Optimal. Leaf size=33 \[ \frac{a}{5 b^2 \left (a+b x^5\right )}+\frac{\log \left (a+b x^5\right )}{5 b^2} \]
[Out]
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Rubi [A] time = 0.0593079, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a}{5 b^2 \left (a+b x^5\right )}+\frac{\log \left (a+b x^5\right )}{5 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^9/(a + b*x^5)^2,x]
[Out]
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Rubi in Sympy [A] time = 7.77699, size = 26, normalized size = 0.79 \[ \frac{a}{5 b^{2} \left (a + b x^{5}\right )} + \frac{\log{\left (a + b x^{5} \right )}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(b*x**5+a)**2,x)
[Out]
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Mathematica [A] time = 0.0155022, size = 27, normalized size = 0.82 \[ \frac{\frac{a}{a+b x^5}+\log \left (a+b x^5\right )}{5 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(a + b*x^5)^2,x]
[Out]
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Maple [A] time = 0.007, size = 30, normalized size = 0.9 \[{\frac{a}{5\,{b}^{2} \left ( b{x}^{5}+a \right ) }}+{\frac{\ln \left ( b{x}^{5}+a \right ) }{5\,{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(b*x^5+a)^2,x)
[Out]
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Maxima [A] time = 1.42643, size = 43, normalized size = 1.3 \[ \frac{a}{5 \,{\left (b^{3} x^{5} + a b^{2}\right )}} + \frac{\log \left (b x^{5} + a\right )}{5 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^5 + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216524, size = 47, normalized size = 1.42 \[ \frac{{\left (b x^{5} + a\right )} \log \left (b x^{5} + a\right ) + a}{5 \,{\left (b^{3} x^{5} + a b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^5 + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.54323, size = 29, normalized size = 0.88 \[ \frac{a}{5 a b^{2} + 5 b^{3} x^{5}} + \frac{\log{\left (a + b x^{5} \right )}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(b*x**5+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.231069, size = 65, normalized size = 1.97 \[ -\frac{\frac{{\rm ln}\left (\frac{{\left | b x^{5} + a \right |}}{{\left (b x^{5} + a\right )}^{2}{\left | b \right |}}\right )}{b} - \frac{a}{{\left (b x^{5} + a\right )} b}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^5 + a)^2,x, algorithm="giac")
[Out]