3.46 \(\int e^x (3+2 x) \, dx\)

Optimal. Leaf size=15 \[ e^x (2 x+3)-2 e^x \]

[Out]

-2*E^x + E^x*(3 + 2*x)

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Rubi [A]  time = 0.0151646, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ e^x (2 x+3)-2 e^x \]

Antiderivative was successfully verified.

[In]  Int[E^x*(3 + 2*x),x]

[Out]

-2*E^x + E^x*(3 + 2*x)

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Rubi in Sympy [A]  time = 1.3574, size = 12, normalized size = 0.8 \[ \left (2 x + 3\right ) e^{x} - 2 e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x)*(3+2*x),x)

[Out]

(2*x + 3)*exp(x) - 2*exp(x)

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Mathematica [A]  time = 0.00281233, size = 9, normalized size = 0.6 \[ e^x (2 x+1) \]

Antiderivative was successfully verified.

[In]  Integrate[E^x*(3 + 2*x),x]

[Out]

E^x*(1 + 2*x)

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Maple [A]  time = 0.002, size = 9, normalized size = 0.6 \[ \left ( 1+2\,x \right ){{\rm e}^{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x)*(3+2*x),x)

[Out]

(1+2*x)*exp(x)

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Maxima [A]  time = 1.34867, size = 16, normalized size = 1.07 \[ 2 \,{\left (x - 1\right )} e^{x} + 3 \, e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)*e^x,x, algorithm="maxima")

[Out]

2*(x - 1)*e^x + 3*e^x

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Fricas [A]  time = 0.21919, size = 11, normalized size = 0.73 \[{\left (2 \, x + 1\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)*e^x,x, algorithm="fricas")

[Out]

(2*x + 1)*e^x

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Sympy [A]  time = 0.064496, size = 7, normalized size = 0.47 \[ \left (2 x + 1\right ) e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x)*(3+2*x),x)

[Out]

(2*x + 1)*exp(x)

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GIAC/XCAS [A]  time = 0.201512, size = 11, normalized size = 0.73 \[{\left (2 \, x + 1\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)*e^x,x, algorithm="giac")

[Out]

(2*x + 1)*e^x