Optimal. Leaf size=22 \[ e^{3 x+2 x \left (x-\frac {x^4}{16}\right )}+x^2 \]
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Rubi [A] time = 0.05, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 3, number of rules used = 2, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {12, 6706} \begin {gather*} x^2+e^{\frac {1}{8} \left (-x^5+16 x^2+24 x\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \left (16 x+e^{\frac {1}{8} \left (24 x+16 x^2-x^5\right )} \left (24+32 x-5 x^4\right )\right ) \, dx\\ &=x^2+\frac {1}{8} \int e^{\frac {1}{8} \left (24 x+16 x^2-x^5\right )} \left (24+32 x-5 x^4\right ) \, dx\\ &=e^{\frac {1}{8} \left (24 x+16 x^2-x^5\right )}+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 22, normalized size = 1.00 \begin {gather*} e^{3 x+2 x^2-\frac {x^5}{8}}+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 19, normalized size = 0.86 \begin {gather*} x^{2} + e^{\left (-\frac {1}{8} \, x^{5} + 2 \, x^{2} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 19, normalized size = 0.86 \begin {gather*} x^{2} + e^{\left (-\frac {1}{8} \, x^{5} + 2 \, x^{2} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.77
method | result | size |
risch | \(x^{2}+{\mathrm e}^{-\frac {x \left (x^{4}-16 x -24\right )}{8}}\) | \(17\) |
default | \(x^{2}+{\mathrm e}^{-\frac {1}{8} x^{5}+2 x^{2}+3 x}\) | \(20\) |
norman | \(x^{2}+{\mathrm e}^{-\frac {1}{8} x^{5}+2 x^{2}+3 x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 19, normalized size = 0.86 \begin {gather*} x^{2} + e^{\left (-\frac {1}{8} \, x^{5} + 2 \, x^{2} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.18, size = 19, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{-\frac {x^5}{8}+2\,x^2+3\,x}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 17, normalized size = 0.77 \begin {gather*} x^{2} + e^{- \frac {x^{5}}{8} + 2 x^{2} + 3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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