3.673 \(\int e^x \left (-5 x+x^2\right ) \, dx\)

Optimal. Leaf size=19 \[ e^x x^2-7 e^x x+7 e^x \]

[Out]

7*E^x - 7*E^x*x + E^x*x^2

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Rubi [A]  time = 0.0618329, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.364 \[ e^x x^2-7 e^x x+7 e^x \]

Antiderivative was successfully verified.

[In]  Int[E^x*(-5*x + x^2),x]

[Out]

7*E^x - 7*E^x*x + E^x*x^2

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Rubi in Sympy [A]  time = 6.88675, size = 17, normalized size = 0.89 \[ x^{2} e^{x} - 7 x e^{x} + 7 e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x)*(x**2-5*x),x)

[Out]

x**2*exp(x) - 7*x*exp(x) + 7*exp(x)

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Mathematica [A]  time = 0.00369516, size = 12, normalized size = 0.63 \[ e^x \left (x^2-7 x+7\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[E^x*(-5*x + x^2),x]

[Out]

E^x*(7 - 7*x + x^2)

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Maple [A]  time = 0.004, size = 12, normalized size = 0.6 \[{{\rm e}^{x}} \left ({x}^{2}-7\,x+7 \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x)*(x^2-5*x),x)

[Out]

exp(x)*(x^2-7*x+7)

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Maxima [A]  time = 0.771672, size = 26, normalized size = 1.37 \[{\left (x^{2} - 2 \, x + 2\right )} e^{x} - 5 \,{\left (x - 1\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 5*x)*e^x,x, algorithm="maxima")

[Out]

(x^2 - 2*x + 2)*e^x - 5*(x - 1)*e^x

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Fricas [A]  time = 0.229057, size = 15, normalized size = 0.79 \[{\left (x^{2} - 7 \, x + 7\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 5*x)*e^x,x, algorithm="fricas")

[Out]

(x^2 - 7*x + 7)*e^x

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Sympy [A]  time = 0.066902, size = 10, normalized size = 0.53 \[ \left (x^{2} - 7 x + 7\right ) e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x)*(x**2-5*x),x)

[Out]

(x**2 - 7*x + 7)*exp(x)

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GIAC/XCAS [A]  time = 0.257759, size = 15, normalized size = 0.79 \[{\left (x^{2} - 7 \, x + 7\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 5*x)*e^x,x, algorithm="giac")

[Out]

(x^2 - 7*x + 7)*e^x