Optimal. Leaf size=23 \[ \frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2} \]
[Out]
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Rubi [A] time = 0.0397896, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a*x^2 + b*x^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 6.83493, size = 19, normalized size = 0.83 \[ \frac{a}{b^{2} \left (a + b x\right )} + \frac{\log{\left (a + b x \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**3+a*x**2)**2,x)
[Out]
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Mathematica [A] time = 0.0102577, size = 20, normalized size = 0.87 \[ \frac{\frac{a}{a+b x}+\log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a*x^2 + b*x^3)^2,x]
[Out]
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Maple [A] time = 0.01, size = 24, normalized size = 1. \[{\frac{a}{{b}^{2} \left ( bx+a \right ) }}+{\frac{\ln \left ( bx+a \right ) }{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^3+a*x^2)^2,x)
[Out]
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Maxima [A] time = 1.45213, size = 35, normalized size = 1.52 \[ \frac{a}{b^{3} x + a b^{2}} + \frac{\log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a*x^2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205626, size = 38, normalized size = 1.65 \[ \frac{{\left (b x + a\right )} \log \left (b x + a\right ) + a}{b^{3} x + a b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a*x^2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.18563, size = 20, normalized size = 0.87 \[ \frac{a}{a b^{2} + b^{3} x} + \frac{\log{\left (a + b x \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**3+a*x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217479, size = 32, normalized size = 1.39 \[ \frac{{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{2}} + \frac{a}{{\left (b x + a\right )} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a*x^2)^2,x, algorithm="giac")
[Out]