Optimal. Leaf size=27 \[ e^{x-e^4 (-5+x \log (2))} x^{\frac {1-x}{x^2}} \]
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Rubi [A]
time = 0.23, antiderivative size = 31, normalized size of antiderivative = 1.15, number of steps
used = 3, number of rules used = 3, integrand size = 74, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6820, 2325,
2326} \begin {gather*} x^{\frac {1}{x^2}-\frac {1}{x}} e^{x \left (1-e^4 \log (2)\right )+5 e^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 2325
Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 2^{-e^4 x} e^{5 e^4+x} x^{-3+\frac {1}{x^2}-\frac {1}{x}} \left (1-x-x^3 \left (-1+e^4 \log (2)\right )+(-2+x) \log (x)\right ) \, dx\\ &=\int e^{5 e^4+x \left (1-e^4 \log (2)\right )} x^{-3+\frac {1}{x^2}-\frac {1}{x}} \left (1-x-x^3 \left (-1+e^4 \log (2)\right )+(-2+x) \log (x)\right ) \, dx\\ &=e^{5 e^4+x \left (1-e^4 \log (2)\right )} x^{\frac {1}{x^2}-\frac {1}{x}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 27, normalized size = 1.00 \begin {gather*} e^{x+e^4 (5-x \log (2))} x^{\frac {1-x}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 25, normalized size = 0.93
method | result | size |
risch | \(\left (\frac {1}{2}\right )^{x \,{\mathrm e}^{4}} {\mathrm e}^{5 \,{\mathrm e}^{4}+x} x^{-\frac {x -1}{x^{2}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.57, size = 27, normalized size = 1.00 \begin {gather*} e^{\left (-x e^{4} \log \left (2\right ) + x - \frac {\log \left (x\right )}{x} + \frac {\log \left (x\right )}{x^{2}} + 5 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 26, normalized size = 0.96 \begin {gather*} \frac {e^{\left (-x e^{4} \log \left (2\right ) + x + 5 \, e^{4}\right )}}{x^{\frac {x - 1}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 118.37, size = 27, normalized size = 1.00 \begin {gather*} e^{\frac {\left (1 - x\right ) \log {\left (x \right )}}{x^{2}}} e^{- x e^{4} \log {\left (2 \right )} + x + 5 e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.84, size = 35, normalized size = 1.30 \begin {gather*} e^{\left (-\frac {x^{3} e^{4} \log \left (2\right ) - x^{3} - 5 \, x^{2} e^{4} + x \log \left (x\right ) - \log \left (x\right )}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.94, size = 25, normalized size = 0.93 \begin {gather*} {\left (\frac {1}{2}\right )}^{x\,{\mathrm {e}}^4}\,x^{\frac {1}{x^2}-\frac {1}{x}}\,{\mathrm {e}}^{5\,{\mathrm {e}}^4}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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