Optimal. Leaf size=16 \[ -\frac{2}{3 d (c+d x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0072233, antiderivative size = 16, 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 \[ -\frac{2}{3 d (c+d x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^(-5/2),x]
[Out]
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Rubi in Sympy [A] time = 1.29436, size = 14, normalized size = 0.88 \[ - \frac{2}{3 d \left (c + d x\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(d*x+c)**(5/2),x)
[Out]
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Mathematica [A] time = 0.00546563, size = 16, normalized size = 1. \[ -\frac{2}{3 d (c+d x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^(-5/2),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{2}{3\,d} \left ( dx+c \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(d*x+c)^(5/2),x)
[Out]
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Maxima [A] time = 1.34382, size = 16, normalized size = 1. \[ -\frac{2}{3 \,{\left (d x + c\right )}^{\frac{3}{2}} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20619, size = 27, normalized size = 1.69 \[ -\frac{2}{3 \,{\left (d^{2} x + c d\right )} \sqrt{d x + c}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.046771, size = 14, normalized size = 0.88 \[ - \frac{2}{3 d \left (c + d x\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(d*x+c)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220043, size = 16, normalized size = 1. \[ -\frac{2}{3 \,{\left (d x + c\right )}^{\frac{3}{2}} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-5/2),x, algorithm="giac")
[Out]