Optimal. Leaf size=18 \[ -2+x+5 \left (e^{3-\frac {9 x^4}{2500}}+x\right ) \]
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Rubi [A] time = 0.08, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 4, number of rules used = 3, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {12, 6688, 2209} \begin {gather*} 5 e^{3-\frac {9 x^4}{2500}}+6 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{125} \int e^{\frac {7500-9 x^4}{2500}} \left (750 e^{\frac {-7500+9 x^4}{2500}}-9 x^3\right ) \, dx\\ &=\frac {1}{125} \int \left (750-9 e^{3-\frac {9 x^4}{2500}} x^3\right ) \, dx\\ &=6 x-\frac {9}{125} \int e^{3-\frac {9 x^4}{2500}} x^3 \, dx\\ &=5 e^{3-\frac {9 x^4}{2500}}+6 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.94 \begin {gather*} 5 e^{3-\frac {9 x^4}{2500}}+6 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.08, size = 22, normalized size = 1.22 \begin {gather*} {\left (6 \, x e^{\left (\frac {9}{2500} \, x^{4} - 3\right )} + 5\right )} e^{\left (-\frac {9}{2500} \, x^{4} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 0.78 \begin {gather*} 6 \, x + 5 \, e^{\left (-\frac {9}{2500} \, x^{4} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 0.83
method | result | size |
risch | \(6 x +5 \,{\mathrm e}^{-\frac {9 x^{4}}{2500}+3}\) | \(15\) |
default | \(6 x +5 \,{\mathrm e}^{-\frac {9 x^{4}}{2500}} {\mathrm e}^{3}\) | \(19\) |
norman | \(\left (5+6 x \,{\mathrm e}^{\frac {9 x^{4}}{2500}-3}\right ) {\mathrm e}^{-\frac {9 x^{4}}{2500}+3}\) | \(25\) |
meijerg | \(-\frac {5 \sqrt {3}\, \sqrt {2}\, \left (-1\right )^{\frac {3}{4}} {\mathrm e}^{-\frac {9 x^{4}}{2500}+\frac {9 x^{4} {\mathrm e}^{3}}{2500}} \left (\frac {\sqrt {2}\, x \left (-1\right )^{\frac {1}{4}} \left (-{\mathrm e}^{3}+1\right )^{\frac {1}{4}} \pi }{\left (-x^{4} \left (-{\mathrm e}^{3}+1\right )\right )^{\frac {1}{4}} \Gamma \left (\frac {3}{4}\right )}-\frac {\left (-1\right )^{\frac {1}{4}} x \left (-{\mathrm e}^{3}+1\right )^{\frac {1}{4}} \Gamma \left (\frac {1}{4}, -\frac {9 x^{4} \left (-{\mathrm e}^{3}+1\right )}{2500}\right )}{\left (-x^{4} \left (-{\mathrm e}^{3}+1\right )\right )^{\frac {1}{4}}}\right )}{2 \left (-{\mathrm e}^{3}+1\right )^{\frac {1}{4}}}-5 \,{\mathrm e}^{-\frac {9 x^{4}}{2500}+\frac {9 x^{4} {\mathrm e}^{3}}{2500}} \left (1-{\mathrm e}^{-\frac {9 x^{4} {\mathrm e}^{3}}{2500}}\right )\) | \(138\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 14, normalized size = 0.78 \begin {gather*} 6 \, x + 5 \, e^{\left (-\frac {9}{2500} \, x^{4} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 14, normalized size = 0.78 \begin {gather*} 6\,x+5\,{\mathrm {e}}^{3-\frac {9\,x^4}{2500}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.78 \begin {gather*} 6 x + 5 e^{3 - \frac {9 x^{4}}{2500}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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