Optimal. Leaf size=16 \[ -10. e^{-0.1 x} x-100. e^{-0.1 x} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 0.69 \[ e^{-0.1 x} (-10. x-100.) \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 10, normalized size = 0.62 \[ {\left (-10.0000000000000 \, x - 100.000000000000\right )} e^{\left (-0.100000000000000 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.62 \[ - 10.0 \left (x + 10.0\right ) {\mathrm e}^{- 0.1000000000 x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 9, normalized size = 0.56 \[ -10 \, {\left (x + 10\right )} e^{\left (-\frac {1}{10} \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.56 \[ -10\,{\mathrm {e}}^{-0.1\,x}\,\left (x+10.0\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.62 \[ 1.0 \left (- 10.0 x - 100.0\right ) e^{- 0.1 x} \]
Verification of antiderivative is not currently implemented for this CAS.
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