Optimal. Leaf size=22 \[ \left (6+e^{\frac {5}{4}+\left (1-x-x^2\right )^2}\right ) x \]
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Rubi [B] time = 0.11, antiderivative size = 61, normalized size of antiderivative = 2.77, number of steps used = 2, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2288} \begin {gather*} \frac {e^{\frac {1}{4} \left (4 x^4+8 x^3-4 x^2-8 x+9\right )} \left (-2 x^4-3 x^3+x^2+x\right )}{-2 x^3-3 x^2+x+1}+6 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=6 x+\int e^{\frac {1}{4} \left (9-8 x-4 x^2+8 x^3+4 x^4\right )} \left (1-2 x-2 x^2+6 x^3+4 x^4\right ) \, dx\\ &=6 x+\frac {e^{\frac {1}{4} \left (9-8 x-4 x^2+8 x^3+4 x^4\right )} \left (x+x^2-3 x^3-2 x^4\right )}{1+x-3 x^2-2 x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 24, normalized size = 1.09 \begin {gather*} \left (6+e^{\frac {9}{4}+2 x^3+x^4-x (2+x)}\right ) x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 25, normalized size = 1.14 \begin {gather*} x e^{\left (x^{4} + 2 \, x^{3} - x^{2} - 2 \, x + \frac {9}{4}\right )} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 25, normalized size = 1.14 \begin {gather*} x e^{\left (x^{4} + 2 \, x^{3} - x^{2} - 2 \, x + \frac {9}{4}\right )} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 26, normalized size = 1.18
method | result | size |
default | \(6 x +{\mathrm e}^{x^{4}+2 x^{3}-x^{2}-2 x +\frac {9}{4}} x\) | \(26\) |
norman | \(6 x +{\mathrm e}^{x^{4}+2 x^{3}-x^{2}-2 x +\frac {9}{4}} x\) | \(26\) |
risch | \(6 x +{\mathrm e}^{x^{4}+2 x^{3}-x^{2}-2 x +\frac {9}{4}} x\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.89, size = 25, normalized size = 1.14 \begin {gather*} x e^{\left (x^{4} + 2 \, x^{3} - x^{2} - 2 \, x + \frac {9}{4}\right )} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 27, normalized size = 1.23 \begin {gather*} x\,\left ({\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{9/4}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{2\,x^3}+6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 24, normalized size = 1.09 \begin {gather*} x e^{x^{4} + 2 x^{3} - x^{2} - 2 x + \frac {9}{4}} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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