Optimal. Leaf size=13 \[ d \log \left (a+b x+c x^2\right ) \]
[Out]
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Rubi [A] time = 0.0135273, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ d \log \left (a+b x+c x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(b*d + 2*c*d*x)/(a + b*x + c*x^2),x]
[Out]
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Rubi in Sympy [A] time = 4.81599, size = 12, normalized size = 0.92 \[ d \log{\left (a + b x + c x^{2} \right )} \]
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),x)
[Out]
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Mathematica [A] time = 0.00380972, size = 12, normalized size = 0.92 \[ d \log (a+x (b+c x)) \]
Antiderivative was successfully verified.
[In] Integrate[(b*d + 2*c*d*x)/(a + b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 14, normalized size = 1.1 \[ d\ln \left ( c{x}^{2}+bx+a \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*d*x+b*d)/(c*x^2+b*x+a),x)
[Out]
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Maxima [A] time = 0.699025, size = 18, normalized size = 1.38 \[ d \log \left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)/(c*x^2 + b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204295, size = 18, normalized size = 1.38 \[ d \log \left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)/(c*x^2 + b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.33729, size = 12, normalized size = 0.92 \[ d \log{\left (a + b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x+b*d)/(c*x**2+b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.215676, size = 18, normalized size = 1.38 \[ d{\rm ln}\left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)/(c*x^2 + b*x + a),x, algorithm="giac")
[Out]