Optimal. Leaf size=17 \[ -\frac{c}{2 b \left (a+b x^2\right )} \]
[Out]
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Rubi [A] time = 0.0131958, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ -\frac{c}{2 b \left (a+b x^2\right )} \]
Antiderivative was successfully verified.
[In] Int[(x*(a*c + b*c*x^2))/(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 4.76808, size = 12, normalized size = 0.71 \[ - \frac{c}{2 b \left (a + b x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*c*x**2+a*c)/(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.00378476, size = 17, normalized size = 1. \[ -\frac{c}{2 b \left (a+b x^2\right )} \]
Antiderivative was successfully verified.
[In] Integrate[(x*(a*c + b*c*x^2))/(a + b*x^2)^3,x]
[Out]
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \[ -{\frac{c}{2\,b \left ( b{x}^{2}+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*c*x^2+a*c)/(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.34255, size = 22, normalized size = 1.29 \[ -\frac{c}{2 \,{\left (b^{2} x^{2} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)*x/(b*x^2 + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211298, size = 22, normalized size = 1.29 \[ -\frac{c}{2 \,{\left (b^{2} x^{2} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)*x/(b*x^2 + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.29719, size = 15, normalized size = 0.88 \[ - \frac{c}{2 a b + 2 b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*c*x**2+a*c)/(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.230283, size = 20, normalized size = 1.18 \[ -\frac{c}{2 \,{\left (b x^{2} + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)*x/(b*x^2 + a)^3,x, algorithm="giac")
[Out]