Optimal. Leaf size=46 \[ \frac{a^3}{b^4 (a+b x)}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{2 a x}{b^3}+\frac{x^2}{2 b^2} \]
[Out]
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Rubi [A] time = 0.0582561, antiderivative size = 46, 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 \[ \frac{a^3}{b^4 (a+b x)}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{2 a x}{b^3}+\frac{x^2}{2 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{3}}{b^{4} \left (a + b x\right )} + \frac{3 a^{2} \log{\left (a + b x \right )}}{b^{4}} - \frac{2 a x}{b^{3}} + \frac{\int x\, dx}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.0268376, size = 43, normalized size = 0.93 \[ \frac{\frac{2 a^3}{a+b x}+6 a^2 \log (a+b x)-4 a b x+b^2 x^2}{2 b^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 45, normalized size = 1. \[ -2\,{\frac{ax}{{b}^{3}}}+{\frac{{x}^{2}}{2\,{b}^{2}}}+{\frac{{a}^{3}}{{b}^{4} \left ( bx+a \right ) }}+3\,{\frac{{a}^{2}\ln \left ( bx+a \right ) }{{b}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.35873, size = 63, normalized size = 1.37 \[ \frac{a^{3}}{b^{5} x + a b^{4}} + \frac{3 \, a^{2} \log \left (b x + a\right )}{b^{4}} + \frac{b x^{2} - 4 \, a x}{2 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191224, size = 84, normalized size = 1.83 \[ \frac{b^{3} x^{3} - 3 \, a b^{2} x^{2} - 4 \, a^{2} b x + 2 \, a^{3} + 6 \,{\left (a^{2} b x + a^{3}\right )} \log \left (b x + a\right )}{2 \,{\left (b^{5} x + a b^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.31883, size = 44, normalized size = 0.96 \[ \frac{a^{3}}{a b^{4} + b^{5} x} + \frac{3 a^{2} \log{\left (a + b x \right )}}{b^{4}} - \frac{2 a x}{b^{3}} + \frac{x^{2}}{2 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211341, size = 89, normalized size = 1.93 \[ -\frac{{\left (b x + a\right )}^{2}{\left (\frac{6 \, a}{b x + a} - 1\right )}}{2 \, b^{4}} - \frac{3 \, a^{2}{\rm ln}\left (\frac{{\left | b x + a \right |}}{{\left (b x + a\right )}^{2}{\left | b \right |}}\right )}{b^{4}} + \frac{a^{3}}{{\left (b x + a\right )} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^2,x, algorithm="giac")
[Out]