Optimal. Leaf size=15 \[ \frac{1}{2 b (a-b x)^2} \]
[Out]
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Rubi [A] time = 0.0189244, antiderivative size = 15, 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 \[ \frac{1}{2 b (a-b x)^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^3/(a^2 - b^2*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 4.50872, size = 10, normalized size = 0.67 \[ \frac{1}{2 b \left (a - b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3/(-b**2*x**2+a**2)**3,x)
[Out]
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Mathematica [A] time = 0.00268562, size = 15, normalized size = 1. \[ \frac{1}{2 b (a-b x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^3/(a^2 - b^2*x^2)^3,x]
[Out]
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Maple [A] time = 0.001, size = 15, normalized size = 1. \[{\frac{1}{2\,b \left ( bx-a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3/(-b^2*x^2+a^2)^3,x)
[Out]
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Maxima [A] time = 0.6794, size = 32, normalized size = 2.13 \[ \frac{1}{2 \,{\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^3/(b^2*x^2 - a^2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.196722, size = 32, normalized size = 2.13 \[ \frac{1}{2 \,{\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^3/(b^2*x^2 - a^2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.3628, size = 24, normalized size = 1.6 \[ \frac{1}{2 a^{2} b - 4 a b^{2} x + 2 b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3/(-b**2*x**2+a**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.21706, size = 19, normalized size = 1.27 \[ \frac{1}{2 \,{\left (b x - a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^3/(b^2*x^2 - a^2)^3,x, algorithm="giac")
[Out]