Optimal. Leaf size=31 \[ e^{\frac {5 \left (1+4 x^2-\log \left (\frac {4+e^{2 x}}{5 x^2}\right )\right )}{x}} \]
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Rubi [A]
time = 0.98, antiderivative size = 39, normalized size of antiderivative = 1.26, number of steps
used = 1, number of rules used = 1, integrand size = 96, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6838}
\begin {gather*} 5^{5/x} e^{\frac {5 \left (4 x^2+1\right )}{x}} \left (\frac {e^{2 x}+4}{x^2}\right )^{-5/x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5^{5/x} e^{\frac {5 \left (1+4 x^2\right )}{x}} \left (\frac {4+e^{2 x}}{x^2}\right )^{-5/x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.63, size = 36, normalized size = 1.16 \begin {gather*} 5^{5/x} e^{\frac {5}{x}+20 x} \left (\frac {4+e^{2 x}}{x^2}\right )^{-5/x} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.23, size = 188, normalized size = 6.06
method | result | size |
risch | \({\mathrm e}^{\frac {-\frac {5 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}+5 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\frac {5 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}+\frac {5 i \pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x}+4\right )}{x^{2}}\right )^{3}}{2}-\frac {5 i \pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x}+4\right )}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )}{2}-\frac {5 i \pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x}+4\right )}{x^{2}}\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{2 x}+4\right )\right )}{2}+\frac {5 i \pi \,\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x}+4\right )}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{2 x}+4\right )\right )}{2}+20 x^{2}+10 \ln \left (x \right )+5 \ln \left (5\right )-5 \ln \left ({\mathrm e}^{2 x}+4\right )+5}{x}}\) | \(188\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.57, size = 36, normalized size = 1.16 \begin {gather*} e^{\left (20 \, x + \frac {5 \, \log \left (5\right )}{x} + \frac {10 \, \log \left (x\right )}{x} - \frac {5 \, \log \left (e^{\left (2 \, x\right )} + 4\right )}{x} + \frac {5}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 27, normalized size = 0.87 \begin {gather*} e^{\left (\frac {5 \, {\left (4 \, x^{2} - \log \left (\frac {e^{\left (2 \, x\right )} + 4}{5 \, x^{2}}\right ) + 1\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.62, size = 31, normalized size = 1.00 \begin {gather*} e^{\left (20 \, x - \frac {5 \, \log \left (\frac {e^{\left (2 \, x\right )}}{5 \, x^{2}} + \frac {4}{5 \, x^{2}}\right )}{x} + \frac {5}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.77, size = 28, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{20\,x+\frac {5}{x}}\,{\left (\frac {3125\,x^{10}}{{\left ({\mathrm {e}}^{2\,x}+4\right )}^5}\right )}^{1/x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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