Optimal. Leaf size=14 \[ -\frac{1}{2 b (a+b x)^2} \]
[Out]
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Rubi [A] time = 0.00692411, antiderivative size = 14, 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 \[ -\frac{1}{2 b (a+b x)^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(-3),x]
[Out]
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Rubi in Sympy [A] time = 1.26706, size = 12, normalized size = 0.86 \[ - \frac{1}{2 b \left (a + b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**3,x)
[Out]
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Mathematica [A] time = 0.00333774, size = 14, normalized size = 1. \[ -\frac{1}{2 b (a+b x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^(-3),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[ -{\frac{1}{2\,b \left ( bx+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^3,x)
[Out]
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Maxima [A] time = 1.48088, size = 16, normalized size = 1.14 \[ -\frac{1}{2 \,{\left (b x + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206673, size = 32, normalized size = 2.29 \[ -\frac{1}{2 \,{\left (b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.30741, size = 26, normalized size = 1.86 \[ - \frac{1}{2 a^{2} b + 4 a b^{2} x + 2 b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.22274, size = 16, normalized size = 1.14 \[ -\frac{1}{2 \,{\left (b x + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-3),x, algorithm="giac")
[Out]