Optimal. Leaf size=14 \[ e^{x+25 x \left (-4+x^2\right )^4} \]
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Rubi [A] time = 0.12, antiderivative size = 26, normalized size of antiderivative = 1.86, number of steps used = 1, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6706} \begin {gather*} e^{25 x^9-400 x^7+2400 x^5-6400 x^3+6401 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{6401 x-6400 x^3+2400 x^5-400 x^7+25 x^9}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 26, normalized size = 1.86 \begin {gather*} e^{6401 x-6400 x^3+2400 x^5-400 x^7+25 x^9} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 25, normalized size = 1.79 \begin {gather*} e^{\left (25 \, x^{9} - 400 \, x^{7} + 2400 \, x^{5} - 6400 \, x^{3} + 6401 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 25, normalized size = 1.79 \begin {gather*} e^{\left (25 \, x^{9} - 400 \, x^{7} + 2400 \, x^{5} - 6400 \, x^{3} + 6401 \, x\right )} \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 = 1.86
method | result | size |
gosper | \({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\) | \(26\) |
derivativedivides | \({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\) | \(26\) |
default | \({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\) | \(26\) |
norman | \({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\) | \(26\) |
risch | \({\mathrm e}^{x \left (25 x^{8}-400 x^{6}+2400 x^{4}-6400 x^{2}+6401\right )}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 25, normalized size = 1.79 \begin {gather*} e^{\left (25 \, x^{9} - 400 \, x^{7} + 2400 \, x^{5} - 6400 \, x^{3} + 6401 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 29, normalized size = 2.07 \begin {gather*} {\mathrm {e}}^{6401\,x}\,{\mathrm {e}}^{25\,x^9}\,{\mathrm {e}}^{-400\,x^7}\,{\mathrm {e}}^{2400\,x^5}\,{\mathrm {e}}^{-6400\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 24, normalized size = 1.71 \begin {gather*} e^{25 x^{9} - 400 x^{7} + 2400 x^{5} - 6400 x^{3} + 6401 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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