Optimal. Leaf size=43 \[ \frac{201}{15125 (5 x+3)}-\frac{12}{1375 (5 x+3)^2}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (5 x+3)}{499125} \]
[Out]
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Rubi [A] time = 0.0615206, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{201}{15125 (5 x+3)}-\frac{12}{1375 (5 x+3)^2}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (5 x+3)}{499125} \]
Antiderivative was successfully verified.
[In] Int[(-x^2 + x^3)/((-6 + x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 3.97143, size = 34, normalized size = 0.79 \[ \frac{20 \log{\left (- x + 6 \right )}}{3993} + \frac{1493 \log{\left (5 x + 3 \right )}}{499125} + \frac{201}{15125 \left (5 x + 3\right )} - \frac{12}{1375 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-x**2)/(-6+x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0339592, size = 33, normalized size = 0.77 \[ \frac{\frac{99 (335 x+157)}{(5 x+3)^2}+2500 \log (x-6)+1493 \log (5 x+3)}{499125} \]
Antiderivative was successfully verified.
[In] Integrate[(-x^2 + x^3)/((-6 + x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.013, size = 34, normalized size = 0.8 \[ -{\frac{12}{1375\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{201}{45375+75625\,x}}+{\frac{1493\,\ln \left ( 3+5\,x \right ) }{499125}}+{\frac{20\,\ln \left ( -6+x \right ) }{3993}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-x^2)/(-6+x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.38515, size = 46, normalized size = 1.07 \[ \frac{3 \,{\left (335 \, x + 157\right )}}{15125 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{1493}{499125} \, \log \left (5 \, x + 3\right ) + \frac{20}{3993} \, \log \left (x - 6\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - x^2)/((5*x + 3)^3*(x - 6)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230355, size = 72, normalized size = 1.67 \[ \frac{1493 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (x - 6\right ) + 33165 \, x + 15543}{499125 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - x^2)/((5*x + 3)^3*(x - 6)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.183053, size = 32, normalized size = 0.74 \[ \frac{1005 x + 471}{378125 x^{2} + 453750 x + 136125} + \frac{20 \log{\left (x - 6 \right )}}{3993} + \frac{1493 \log{\left (x + \frac{3}{5} \right )}}{499125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-x**2)/(-6+x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.218564, size = 42, normalized size = 0.98 \[ \frac{3 \,{\left (335 \, x + 157\right )}}{15125 \,{\left (5 \, x + 3\right )}^{2}} + \frac{1493}{499125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) + \frac{20}{3993} \,{\rm ln}\left ({\left | x - 6 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - x^2)/((5*x + 3)^3*(x - 6)),x, algorithm="giac")
[Out]