Optimal. Leaf size=27 \[ -\frac{2 a c}{b (a+b x)}-\frac{c \log (a+b x)}{b} \]
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Rubi [A] time = 0.0338715, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{2 a c}{b (a+b x)}-\frac{c \log (a+b x)}{b} \]
Antiderivative was successfully verified.
[In] Int[(a*c - b*c*x)/(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 8.59556, size = 22, normalized size = 0.81 \[ - \frac{2 a c}{b \left (a + b x\right )} - \frac{c \log{\left (a + b x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*c*x+a*c)/(b*x+a)**2,x)
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Mathematica [A] time = 0.0143324, size = 23, normalized size = 0.85 \[ -\frac{c \left (\frac{2 a}{a+b x}+\log (a+b x)\right )}{b} \]
Antiderivative was successfully verified.
[In] Integrate[(a*c - b*c*x)/(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 28, normalized size = 1. \[ -2\,{\frac{ac}{b \left ( bx+a \right ) }}-{\frac{c\ln \left ( bx+a \right ) }{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*c*x+a*c)/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.35452, size = 38, normalized size = 1.41 \[ -\frac{2 \, a c}{b^{2} x + a b} - \frac{c \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)/(b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199769, size = 45, normalized size = 1.67 \[ -\frac{2 \, a c +{\left (b c x + a c\right )} \log \left (b x + a\right )}{b^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)/(b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.28021, size = 24, normalized size = 0.89 \[ - \frac{2 a c}{a b + b^{2} x} - \frac{c \log{\left (a + b x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*c*x+a*c)/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.206808, size = 73, normalized size = 2.7 \[ c{\left (\frac{{\rm ln}\left (\frac{{\left | b x + a \right |}}{{\left (b x + a\right )}^{2}{\left | b \right |}}\right )}{b} - \frac{a}{{\left (b x + a\right )} b}\right )} - \frac{a c}{{\left (b x + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)/(b*x + a)^2,x, algorithm="giac")
[Out]