Optimal. Leaf size=37 \[ -\frac{8 x}{75}-\frac{1331}{125 (5 x+3)}+\frac{343}{9} \log (3 x+2)-\frac{4719}{125} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0464686, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{8 x}{75}-\frac{1331}{125 (5 x+3)}+\frac{343}{9} \log (3 x+2)-\frac{4719}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{343 \log{\left (3 x + 2 \right )}}{9} - \frac{4719 \log{\left (5 x + 3 \right )}}{125} + \int \left (- \frac{8}{75}\right )\, dx - \frac{1331}{125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3/(2+3*x)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0358256, size = 36, normalized size = 0.97 \[ \frac{-120 x-\frac{11979}{5 x+3}+42875 \log (3 x+2)-42471 \log (-3 (5 x+3))-80}{1125} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.011, size = 30, normalized size = 0.8 \[ -{\frac{8\,x}{75}}-{\frac{1331}{375+625\,x}}+{\frac{343\,\ln \left ( 2+3\,x \right ) }{9}}-{\frac{4719\,\ln \left ( 3+5\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3/(2+3*x)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.32058, size = 39, normalized size = 1.05 \[ -\frac{8}{75} \, x - \frac{1331}{125 \,{\left (5 \, x + 3\right )}} - \frac{4719}{125} \, \log \left (5 \, x + 3\right ) + \frac{343}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208845, size = 61, normalized size = 1.65 \[ -\frac{600 \, x^{2} + 42471 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 42875 \,{\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 360 \, x + 11979}{1125 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.334, size = 31, normalized size = 0.84 \[ - \frac{8 x}{75} - \frac{4719 \log{\left (x + \frac{3}{5} \right )}}{125} + \frac{343 \log{\left (x + \frac{2}{3} \right )}}{9} - \frac{1331}{625 x + 375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3/(2+3*x)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217821, size = 63, normalized size = 1.7 \[ -\frac{8}{75} \, x - \frac{1331}{125 \,{\left (5 \, x + 3\right )}} - \frac{404}{1125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{343}{9} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{8}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)),x, algorithm="giac")
[Out]