Optimal. Leaf size=46 \[ -e^{-x} x^4-4 e^{-x} x^3-12 e^{-x} x^2-24 e^{-x} x-24 e^{-x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0403911, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2176, 2194} \[ -e^{-x} x^4-4 e^{-x} x^3-12 e^{-x} x^2-24 e^{-x} x-24 e^{-x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{-x} x^4 \, dx &=-e^{-x} x^4+4 \int e^{-x} x^3 \, dx\\ &=-4 e^{-x} x^3-e^{-x} x^4+12 \int e^{-x} x^2 \, dx\\ &=-12 e^{-x} x^2-4 e^{-x} x^3-e^{-x} x^4+24 \int e^{-x} x \, dx\\ &=-24 e^{-x} x-12 e^{-x} x^2-4 e^{-x} x^3-e^{-x} x^4+24 \int e^{-x} \, dx\\ &=-24 e^{-x}-24 e^{-x} x-12 e^{-x} x^2-4 e^{-x} x^3-e^{-x} x^4\\ \end{align*}
Mathematica [A] time = 0.0072785, size = 26, normalized size = 0.57 \[ e^{-x} \left (-x^4-4 x^3-12 x^2-24 x-24\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 25, normalized size = 0.5 \begin{align*} -{\frac{{x}^{4}+4\,{x}^{3}+12\,{x}^{2}+24\,x+24}{{{\rm e}^{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.924995, size = 32, normalized size = 0.7 \begin{align*} -{\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 24 \, x + 24\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.96542, size = 59, normalized size = 1.28 \begin{align*} -{\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 24 \, x + 24\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.082029, size = 22, normalized size = 0.48 \begin{align*} \left (- x^{4} - 4 x^{3} - 12 x^{2} - 24 x - 24\right ) e^{- x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05508, size = 32, normalized size = 0.7 \begin{align*} -{\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 24 \, x + 24\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]