Optimal. Leaf size=37 \[ \frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.045395, 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 \[ \frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{1089 \log{\left (- 2 x + 1 \right )}}{49} - \frac{\log{\left (3 x + 2 \right )}}{441} + \int \frac{125}{12}\, dx + \frac{1331}{56 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**2/(2+3*x),x)
[Out]
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Mathematica [A] time = 0.0401771, size = 37, normalized size = 1. \[ \frac{12250 (3 x+2)+\frac{83853}{1-2 x}+78408 \log (3-6 x)-8 \log (3 x+2)}{3528} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)),x]
[Out]
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Maple [A] time = 0.011, size = 30, normalized size = 0.8 \[{\frac{125\,x}{12}}-{\frac{\ln \left ( 2+3\,x \right ) }{441}}-{\frac{1331}{-56+112\,x}}+{\frac{1089\,\ln \left ( -1+2\,x \right ) }{49}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^2/(2+3*x),x)
[Out]
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Maxima [A] time = 1.35868, size = 39, normalized size = 1.05 \[ \frac{125}{12} \, x - \frac{1331}{56 \,{\left (2 \, x - 1\right )}} - \frac{1}{441} \, \log \left (3 \, x + 2\right ) + \frac{1089}{49} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213624, size = 61, normalized size = 1.65 \[ \frac{73500 \, x^{2} - 8 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) + 78408 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 36750 \, x - 83853}{3528 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.317975, size = 29, normalized size = 0.78 \[ \frac{125 x}{12} + \frac{1089 \log{\left (x - \frac{1}{2} \right )}}{49} - \frac{\log{\left (x + \frac{2}{3} \right )}}{441} - \frac{1331}{112 x - 56} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)**2/(2+3*x),x)
[Out]
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GIAC/XCAS [A] time = 0.205266, size = 63, normalized size = 1.7 \[ \frac{125}{12} \, x - \frac{1331}{56 \,{\left (2 \, x - 1\right )}} - \frac{200}{9} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{1}{441} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) - \frac{125}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)*(2*x - 1)^2),x, algorithm="giac")
[Out]