Optimal. Leaf size=15 \[ e^{e^{5-4 e^3 \log (16 x)}} \]
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Rubi [A]
time = 0.21, antiderivative size = 20, normalized size of antiderivative = 1.33, number of steps
used = 4, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 2306, 6838}
\begin {gather*} e^{16^{-4 e^3} e^5 x^{-4 e^3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2306
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (4 \int \frac {e^{8+e^{5-4 e^3 \log (16 x)}-4 e^3 \log (16 x)}}{x} \, dx\right )\\ &=-\left (4 \int 16^{-4 e^3} e^{8+e^{5-4 e^3 \log (16 x)}} x^{-1-4 e^3} \, dx\right )\\ &=-\left (4^{1-8 e^3} \int e^{8+e^{5-4 e^3 \log (16 x)}} x^{-1-4 e^3} \, dx\right )\\ &=e^{16^{-4 e^3} e^5 x^{-4 e^3}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.22, size = 15, normalized size = 1.00 \begin {gather*} e^{e^{5-4 e^3 \log (16 x)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.72, size = 13, normalized size = 0.87
method | result | size |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{-4 \,{\mathrm e}^{3} \ln \left (16 x \right )+5}}\) | \(13\) |
default | \({\mathrm e}^{{\mathrm e}^{-4 \,{\mathrm e}^{3} \ln \left (16 x \right )+5}}\) | \(13\) |
norman | \({\mathrm e}^{{\mathrm e}^{-4 \,{\mathrm e}^{3} \ln \left (16 x \right )+5}}\) | \(13\) |
risch | \({\mathrm e}^{\left (16 x \right )^{-4 \,{\mathrm e}^{3}} {\mathrm e}^{5}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.80 \begin {gather*} e^{\left (e^{\left (-4 \, e^{3} \log \left (16 \, x\right ) + 5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 12, normalized size = 0.80 \begin {gather*} e^{\left (e^{\left (-4 \, e^{3} \log \left (16 \, x\right ) + 5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.49, size = 15, normalized size = 1.00 \begin {gather*} e^{\frac {e^{5}}{65536^{e^{3}} x^{4 e^{3}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 12, normalized size = 0.80 \begin {gather*} e^{\left (e^{\left (-4 \, e^{3} \log \left (16 \, x\right ) + 5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.27, size = 20, normalized size = 1.33 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^5}{2^{16\,{\mathrm {e}}^3}\,x^{4\,{\mathrm {e}}^3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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