Optimal. Leaf size=17 \[ -\frac{b^2}{3 d^3 (a+b x)^3} \]
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Rubi [A] time = 0.0110823, 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 \[ -\frac{b^2}{3 d^3 (a+b x)^3} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)*((a*d)/b + d*x)^3),x]
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Rubi in Sympy [A] time = 4.40689, size = 15, normalized size = 0.88 \[ - \frac{b^{2}}{3 d^{3} \left (a + b x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)/(a*d/b+d*x)**3,x)
[Out]
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Mathematica [A] time = 0.00754392, size = 17, normalized size = 1. \[ -\frac{b^2}{3 d^3 (a+b x)^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)*((a*d)/b + d*x)^3),x]
[Out]
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Maple [A] time = 0., size = 16, normalized size = 0.9 \[ -{\frac{{b}^{2}}{3\,{d}^{3} \left ( bx+a \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)/(a*d/b+d*x)^3,x)
[Out]
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Maxima [A] time = 1.34058, size = 63, normalized size = 3.71 \[ -\frac{b^{2}}{3 \,{\left (b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + a*d/b)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199678, size = 63, normalized size = 3.71 \[ -\frac{b^{2}}{3 \,{\left (b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + a*d/b)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.65115, size = 53, normalized size = 3.12 \[ - \frac{b^{3}}{3 a^{3} b d^{3} + 9 a^{2} b^{2} d^{3} x + 9 a b^{3} d^{3} x^{2} + 3 b^{4} d^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)/(a*d/b+d*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210949, size = 20, normalized size = 1.18 \[ -\frac{b^{2}}{3 \,{\left (b x + a\right )}^{3} d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + a*d/b)^3),x, algorithm="giac")
[Out]