Optimal. Leaf size=10 \[ \frac{\log (c+d x)}{d} \]
[Out]
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Rubi [A] time = 0.0245865, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074 \[ \frac{\log (c+d x)}{d} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/(a*c + (b*c + a*d)*x + b*d*x^2),x]
[Out]
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Rubi in Sympy [A] time = 6.42447, size = 7, normalized size = 0.7 \[ \frac{\log{\left (c + d x \right )}}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2),x)
[Out]
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Mathematica [A] time = 0.0018559, size = 10, normalized size = 1. \[ \frac{\log (c+d x)}{d} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/(a*c + (b*c + a*d)*x + b*d*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 11, normalized size = 1.1 \[{\frac{\ln \left ( dx+c \right ) }{d}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/(a*c+(a*d+b*c)*x+x^2*b*d),x)
[Out]
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Maxima [A] time = 0.749165, size = 14, normalized size = 1.4 \[ \frac{\log \left (d x + c\right )}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(b*d*x^2 + a*c + (b*c + a*d)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198618, size = 14, normalized size = 1.4 \[ \frac{\log \left (d x + c\right )}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(b*d*x^2 + a*c + (b*c + a*d)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.125263, size = 7, normalized size = 0.7 \[ \frac{\log{\left (c + d x \right )}}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.21201, size = 15, normalized size = 1.5 \[ \frac{{\rm ln}\left ({\left | d x + c \right |}\right )}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(b*d*x^2 + a*c + (b*c + a*d)*x),x, algorithm="giac")
[Out]