 1.15 \begin {gather*} \frac {e^{\left (4 \, x^{2} + 16 \, x \log \relax (2) + 16 \, \log \relax (2)^{2}\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.60, size = 23, normalized size = 1.15 \begin {gather*} \frac {e^{\left (4 \, x^{2} + 16 \, x \log \relax (2) + 16 \, \log \relax (2)^{2}\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 22, normalized size = 1.10
method | result | size |
risch | \(\frac {65536^{x} {\mathrm e}^{16 \ln \relax (2)^{2}+4 x^{2}}}{2 x}\) | \(22\) |
gosper | \(\frac {{\mathrm e}^{16 \ln \relax (2)^{2}+16 x \ln \relax (2)+4 x^{2}}}{2 x}\) | \(24\) |
norman | \(\frac {{\mathrm e}^{16 \ln \relax (2)^{2}+16 x \ln \relax (2)+4 x^{2}}}{2 x}\) | \(24\) |
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*} -i \, \sqrt {\pi } \operatorname {erf}\left (2 i \, x + 4 i \, \log \relax (2)\right ) + \frac {1}{2} \, \int \frac {{\left (16 \, x e^{\left (16 \, \log \relax (2)^{2}\right )} \log \relax (2) - e^{\left (16 \, \log \relax (2)^{2}\right )}\right )} e^{\left (4 \, x^{2} + 16 \, x \log \relax (2)\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 23, normalized size = 1.15 \begin {gather*} \frac {2^{16\,x}\,{\mathrm {e}}^{16\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{4\,x^2}}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 22, normalized size = 1.10 \begin {gather*} \frac {e^{4 x^{2} + 16 x \log {\relax (2 )} + 16 \log {\relax (2 )}^{2}}}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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