Optimal. Leaf size=22 \[ e^{5+x^3-\frac {x}{\log \left (e^{e^{6 x}} x\right )}} \]
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Rubi [A] time = 1.36, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 87, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6688, 6706} \begin {gather*} e^{x^3-\frac {x}{\log \left (e^{e^{6 x}} x\right )}+5} \end {gather*}
Antiderivative was successfully verified.
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Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{5+x^3-\frac {x}{\log \left (e^{e^{6 x}} x\right )}} \left (1+6 e^{6 x} x-\log \left (e^{e^{6 x}} x\right )+3 x^2 \log ^2\left (e^{e^{6 x}} x\right )\right )}{\log ^2\left (e^{e^{6 x}} x\right )} \, dx\\ &=e^{5+x^3-\frac {x}{\log \left (e^{e^{6 x}} x\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.01, size = 22, normalized size = 1.00 \begin {gather*} e^{5+x^3-\frac {x}{\log \left (e^{e^{6 x}} x\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 30, normalized size = 1.36 \begin {gather*} e^{\left (\frac {{\left (x^{3} + 5\right )} \log \left (x e^{\left (e^{\left (6 \, x\right )}\right )}\right ) - x}{\log \left (x e^{\left (e^{\left (6 \, x\right )}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.55, size = 19, normalized size = 0.86 \begin {gather*} e^{\left (x^{3} - \frac {x}{\log \left (x e^{\left (e^{\left (6 \, x\right )}\right )}\right )} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.57, size = 334, normalized size = 15.18
method | result | size |
risch | \({\mathrm e}^{\frac {-i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{3} x^{3}+i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{2} \mathrm {csgn}\left (i x \right ) x^{3}+i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{6 x}}\right ) x^{3}-i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{6 x}}\right ) x^{3}-5 i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{3}+5 i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{2} \mathrm {csgn}\left (i x \right )+5 i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{6 x}}\right )-5 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{6 x}}\right )+2 x^{3} \ln \relax (x )+2 \ln \left ({\mathrm e}^{{\mathrm e}^{6 x}}\right ) x^{3}+10 \ln \relax (x )+10 \ln \left ({\mathrm e}^{{\mathrm e}^{6 x}}\right )-2 x}{-i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{3}+i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{2} \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{6 x}}\right )-i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{{\mathrm e}^{6 x}}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{6 x}}\right )+2 \ln \relax (x )+2 \ln \left ({\mathrm e}^{{\mathrm e}^{6 x}}\right )}}\) | \(334\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 18, normalized size = 0.82 \begin {gather*} e^{\left (x^{3} - \frac {x}{e^{\left (6 \, x\right )} + \log \relax (x)} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.38, size = 65, normalized size = 2.95 \begin {gather*} x^{\frac {x^3+5}{{\mathrm {e}}^{6\,x}+\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {x}{{\mathrm {e}}^{6\,x}+\ln \relax (x)}}\,{\mathrm {e}}^{\frac {x^3\,{\mathrm {e}}^{6\,x}}{{\mathrm {e}}^{6\,x}+\ln \relax (x)}}\,{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^{6\,x}}{{\mathrm {e}}^{6\,x}+\ln \relax (x)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] 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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