Optimal. Leaf size=11 \[ \text{ExpIntegralEi}\left (a+b x+c x^2\right ) \]
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Rubi [A] time = 0.266157, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.065 \[ \text{ExpIntegralEi}\left (a+b x+c x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2),x]
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Rubi in Sympy [A] time = 79.4201, size = 10, normalized size = 0.91 \[ \operatorname{Ei}{\left (a + b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(c*x**2+b*x+a)*(2*c*x+b)/(c*x**2+b*x+a),x)
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Mathematica [A] time = 0.008948, size = 10, normalized size = 0.91 \[ \text{ExpIntegralEi}(a+x (b+c x)) \]
Antiderivative was successfully verified.
[In] Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.008, size = 19, normalized size = 1.7 \[ -{\it Ei} \left ( 1,-c{x}^{2}-bx-a \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(c*x^2+b*x+a)*(2*c*x+b)/(c*x^2+b*x+a),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (2 \, c x + b\right )} e^{\left (c x^{2} + b x + a\right )}}{c x^{2} + b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*e^(c*x^2 + b*x + a)/(c*x^2 + b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232682, size = 15, normalized size = 1.36 \[{\rm Ei}\left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*e^(c*x^2 + b*x + a)/(c*x^2 + b*x + a),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(c*x**2+b*x+a)*(2*c*x+b)/(c*x**2+b*x+a),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (2 \, c x + b\right )} e^{\left (c x^{2} + b x + a\right )}}{c x^{2} + b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*e^(c*x^2 + b*x + a)/(c*x^2 + b*x + a),x, algorithm="giac")
[Out]