Optimal. Leaf size=16 \[ -e^{-x} x-e^{-x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0068846, 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} \[ -e^{-x} x-e^{-x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{-x} x \, dx &=-e^{-x} x+\int e^{-x} \, dx\\ &=-e^{-x}-e^{-x} x\\ \end{align*}
Mathematica [A] time = 0.0041336, size = 11, normalized size = 0.69 \[ e^{-x} (-x-1) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 10, normalized size = 0.6 \begin{align*} -{\frac{1+x}{{{\rm e}^{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.951513, size = 12, normalized size = 0.75 \begin{align*} -{\left (x + 1\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.516459, size = 23, normalized size = 1.44 \begin{align*} -{\left (x + 1\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.080846, size = 7, normalized size = 0.44 \begin{align*} \left (- x - 1\right ) e^{- x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08864, size = 12, normalized size = 0.75 \begin{align*} -{\left (x + 1\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]