Optimal. Leaf size=19 \[ e^{\frac {5 x^2}{5-\frac {-5+x}{x^4}}} \]
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Rubi [A]
time = 0.40, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 4, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.066, Rules used = {1608, 6820, 12,
6838} \begin {gather*} e^{\frac {5 x^6}{5 x^4-x+5}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1608
Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {5 x^6}{5-x+5 x^4}} x^5 \left (150-25 x+50 x^4\right )}{25-10 x+x^2+50 x^4-10 x^5+25 x^8} \, dx\\ &=\int \frac {25 e^{\frac {5 x^6}{5-x+5 x^4}} x^5 \left (6-x+2 x^4\right )}{\left (5-x+5 x^4\right )^2} \, dx\\ &=25 \int \frac {e^{\frac {5 x^6}{5-x+5 x^4}} x^5 \left (6-x+2 x^4\right )}{\left (5-x+5 x^4\right )^2} \, dx\\ &=e^{\frac {5 x^6}{5-x+5 x^4}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {5 x^6}{5-x+5 x^4}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 19, normalized size = 1.00
method | result | size |
gosper | \({\mathrm e}^{\frac {5 x^{6}}{5 x^{4}-x +5}}\) | \(19\) |
risch | \({\mathrm e}^{\frac {5 x^{6}}{5 x^{4}-x +5}}\) | \(19\) |
norman | \(\frac {-x \,{\mathrm e}^{\frac {5 x^{6}}{5 x^{4}-x +5}}+5 x^{4} {\mathrm e}^{\frac {5 x^{6}}{5 x^{4}-x +5}}+5 \,{\mathrm e}^{\frac {5 x^{6}}{5 x^{4}-x +5}}}{5 x^{4}-x +5}\) | \(79\) |
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. 38 vs.
\(2 (17) = 34\).
time = 0.34, size = 38, normalized size = 2.00 \begin {gather*} e^{\left (x^{2} + \frac {x^{3}}{5 \, x^{4} - x + 5} - \frac {5 \, x^{2}}{5 \, x^{4} - x + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (\frac {5 \, x^{6}}{5 \, x^{4} - x + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 14, normalized size = 0.74 \begin {gather*} e^{\frac {5 x^{6}}{5 x^{4} - x + 5}} \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 (\frac {5 \, x^{6}}{5 \, x^{4} - x + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.25, size = 18, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^{\frac {5\,x^6}{5\,x^4-x+5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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