Optimal. Leaf size=16 \[ -\frac{1}{5 b \left (a+b x^5\right )} \]
[Out]
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Rubi [A] time = 0.00987596, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{5 b \left (a+b x^5\right )} \]
Antiderivative was successfully verified.
[In] Int[x^4/(a + b*x^5)^2,x]
[Out]
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Rubi in Sympy [A] time = 2.11381, size = 12, normalized size = 0.75 \[ - \frac{1}{5 b \left (a + b x^{5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(b*x**5+a)**2,x)
[Out]
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Mathematica [A] time = 0.00786806, size = 16, normalized size = 1. \[ -\frac{1}{5 b \left (a+b x^5\right )} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(a + b*x^5)^2,x]
[Out]
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Maple [A] time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{5\,b \left ( b{x}^{5}+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(b*x^5+a)^2,x)
[Out]
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Maxima [A] time = 1.43769, size = 19, normalized size = 1.19 \[ -\frac{1}{5 \,{\left (b x^{5} + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^5 + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219039, size = 20, normalized size = 1.25 \[ -\frac{1}{5 \,{\left (b^{2} x^{5} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^5 + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.19796, size = 15, normalized size = 0.94 \[ - \frac{1}{5 a b + 5 b^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(b*x**5+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.227402, size = 19, normalized size = 1.19 \[ -\frac{1}{5 \,{\left (b x^{5} + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^5 + a)^2,x, algorithm="giac")
[Out]