Optimal. Leaf size=12 \[ \frac{1}{b (a-b x)} \]
[Out]
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Rubi [A] time = 0.0177434, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{b (a-b x)} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2/(a^2 - b^2*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 4.47588, size = 7, normalized size = 0.58 \[ \frac{1}{b \left (a - b x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2/(-b**2*x**2+a**2)**2,x)
[Out]
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Mathematica [A] time = 0.00386891, size = 12, normalized size = 1. \[ \frac{1}{b (a-b x)} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2/(a^2 - b^2*x^2)^2,x]
[Out]
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Maple [A] time = 0.002, size = 15, normalized size = 1.3 \[ -{\frac{1}{b \left ( bx-a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2/(-b^2*x^2+a^2)^2,x)
[Out]
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Maxima [A] time = 0.684583, size = 19, normalized size = 1.58 \[ -\frac{1}{b^{2} x - a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/(b^2*x^2 - a^2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203691, size = 19, normalized size = 1.58 \[ -\frac{1}{b^{2} x - a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/(b^2*x^2 - a^2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.21084, 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((b*x+a)**2/(-b**2*x**2+a**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.215095, size = 19, normalized size = 1.58 \[ -\frac{1}{{\left (b x - a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/(b^2*x^2 - a^2)^2,x, algorithm="giac")
[Out]