Optimal. Leaf size=17 \[ 2 d \sqrt{a+b x+c x^2} \]
[Out]
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Rubi [A] time = 0.013782, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ 2 d \sqrt{a+b x+c x^2} \]
Antiderivative was successfully verified.
[In] Int[(b*d + 2*c*d*x)/Sqrt[a + b*x + c*x^2],x]
[Out]
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Rubi in Sympy [A] time = 4.85015, size = 15, normalized size = 0.88 \[ 2 d \sqrt{a + b x + c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0200089, size = 16, normalized size = 0.94 \[ 2 d \sqrt{a+x (b+c x)} \]
Antiderivative was successfully verified.
[In] Integrate[(b*d + 2*c*d*x)/Sqrt[a + b*x + c*x^2],x]
[Out]
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Maple [A] time = 0.005, size = 16, normalized size = 0.9 \[ 2\,d\sqrt{c{x}^{2}+bx+a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.674003, size = 20, normalized size = 1.18 \[ 2 \, \sqrt{c x^{2} + b x + a} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.251782, size = 20, normalized size = 1.18 \[ 2 \, \sqrt{c x^{2} + b x + a} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.341007, size = 15, normalized size = 0.88 \[ 2 d \sqrt{a + b x + c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215587, size = 20, normalized size = 1.18 \[ 2 \, \sqrt{c x^{2} + b x + a} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a),x, algorithm="giac")
[Out]