Optimal. Leaf size=8 \[ \frac{b^3 x}{d^3} \]
[Out]
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Rubi [A] time = 0.00696827, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{b^3 x}{d^3} \]
Antiderivative was successfully verified.
[In] Int[((b*c)/d + b*x)^3/(c + d*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 4.00453, size = 7, normalized size = 0.88 \[ \frac{b^{3} x}{d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*c/d+b*x)**3/(d*x+c)**3,x)
[Out]
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Mathematica [A] time = 0.00057373, size = 8, normalized size = 1. \[ \frac{b^3 x}{d^3} \]
Antiderivative was successfully verified.
[In] Integrate[((b*c)/d + b*x)^3/(c + d*x)^3,x]
[Out]
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Maple [A] time = 0., size = 9, normalized size = 1.1 \[{\frac{{b}^{3}x}{{d}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*c/d+b*x)^3/(d*x+c)^3,x)
[Out]
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Maxima [A] time = 1.35011, size = 11, normalized size = 1.38 \[ \frac{b^{3} x}{d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + b*c/d)^3/(d*x + c)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19321, size = 11, normalized size = 1.38 \[ \frac{b^{3} x}{d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + b*c/d)^3/(d*x + c)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.201996, size = 7, normalized size = 0.88 \[ \frac{b^{3} x}{d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c/d+b*x)**3/(d*x+c)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207654, size = 11, normalized size = 1.38 \[ \frac{b^{3} x}{d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + b*c/d)^3/(d*x + c)^3,x, algorithm="giac")
[Out]