Optimal. Leaf size=19 \[ e^{2+e^x+x+x^3 (4+4 x \log (x))} \]
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Rubi [A]
time = 0.46, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps
used = 1, number of rules used = 1, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6838}
\begin {gather*} e^{4 x^3+x+e^x+2} x^{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{2+e^x+x+4 x^3} x^{4 x^4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.19, size = 21, normalized size = 1.11 \begin {gather*} e^{2+e^x+x+4 x^3} x^{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 19, normalized size = 1.00
method | result | size |
derivativedivides | \({\mathrm e}^{4 x^{4} \ln \left (x \right )+{\mathrm e}^{x}+4 x^{3}+x +2}\) | \(19\) |
default | \({\mathrm e}^{4 x^{4} \ln \left (x \right )+{\mathrm e}^{x}+4 x^{3}+x +2}\) | \(19\) |
risch | \(x^{4 x^{4}} {\mathrm e}^{2+{\mathrm e}^{x}+4 x^{3}+x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (4 \, x^{4} \log \left (x\right ) + 4 \, x^{3} + x + e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (4 \, x^{4} \log \left (x\right ) + 4 \, x^{3} + x + e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 20, normalized size = 1.05 \begin {gather*} e^{4 x^{4} \log {\left (x \right )} + 4 x^{3} + x + e^{x} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (4 \, x^{4} \log \left (x\right ) + 4 \, x^{3} + x + e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.08, size = 21, normalized size = 1.11 \begin {gather*} x^{4\,x^4}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{4\,x^3}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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