Optimal. Leaf size=22 \[ \frac {3}{e^3 \left (5+e \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )\right )} \]
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Rubi [A] time = 0.16, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 6688, 6686} \begin {gather*} \frac {3}{e^3 \left (e \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )+5\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e \int \frac {3+3 x}{25 e^3 x^2+10 e^4 x^2 \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )+e^5 x^2 \log ^2\left (\frac {8 e^{\frac {1}{x}}}{x}\right )} \, dx\\ &=e \int \frac {3 (1+x)}{e^3 x^2 \left (5+e \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )\right )^2} \, dx\\ &=\frac {3 \int \frac {1+x}{x^2 \left (5+e \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )\right )^2} \, dx}{e^2}\\ &=\frac {3}{e^3 \left (5+e \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 22, normalized size = 1.00 \begin {gather*} \frac {3}{e^3 \left (5+e \log \left (\frac {8 e^{\frac {1}{x}}}{x}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 22, normalized size = 1.00 \begin {gather*} \frac {3}{e^{4} \log \left (\frac {8 \, e^{\frac {1}{x}}}{x}\right ) + 5 \, e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 29, normalized size = 1.32 \begin {gather*} \frac {3 \, x e}{3 \, x e^{5} \log \relax (2) - x e^{5} \log \relax (x) + 5 \, x e^{4} + e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.52, size = 36, normalized size = 1.64
method | result | size |
norman | \(-\frac {3 \,{\mathrm e}^{-3} {\mathrm e} \ln \left (\frac {8 \,{\mathrm e}^{\frac {1}{x}}}{x}\right )}{5 \left (5+\ln \left (\frac {8 \,{\mathrm e}^{\frac {1}{x}}}{x}\right ) {\mathrm e}\right )}\) | \(36\) |
default | \(-\frac {3 \,{\mathrm e}^{-3} x}{x \,{\mathrm e} \ln \relax (x )-{\mathrm e} x \left (\ln \left (\frac {8 \,{\mathrm e}^{\frac {1}{x}}}{x}\right )-\frac {1}{x}+\ln \relax (x )\right )-{\mathrm e}-5 x}\) | \(47\) |
risch | \(\frac {6 i {\mathrm e}^{-3}}{\pi \,{\mathrm e} \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {1}{x}}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{\frac {1}{x}}}{x}\right )-\pi \,{\mathrm e} \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{\frac {1}{x}}}{x}\right )^{2}-\pi \,{\mathrm e} \,\mathrm {csgn}\left (i {\mathrm e}^{\frac {1}{x}}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{\frac {1}{x}}}{x}\right )^{2}+\pi \,{\mathrm e} \mathrm {csgn}\left (\frac {i {\mathrm e}^{\frac {1}{x}}}{x}\right )^{3}+6 i {\mathrm e} \ln \relax (2)-2 i {\mathrm e} \ln \relax (x )+2 i {\mathrm e} \ln \left ({\mathrm e}^{\frac {1}{x}}\right )+10 i}\) | \(133\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 32, normalized size = 1.45 \begin {gather*} -\frac {3 \, x e}{x e^{5} \log \relax (x) - {\left (3 \, e^{5} \log \relax (2) + 5 \, e^{4}\right )} x - e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.09, size = 20, normalized size = 0.91 \begin {gather*} \frac {3\,{\mathrm {e}}^{-4}}{5\,{\mathrm {e}}^{-1}+\ln \left (\frac {8}{x}\right )+\frac {1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 19, normalized size = 0.86 \begin {gather*} \frac {3}{e^{4} \log {\left (\frac {8 e^{\frac {1}{x}}}{x} \right )} + 5 e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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