Optimal. Leaf size=14 \[ -\frac{2}{d \sqrt{c+d x}} \]
[Out]
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Rubi [A] time = 0.00708826, 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 \[ -\frac{2}{d \sqrt{c+d x}} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.35269, size = 12, normalized size = 0.86 \[ - \frac{2}{d \sqrt{c + d x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(d*x+c)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00438601, size = 14, normalized size = 1. \[ -\frac{2}{d \sqrt{c+d x}} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^(-3/2),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.9 \[ -2\,{\frac{1}{d\sqrt{dx+c}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(d*x+c)^(3/2),x)
[Out]
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Maxima [A] time = 1.34711, size = 16, normalized size = 1.14 \[ -\frac{2}{\sqrt{d x + c} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206818, size = 16, normalized size = 1.14 \[ -\frac{2}{\sqrt{d x + c} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.039206, size = 12, normalized size = 0.86 \[ - \frac{2}{d \sqrt{c + d x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(d*x+c)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21695, size = 16, normalized size = 1.14 \[ -\frac{2}{\sqrt{d x + c} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-3/2),x, algorithm="giac")
[Out]