Optimal. Leaf size=41 \[ -\frac{a^2}{2 b^3 (a+b x)^2}+\frac{2 a}{b^3 (a+b x)}+\frac{\log (a+b x)}{b^3} \]
[Out]
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Rubi [A] time = 0.0480858, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^2}{2 b^3 (a+b x)^2}+\frac{2 a}{b^3 (a+b x)}+\frac{\log (a+b x)}{b^3} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 8.8587, size = 36, normalized size = 0.88 \[ - \frac{a^{2}}{2 b^{3} \left (a + b x\right )^{2}} + \frac{2 a}{b^{3} \left (a + b x\right )} + \frac{\log{\left (a + b x \right )}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x+a)**3,x)
[Out]
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Mathematica [A] time = 0.0262066, size = 33, normalized size = 0.8 \[ \frac{\frac{a (3 a+4 b x)}{(a+b x)^2}+2 \log (a+b x)}{2 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b*x)^3,x]
[Out]
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Maple [A] time = 0.009, size = 40, normalized size = 1. \[ -{\frac{{a}^{2}}{2\,{b}^{3} \left ( bx+a \right ) ^{2}}}+2\,{\frac{a}{{b}^{3} \left ( bx+a \right ) }}+{\frac{\ln \left ( bx+a \right ) }{{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x+a)^3,x)
[Out]
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Maxima [A] time = 1.33496, size = 65, normalized size = 1.59 \[ \frac{4 \, a b x + 3 \, a^{2}}{2 \,{\left (b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right )}} + \frac{\log \left (b x + a\right )}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208947, size = 82, normalized size = 2. \[ \frac{4 \, a b x + 3 \, a^{2} + 2 \,{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )} \log \left (b x + a\right )}{2 \,{\left (b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.38224, size = 46, normalized size = 1.12 \[ \frac{3 a^{2} + 4 a b x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{\log{\left (a + b x \right )}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210155, size = 50, normalized size = 1.22 \[ \frac{{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{3}} + \frac{4 \, a x + \frac{3 \, a^{2}}{b}}{2 \,{\left (b x + a\right )}^{2} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^3,x, algorithm="giac")
[Out]