Optimal. Leaf size=17 \[ -\frac{b^2}{5 d^3 (a+b x)^5} \]
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Rubi [A] time = 0.0107054, 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 \[ -\frac{b^2}{5 d^3 (a+b x)^5} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^3*((a*d)/b + d*x)^3),x]
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Rubi in Sympy [A] time = 4.50113, size = 15, normalized size = 0.88 \[ - \frac{b^{2}}{5 d^{3} \left (a + b x\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**3/(a*d/b+d*x)**3,x)
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Mathematica [A] time = 0.00959981, size = 17, normalized size = 1. \[ -\frac{b^2}{5 d^3 (a+b x)^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^3*((a*d)/b + d*x)^3),x]
[Out]
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \[ -{\frac{{b}^{2}}{5\,{d}^{3} \left ( bx+a \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^3/(a*d/b+d*x)^3,x)
[Out]
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Maxima [A] time = 1.34774, size = 101, normalized size = 5.94 \[ -\frac{b^{2}}{5 \,{\left (b^{5} d^{3} x^{5} + 5 \, a b^{4} d^{3} x^{4} + 10 \, a^{2} b^{3} d^{3} x^{3} + 10 \, a^{3} b^{2} d^{3} x^{2} + 5 \, a^{4} b d^{3} x + a^{5} d^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^3*(d*x + a*d/b)^3),x, algorithm="maxima")
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Fricas [A] time = 0.194533, size = 101, normalized size = 5.94 \[ -\frac{b^{2}}{5 \,{\left (b^{5} d^{3} x^{5} + 5 \, a b^{4} d^{3} x^{4} + 10 \, a^{2} b^{3} d^{3} x^{3} + 10 \, a^{3} b^{2} d^{3} x^{2} + 5 \, a^{4} b d^{3} x + a^{5} d^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^3*(d*x + a*d/b)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.14561, size = 83, normalized size = 4.88 \[ - \frac{b^{3}}{5 a^{5} b d^{3} + 25 a^{4} b^{2} d^{3} x + 50 a^{3} b^{3} d^{3} x^{2} + 50 a^{2} b^{4} d^{3} x^{3} + 25 a b^{5} d^{3} x^{4} + 5 b^{6} d^{3} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**3/(a*d/b+d*x)**3,x)
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GIAC/XCAS [A] time = 0.213264, size = 20, normalized size = 1.18 \[ -\frac{b^{2}}{5 \,{\left (b x + a\right )}^{5} d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^3*(d*x + a*d/b)^3),x, algorithm="giac")
[Out]