Optimal. Leaf size=12 \[ 4+3 e^{-x}-x \]
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Rubi [A] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2248, 43} \begin {gather*} 3 e^{-x}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 2248
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {-3-x}{x^2} \, dx,x,e^x\right )\\ &=\operatorname {Subst}\left (\int \left (-\frac {3}{x^2}-\frac {1}{x}\right ) \, dx,x,e^x\right )\\ &=3 e^{-x}-x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} 3 e^{-x}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 12, normalized size = 1.00 \begin {gather*} -{\left (x e^{x} - 3\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 10, normalized size = 0.83 \begin {gather*} -x + 3 \, e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 11, normalized size = 0.92
method | result | size |
risch | \(-x +3 \,{\mathrm e}^{-x}\) | \(11\) |
derivativedivides | \(-\ln \left ({\mathrm e}^{x}\right )+3 \,{\mathrm e}^{-x}\) | \(13\) |
default | \(-\ln \left ({\mathrm e}^{x}\right )+3 \,{\mathrm e}^{-x}\) | \(13\) |
norman | \(\left (-{\mathrm e}^{x} x +3\right ) {\mathrm e}^{-x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 10, normalized size = 0.83 \begin {gather*} -x + 3 \, e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 10, normalized size = 0.83 \begin {gather*} 3\,{\mathrm {e}}^{-x}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.42 \begin {gather*} - x + 3 e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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