Optimal. Leaf size=14 \[ -\frac{2}{b \sqrt{a+b x}} \]
[Out]
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Rubi [A] time = 0.00670844, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{2}{b \sqrt{a+b x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.28241, size = 12, normalized size = 0.86 \[ - \frac{2}{b \sqrt{a + b x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00421834, size = 14, normalized size = 1. \[ -\frac{2}{b \sqrt{a+b x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^(-3/2),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.9 \[ -2\,{\frac{1}{b\sqrt{bx+a}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.3345, size = 16, normalized size = 1.14 \[ -\frac{2}{\sqrt{b x + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216789, size = 16, normalized size = 1.14 \[ -\frac{2}{\sqrt{b x + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.077346, size = 12, normalized size = 0.86 \[ - \frac{2}{b \sqrt{a + b x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.204708, size = 16, normalized size = 1.14 \[ -\frac{2}{\sqrt{b x + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-3/2),x, algorithm="giac")
[Out]