Optimal. Leaf size=28 \[ -\frac {1}{x^4}+x+e^{\frac {1}{5} \left (x+\frac {x}{1+4 x}\right )} x^2 \]
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Rubi [F]
time = 0.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A]
time = 0.06, size = 30, normalized size = 1.07 \begin {gather*} \frac {-1+x^5+e^{\frac {2 x (1+2 x)}{5+20 x}} x^6}{x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 28, normalized size = 1.00
method | result | size |
risch | \(x -\frac {1}{x^{4}}+x^{2} {\mathrm e}^{\frac {2 \left (2 x +1\right ) x}{5 \left (4 x +1\right )}}\) | \(28\) |
norman | \(\frac {\left (x^{6}+x^{5} {\mathrm e}^{\frac {-4 x^{2}-2 x}{20 x +5}}+4 x^{7}-4 x \,{\mathrm e}^{\frac {-4 x^{2}-2 x}{20 x +5}}+4 x^{6} {\mathrm e}^{\frac {-4 x^{2}-2 x}{20 x +5}}-{\mathrm e}^{\frac {-4 x^{2}-2 x}{20 x +5}}\right ) {\mathrm e}^{-\frac {-4 x^{2}-2 x}{20 x +5}}}{x^{4} \left (4 x +1\right )}\) | \(127\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 105 vs.
\(2 (26) = 52\).
time = 0.34, size = 105, normalized size = 3.75 \begin {gather*} x^{2} e^{\left (\frac {1}{5} \, x - \frac {1}{20 \, {\left (4 \, x + 1\right )}} + \frac {1}{20}\right )} + x + \frac {15360 \, x^{4} + 1920 \, x^{3} - 160 \, x^{2} + 20 \, x - 3}{3 \, {\left (4 \, x^{5} + x^{4}\right )}} - \frac {32 \, {\left (768 \, x^{3} + 96 \, x^{2} - 8 \, x + 1\right )}}{3 \, {\left (4 \, x^{4} + x^{3}\right )}} + \frac {32 \, {\left (96 \, x^{2} + 12 \, x - 1\right )}}{4 \, x^{3} + x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 30, normalized size = 1.07 \begin {gather*} \frac {x^{6} e^{\left (\frac {2 \, {\left (2 \, x^{2} + x\right )}}{5 \, {\left (4 \, x + 1\right )}}\right )} + x^{5} - 1}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 26, normalized size = 0.93 \begin {gather*} x^{2} e^{- \frac {- 4 x^{2} - 2 x}{20 x + 5}} + x - \frac {1}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 30, normalized size = 1.07 \begin {gather*} \frac {x^{6} e^{\left (\frac {2 \, {\left (2 \, x^{2} + x\right )}}{5 \, {\left (4 \, x + 1\right )}}\right )} + x^{5} - 1}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.26, size = 35, normalized size = 1.25 \begin {gather*} x-\frac {1}{x^4}+x^2\,{\mathrm {e}}^{\frac {4\,x^2}{20\,x+5}}\,{\mathrm {e}}^{\frac {2\,x}{20\,x+5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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