Optimal. Leaf size=4 \[ c \log (x) \]
[Out]
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Rubi [A] time = 0.00530692, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.087 \[ c \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a*c + b*c*x^2)/(x*(a + b*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 3.59288, size = 3, normalized size = 0.75 \[ c \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*c*x**2+a*c)/x/(b*x**2+a),x)
[Out]
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Mathematica [A] time = 0.000593888, size = 4, normalized size = 1. \[ c \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a*c + b*c*x^2)/(x*(a + b*x^2)),x]
[Out]
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Maple [A] time = 0.002, size = 5, normalized size = 1.3 \[ c\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*c*x^2+a*c)/x/(b*x^2+a),x)
[Out]
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Maxima [A] time = 1.3403, size = 9, normalized size = 2.25 \[ \frac{1}{2} \, c \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)/((b*x^2 + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220173, size = 5, normalized size = 1.25 \[ c \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)/((b*x^2 + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.115203, size = 3, normalized size = 0.75 \[ c \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x**2+a*c)/x/(b*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.22222, size = 7, normalized size = 1.75 \[ c{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)/((b*x^2 + a)*x),x, algorithm="giac")
[Out]