Optimal. Leaf size=12 \[ -\frac{1}{b (a+b x)} \]
[Out]
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Rubi [A] time = 0.00547363, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{1}{b (a+b x)} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(-2),x]
[Out]
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Rubi in Sympy [A] time = 0.638036, size = 8, normalized size = 0.67 \[ - \frac{1}{b \left (a + b x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.00382892, size = 12, normalized size = 1. \[ -\frac{1}{b (a+b x)} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^(-2),x]
[Out]
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Maple [A] time = 0., size = 13, normalized size = 1.1 \[ -{\frac{1}{b \left ( bx+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.39585, size = 16, normalized size = 1.33 \[ -\frac{1}{{\left (b x + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213944, size = 18, normalized size = 1.5 \[ -\frac{1}{b^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.51837, size = 10, normalized size = 0.83 \[ - \frac{1}{a b + b^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.202497, size = 16, normalized size = 1.33 \[ -\frac{1}{{\left (b x + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-2),x, algorithm="giac")
[Out]