Optimal. Leaf size=15 \[ \frac {1}{e^{10}}-2 e^{-2-25 x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2209} \begin {gather*} -2 e^{-25 x^2-2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=100 \int e^{-2-25 x^2} x \, dx\\ &=-2 e^{-2-25 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.73 \begin {gather*} -2 e^{-2-25 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 10, normalized size = 0.67 \begin {gather*} -2 \, e^{\left (-25 \, x^{2} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 10, normalized size = 0.67 \begin {gather*} -2 \, e^{\left (-25 \, x^{2} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 11, normalized size = 0.73
method | result | size |
risch | \(-2 \,{\mathrm e}^{-25 x^{2}-2}\) | \(11\) |
gosper | \(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\) | \(15\) |
derivativedivides | \(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\) | \(15\) |
default | \(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\) | \(15\) |
norman | \(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\) | \(15\) |
meijerg | \(2 \,{\mathrm e}^{-2} \left (1-{\mathrm e}^{-25 x^{2}}\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 10, normalized size = 0.67 \begin {gather*} -2 \, e^{\left (-25 \, x^{2} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} -2\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{-25\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.80 \begin {gather*} - \frac {2 e^{- 25 x^{2}}}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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