Optimal. Leaf size=24 \[ \frac {3}{25}-e^{-3+(-4+2 x)^2}+3 (5-x) \]
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Rubi [A]
time = 0.09, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps
used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6820, 2268}
\begin {gather*} -e^{4 x^2-16 x+13}-3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2268
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3-8 e^{13-16 x+4 x^2} (-2+x)\right ) \, dx\\ &=-3 x-8 \int e^{13-16 x+4 x^2} (-2+x) \, dx\\ &=-e^{13-16 x+4 x^2}-3 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 18, normalized size = 0.75 \begin {gather*} -e^{13-16 x+4 x^2}-3 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 18, normalized size = 0.75
method | result | size |
default | \(-3 x -{\mathrm e}^{4 x^{2}-16 x +13}\) | \(18\) |
risch | \(-3 x -{\mathrm e}^{4 x^{2}-16 x +13}\) | \(18\) |
norman | \(\left (-1-3 x \,{\mathrm e}^{-4 x^{2}+16 x -13}\right ) {\mathrm e}^{4 x^{2}-16 x +13}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.51, size = 61, normalized size = 2.54 \begin {gather*} -4 i \, \sqrt {\pi } \operatorname {erf}\left (2 i \, x - 4 i\right ) e^{\left (-3\right )} - {\left (\frac {4 \, \sqrt {\pi } {\left (x - 2\right )} {\left (\operatorname {erf}\left (2 \, \sqrt {-{\left (x - 2\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (x - 2\right )}^{2}}} + e^{\left (4 \, {\left (x - 2\right )}^{2}\right )}\right )} e^{\left (-3\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 17, normalized size = 0.71 \begin {gather*} -3 \, x - e^{\left (4 \, x^{2} - 16 \, x + 13\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.62 \begin {gather*} - 3 x - e^{4 x^{2} - 16 x + 13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.71 \begin {gather*} -3 \, x - e^{\left (4 \, x^{2} - 16 \, x + 13\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 18, normalized size = 0.75 \begin {gather*} -3\,x-{\mathrm {e}}^{-16\,x}\,{\mathrm {e}}^{13}\,{\mathrm {e}}^{4\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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