Optimal. Leaf size=44 \[ -\frac{a^3 \log (a+b x)}{b^4}+\frac{a^2 x}{b^3}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b} \]
[Out]
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Rubi [A] time = 0.0535095, antiderivative size = 44, 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 \[ -\frac{a^3 \log (a+b x)}{b^4}+\frac{a^2 x}{b^3}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a*x^2 + b*x^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3} \log{\left (a + b x \right )}}{b^{4}} - \frac{a \int x\, dx}{b^{2}} + \frac{x^{3}}{3 b} + \frac{\int a^{2}\, dx}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**3+a*x**2),x)
[Out]
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Mathematica [A] time = 0.00554499, size = 44, normalized size = 1. \[ -\frac{a^3 \log (a+b x)}{b^4}+\frac{a^2 x}{b^3}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a*x^2 + b*x^3),x]
[Out]
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Maple [A] time = 0.005, size = 41, normalized size = 0.9 \[{\frac{{a}^{2}x}{{b}^{3}}}-{\frac{a{x}^{2}}{2\,{b}^{2}}}+{\frac{{x}^{3}}{3\,b}}-{\frac{{a}^{3}\ln \left ( bx+a \right ) }{{b}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^3+a*x^2),x)
[Out]
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Maxima [A] time = 1.3788, size = 57, normalized size = 1.3 \[ -\frac{a^{3} \log \left (b x + a\right )}{b^{4}} + \frac{2 \, b^{2} x^{3} - 3 \, a b x^{2} + 6 \, a^{2} x}{6 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206827, size = 55, normalized size = 1.25 \[ \frac{2 \, b^{3} x^{3} - 3 \, a b^{2} x^{2} + 6 \, a^{2} b x - 6 \, a^{3} \log \left (b x + a\right )}{6 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.13482, size = 37, normalized size = 0.84 \[ - \frac{a^{3} \log{\left (a + b x \right )}}{b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{3}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**3+a*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.21741, size = 58, normalized size = 1.32 \[ -\frac{a^{3}{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{4}} + \frac{2 \, b^{2} x^{3} - 3 \, a b x^{2} + 6 \, a^{2} x}{6 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a*x^2),x, algorithm="giac")
[Out]