Optimal. Leaf size=16 \[ -10. e^{-0.1 x} x-100. e^{-0.1 x} \]
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Rubi [A] time = 0.0075144, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {2176, 2194} \[ -10. e^{-0.1 x} x-100. e^{-0.1 x} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{-0.1 x} x \, dx &=-10. e^{-0.1 x} x+10. \int e^{-0.1 x} \, dx\\ &=-100. e^{-0.1 x}-10. e^{-0.1 x} x\\ \end{align*}
Mathematica [A] time = 0.0049634, size = 11, normalized size = 0.69 \[ e^{-0.1 x} (-10. x-100.) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.6 \begin{align*} - 10.0\, \left ( x+ 10.0 \right ){{\rm e}^{- 0.1000000000\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04478, size = 12, normalized size = 0.75 \begin{align*} -10 \,{\left (x + 10\right )} e^{\left (-\frac{1}{10} \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090221, size = 10, normalized size = 0.62 \begin{align*} 1.0 \left (- 10.0 x - 100.0\right ) e^{- 0.1 x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21675, size = 14, normalized size = 0.88 \begin{align*}{\left (-10.0 \, x - 100.0\right )} e^{\left (-0.1 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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