Optimal. Leaf size=12 \[ e^{a+b x+c x^2} \]
[Out]
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Rubi [A] time = 0.0278753, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ e^{a+b x+c x^2} \]
Antiderivative was successfully verified.
[In] Int[E^(a + b*x + c*x^2)*(b + 2*c*x),x]
[Out]
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Rubi in Sympy [A] time = 3.41435, size = 10, normalized size = 0.83 \[ e^{a + b x + c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(c*x**2+b*x+a)*(2*c*x+b),x)
[Out]
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Mathematica [A] time = 0.006791, size = 12, normalized size = 1. \[ e^{a+b x+c x^2} \]
Antiderivative was successfully verified.
[In] Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x),x]
[Out]
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Maple [A] time = 0.003, size = 12, normalized size = 1. \[{{\rm e}^{c{x}^{2}+bx+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(c*x^2+b*x+a)*(2*c*x+b),x)
[Out]
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Maxima [A] time = 0.786515, size = 15, normalized size = 1.25 \[ e^{\left (c x^{2} + b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*e^(c*x^2 + b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253149, size = 15, normalized size = 1.25 \[ e^{\left (c x^{2} + b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*e^(c*x^2 + b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.094107, size = 10, normalized size = 0.83 \[ e^{a + b x + c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(c*x**2+b*x+a)*(2*c*x+b),x)
[Out]
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GIAC/XCAS [A] time = 0.242233, size = 15, normalized size = 1.25 \[ e^{\left (c x^{2} + b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*e^(c*x^2 + b*x + a),x, algorithm="giac")
[Out]