Optimal. Leaf size=15 \[ e^{16 e^{-10+\frac {2 \log (x)}{x}}} \]
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Rubi [F]
time = 0.77, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right ) (32-32 \log (x))}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32 \exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right ) (1-\log (x))}{x^2} \, dx\\ &=32 \int \frac {\exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right ) (1-\log (x))}{x^2} \, dx\\ &=32 \int \left (\frac {\exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right )}{x^2}-\frac {\exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right ) \log (x)}{x^2}\right ) \, dx\\ &=32 \int \frac {\exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right )}{x^2} \, dx-32 \int \frac {\exp \left (16 e^{\frac {2 (-5 x+\log (x))}{x}}+\frac {2 (-5 x+\log (x))}{x}\right ) \log (x)}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 14, normalized size = 0.93 \begin {gather*} e^{\frac {16 x^{2/x}}{e^{10}}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 13, normalized size = 0.87
method | result | size |
risch | \({\mathrm e}^{16 x^{\frac {2}{x}} {\mathrm e}^{-10}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.41, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (16 \, e^{\left (\frac {2 \, \log \left (x\right )}{x} - 10\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 43 vs.
\(2 (13) = 26\).
time = 0.39, size = 43, normalized size = 2.87 \begin {gather*} e^{\left (\frac {2 \, {\left (8 \, x e^{\left (-\frac {2 \, {\left (5 \, x - \log \left (x\right )\right )}}{x}\right )} - 5 \, x + \log \left (x\right )\right )}}{x} + \frac {2 \, {\left (5 \, x - \log \left (x\right )\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.23, size = 14, normalized size = 0.93 \begin {gather*} e^{16 e^{\frac {2 \left (- 5 x + \log {\left (x \right )}\right )}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 43 vs.
\(2 (13) = 26\).
time = 0.44, size = 43, normalized size = 2.87 \begin {gather*} e^{\left (\frac {2 \, {\left (8 \, x e^{\left (-\frac {2 \, {\left (5 \, x - \log \left (x\right )\right )}}{x}\right )} - 5 \, x + \log \left (x\right )\right )}}{x} + \frac {2 \, {\left (5 \, x - \log \left (x\right )\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.41, size = 12, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^{16\,x^{2/x}\,{\mathrm {e}}^{-10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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