Optimal. Leaf size=19 \[ \frac{x^4}{4 b \left (a x^2+b\right )^2} \]
[Out]
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Rubi [A] time = 0.0171456, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x^4}{4 b \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
[In] Int[(b/x + a*x)^(-3),x]
[Out]
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Rubi in Sympy [A] time = 3.52927, size = 14, normalized size = 0.74 \[ \frac{x^{4}}{4 b \left (a x^{2} + b\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x+a*x)**3,x)
[Out]
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Mathematica [A] time = 0.0146395, size = 24, normalized size = 1.26 \[ -\frac{2 a x^2+b}{4 a^2 \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x + a*x)^(-3),x]
[Out]
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Maple [A] time = 0.007, size = 31, normalized size = 1.6 \[ -{\frac{1}{ \left ( 2\,a{x}^{2}+2\,b \right ){a}^{2}}}+{\frac{b}{4\,{a}^{2} \left ( a{x}^{2}+b \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x+a*x)^3,x)
[Out]
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Maxima [A] time = 1.37528, size = 49, normalized size = 2.58 \[ -\frac{2 \, a x^{2} + b}{4 \,{\left (a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b/x)^(-3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205972, size = 49, normalized size = 2.58 \[ -\frac{2 \, a x^{2} + b}{4 \,{\left (a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b/x)^(-3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.64192, size = 36, normalized size = 1.89 \[ - \frac{2 a x^{2} + b}{4 a^{4} x^{4} + 8 a^{3} b x^{2} + 4 a^{2} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x+a*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.21962, size = 30, normalized size = 1.58 \[ -\frac{2 \, a x^{2} + b}{4 \,{\left (a x^{2} + b\right )}^{2} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b/x)^(-3),x, algorithm="giac")
[Out]