Optimal. Leaf size=15 \[ \frac {17}{16} e^{-1-80 x^2}+x \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2240}
\begin {gather*} \frac {17}{16} e^{-80 x^2-1}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x-170 \int e^{-1-80 x^2} x \, dx\\ &=\frac {17}{16} e^{-1-80 x^2}+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 15, normalized size = 1.00 \begin {gather*} \frac {17}{16} e^{-1-80 x^2}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 13, normalized size = 0.87
method | result | size |
default | \(x +\frac {17 \,{\mathrm e}^{-80 x^{2}-1}}{16}\) | \(13\) |
norman | \(x +\frac {17 \,{\mathrm e}^{-80 x^{2}-1}}{16}\) | \(13\) |
risch | \(x +\frac {17 \,{\mathrm e}^{-80 x^{2}-1}}{16}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 12, normalized size = 0.80 \begin {gather*} x + \frac {17}{16} \, e^{\left (-80 \, x^{2} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.80 \begin {gather*} x + \frac {17}{16} \, e^{\left (-80 \, x^{2} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.93 \begin {gather*} x + \frac {17 e^{- 80 x^{2} - 1}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 12, normalized size = 0.80 \begin {gather*} x + \frac {17}{16} \, e^{\left (-80 \, x^{2} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 12, normalized size = 0.80 \begin {gather*} x+\frac {17\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-80\,x^2}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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