Optimal. Leaf size=20 \[ \frac {e^{e^{255 e^6}}+x^4}{5 x} \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.20, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14} \begin {gather*} \frac {x^3}{5}+\frac {e^{e^{255 e^6}}}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-e^{e^{255 e^6}}+3 x^4}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-\frac {e^{e^{255 e^6}}}{x^2}+3 x^2\right ) \, dx\\ &=\frac {e^{e^{255 e^6}}}{5 x}+\frac {x^3}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.05 \begin {gather*} \frac {1}{5} \left (\frac {e^{e^{255 e^6}}}{x}+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 15, normalized size = 0.75 \begin {gather*} \frac {x^{4} + e^{\left (e^{\left (255 \, e^{6}\right )}\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 17, normalized size = 0.85 \begin {gather*} \frac {1}{5} \, x^{3} + \frac {e^{\left (e^{\left (255 \, e^{6}\right )}\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 18, normalized size = 0.90
method | result | size |
gosper | \(\frac {x^{4}+{\mathrm e}^{{\mathrm e}^{255 \,{\mathrm e}^{6}}}}{5 x}\) | \(18\) |
default | \(\frac {x^{3}}{5}+\frac {{\mathrm e}^{{\mathrm e}^{255 \,{\mathrm e}^{6}}}}{5 x}\) | \(18\) |
risch | \(\frac {x^{3}}{5}+\frac {{\mathrm e}^{{\mathrm e}^{255 \,{\mathrm e}^{6}}}}{5 x}\) | \(18\) |
norman | \(\frac {\frac {x^{4}}{5}+\frac {{\mathrm e}^{{\mathrm e}^{255 \,{\mathrm e}^{6}}}}{5}}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 0.85 \begin {gather*} \frac {1}{5} \, x^{3} + \frac {e^{\left (e^{\left (255 \, e^{6}\right )}\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.11, size = 15, normalized size = 0.75 \begin {gather*} \frac {x^4+{\mathrm {e}}^{{\mathrm {e}}^{255\,{\mathrm {e}}^6}}}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 15, normalized size = 0.75 \begin {gather*} \frac {x^{3}}{5} + \frac {e^{e^{255 e^{6}}}}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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