Optimal. Leaf size=17 \[ -\frac{d^2}{5 b^3 (c+d x)^5} \]
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Rubi [A] time = 0.0117367, antiderivative size = 17, 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 \[ -\frac{d^2}{5 b^3 (c+d x)^5} \]
Antiderivative was successfully verified.
[In] Int[1/(((b*c)/d + b*x)^3*(c + d*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 4.731, size = 15, normalized size = 0.88 \[ - \frac{d^{2}}{5 b^{3} \left (c + d x\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*c/d+b*x)**3/(d*x+c)**3,x)
[Out]
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Mathematica [A] time = 0.00910416, size = 17, normalized size = 1. \[ -\frac{d^2}{5 b^3 (c+d x)^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/(((b*c)/d + b*x)^3*(c + d*x)^3),x]
[Out]
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \[ -{\frac{{d}^{2}}{5\,{b}^{3} \left ( dx+c \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*c/d+b*x)^3/(d*x+c)^3,x)
[Out]
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Maxima [A] time = 1.43506, size = 101, normalized size = 5.94 \[ -\frac{d^{2}}{5 \,{\left (b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + 10 \, b^{3} c^{2} d^{3} x^{3} + 10 \, b^{3} c^{3} d^{2} x^{2} + 5 \, b^{3} c^{4} d x + b^{3} c^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + b*c/d)^3*(d*x + c)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211353, size = 101, normalized size = 5.94 \[ -\frac{d^{2}}{5 \,{\left (b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + 10 \, b^{3} c^{2} d^{3} x^{3} + 10 \, b^{3} c^{3} d^{2} x^{2} + 5 \, b^{3} c^{4} d x + b^{3} c^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + b*c/d)^3*(d*x + c)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.15747, size = 83, normalized size = 4.88 \[ - \frac{d^{3}}{5 b^{3} c^{5} d + 25 b^{3} c^{4} d^{2} x + 50 b^{3} c^{3} d^{3} x^{2} + 50 b^{3} c^{2} d^{4} x^{3} + 25 b^{3} c d^{5} x^{4} + 5 b^{3} d^{6} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*c/d+b*x)**3/(d*x+c)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206191, size = 20, normalized size = 1.18 \[ -\frac{d^{2}}{5 \,{\left (d x + c\right )}^{5} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + b*c/d)^3*(d*x + c)^3),x, algorithm="giac")
[Out]