Optimal. Leaf size=24 \[ 5 \left (e^{-2+x}+12 e^{5-(8+x)^2}-x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.04, number of steps
used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {2225, 2268}
\begin {gather*} 60 e^{-x^2-16 x-59}-5 x+5 e^{x-2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2268
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-5 x+5 \int e^{-2+x} \, dx+\int e^{-59-16 x-x^2} (-960-120 x) \, dx\\ &=5 e^{-2+x}+60 e^{-59-16 x-x^2}-5 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 25, normalized size = 1.04 \begin {gather*} 5 \left (e^{-2+x}+12 e^{-59-16 x-x^2}-x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 24, normalized size = 1.00
method | result | size |
default | \(-5 x +60 \,{\mathrm e}^{-x^{2}-16 x -59}+5 \,{\mathrm e}^{x -2}\) | \(24\) |
norman | \(-5 x +60 \,{\mathrm e}^{-x^{2}-16 x -59}+5 \,{\mathrm e}^{x -2}\) | \(24\) |
risch | \(-5 x +60 \,{\mathrm e}^{-x^{2}-16 x -59}+5 \,{\mathrm e}^{x -2}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 23, normalized size = 0.96 \begin {gather*} -5 \, x + 60 \, e^{\left (-x^{2} - 16 \, x - 59\right )} + 5 \, e^{\left (x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 23, normalized size = 0.96 \begin {gather*} -5 \, x + 60 \, e^{\left (-x^{2} - 16 \, x - 59\right )} + 5 \, e^{\left (x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 22, normalized size = 0.92 \begin {gather*} - 5 x + 5 e^{x - 2} + 60 e^{- x^{2} - 16 x - 59} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 23, normalized size = 0.96 \begin {gather*} -5 \, x + 60 \, e^{\left (-x^{2} - 16 \, x - 59\right )} + 5 \, e^{\left (x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 24, normalized size = 1.00 \begin {gather*} 5\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^x-5\,x+60\,{\mathrm {e}}^{-16\,x}\,{\mathrm {e}}^{-59}\,{\mathrm {e}}^{-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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