Optimal. Leaf size=29 \[ \left (5+e^{4 e^4+3 (2-x) x}\right )^2+e^5 x (1+x) \]
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Rubi [A] time = 0.04, antiderivative size = 49, normalized size of antiderivative = 1.69, number of steps used = 3, number of rules used = 1, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2236} \begin {gather*} e^{-6 x^2+12 x+8 e^4}+10 e^{-3 x^2+6 x+4 e^4}+\frac {1}{4} e^5 (2 x+1)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 2236
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} e^5 (1+2 x)^2+\int e^{4 e^4+6 x-3 x^2} (60-60 x) \, dx+\int e^{8 e^4+12 x-6 x^2} (12-12 x) \, dx\\ &=e^{8 e^4+12 x-6 x^2}+10 e^{4 e^4+6 x-3 x^2}+\frac {1}{4} e^5 (1+2 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 47, normalized size = 1.62 \begin {gather*} e^{8 e^4+12 x-6 x^2}+10 e^{4 e^4+6 x-3 x^2}+e^5 x+e^5 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 39, normalized size = 1.34 \begin {gather*} {\left (x^{2} + x\right )} e^{5} + 10 \, e^{\left (-3 \, x^{2} + 6 \, x + 4 \, e^{4}\right )} + e^{\left (-6 \, x^{2} + 12 \, x + 8 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 39, normalized size = 1.34 \begin {gather*} {\left (x^{2} + x\right )} e^{5} + 10 \, e^{\left (-3 \, x^{2} + 6 \, x + 4 \, e^{4}\right )} + e^{\left (-6 \, x^{2} + 12 \, x + 8 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 40, normalized size = 1.38
method | result | size |
default | \(10 \,{\mathrm e}^{4 \,{\mathrm e}^{4}-3 x^{2}+6 x}+{\mathrm e}^{8 \,{\mathrm e}^{4}-6 x^{2}+12 x}+{\mathrm e}^{5} \left (x^{2}+x \right )\) | \(40\) |
risch | \({\mathrm e}^{8 \,{\mathrm e}^{4}-6 x^{2}+12 x}+x \,{\mathrm e}^{5}+x^{2} {\mathrm e}^{5}+10 \,{\mathrm e}^{4 \,{\mathrm e}^{4}-3 x^{2}+6 x}\) | \(42\) |
norman | \({\mathrm e}^{8 \,{\mathrm e}^{4}-6 x^{2}+12 x}+x \,{\mathrm e}^{5}+x^{2} {\mathrm e}^{5}+10 \,{\mathrm e}^{4 \,{\mathrm e}^{4}-3 x^{2}+6 x}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 39, normalized size = 1.34 \begin {gather*} {\left (x^{2} + x\right )} e^{5} + 10 \, e^{\left (-3 \, x^{2} + 6 \, x + 4 \, e^{4}\right )} + e^{\left (-6 \, x^{2} + 12 \, x + 8 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 41, normalized size = 1.41 \begin {gather*} 10\,{\mathrm {e}}^{-3\,x^2+6\,x+4\,{\mathrm {e}}^4}+{\mathrm {e}}^{-6\,x^2+12\,x+8\,{\mathrm {e}}^4}+x\,{\mathrm {e}}^5+x^2\,{\mathrm {e}}^5 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 42, normalized size = 1.45 \begin {gather*} x^{2} e^{5} + x e^{5} + e^{- 6 x^{2} + 12 x + 8 e^{4}} + 10 e^{- 3 x^{2} + 6 x + 4 e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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