Optimal. Leaf size=29 \[ -\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)} \]
[Out]
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Rubi [A] time = 0.0420813, antiderivative size = 29, 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 \[ -\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a*x^2 + b*x^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 7.6504, size = 24, normalized size = 0.83 \[ \frac{1}{a \left (a + b x\right )} + \frac{\log{\left (x \right )}}{a^{2}} - \frac{\log{\left (a + b x \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x**3+a*x**2)**2,x)
[Out]
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Mathematica [A] time = 0.0161748, size = 24, normalized size = 0.83 \[ \frac{\frac{a}{a+b x}-\log (a+b x)+\log (x)}{a^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a*x^2 + b*x^3)^2,x]
[Out]
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Maple [A] time = 0.011, size = 30, normalized size = 1. \[{\frac{1}{a \left ( bx+a \right ) }}+{\frac{\ln \left ( x \right ) }{{a}^{2}}}-{\frac{\ln \left ( bx+a \right ) }{{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x^3+a*x^2)^2,x)
[Out]
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Maxima [A] time = 1.40641, size = 38, normalized size = 1.31 \[ \frac{1}{a b x + a^{2}} - \frac{\log \left (b x + a\right )}{a^{2}} + \frac{\log \left (x\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^3 + a*x^2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212578, size = 53, normalized size = 1.83 \[ -\frac{{\left (b x + a\right )} \log \left (b x + a\right ) -{\left (b x + a\right )} \log \left (x\right ) - a}{a^{2} b x + a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^3 + a*x^2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.37572, size = 22, normalized size = 0.76 \[ \frac{1}{a^{2} + a b x} + \frac{\log{\left (x \right )} - \log{\left (\frac{a}{b} + x \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x**3+a*x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219702, size = 42, normalized size = 1.45 \[ -\frac{{\rm ln}\left ({\left | b x + a \right |}\right )}{a^{2}} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a^{2}} + \frac{1}{{\left (b x + a\right )} a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^3 + a*x^2)^2,x, algorithm="giac")
[Out]