3.74 \(\int e^x x \, dx\)

Optimal. Leaf size=11 \[ e^x x-e^x \]

[Out]

-E^x + E^x*x

_______________________________________________________________________________________

Rubi [A]  time = 0.0104852, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4 \[ e^x x-e^x \]

Antiderivative was successfully verified.

[In]  Int[E^x*x,x]

[Out]

-E^x + E^x*x

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 0.926222, size = 7, normalized size = 0.64 \[ x e^{x} - e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x)*x,x)

[Out]

x*exp(x) - exp(x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00151928, size = 7, normalized size = 0.64 \[ e^x (x-1) \]

Antiderivative was successfully verified.

[In]  Integrate[E^x*x,x]

[Out]

E^x*(-1 + x)

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 7, normalized size = 0.6 \[ \left ( -1+x \right ){{\rm e}^{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x)*x,x)

[Out]

(-1+x)*exp(x)

_______________________________________________________________________________________

Maxima [A]  time = 1.37359, size = 8, normalized size = 0.73 \[{\left (x - 1\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^x,x, algorithm="maxima")

[Out]

(x - 1)*e^x

_______________________________________________________________________________________

Fricas [A]  time = 0.198197, size = 8, normalized size = 0.73 \[{\left (x - 1\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^x,x, algorithm="fricas")

[Out]

(x - 1)*e^x

_______________________________________________________________________________________

Sympy [A]  time = 0.057101, size = 5, normalized size = 0.45 \[ \left (x - 1\right ) e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x)*x,x)

[Out]

(x - 1)*exp(x)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.220094, size = 8, normalized size = 0.73 \[{\left (x - 1\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^x,x, algorithm="giac")

[Out]

(x - 1)*e^x