Optimal. Leaf size=34 \[ \frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0439829, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{91 \log{\left (3 x + 2 \right )}}{27} + \int \left (- \frac{104}{27}\right )\, dx + \frac{20 \int x\, dx}{9} + \frac{49}{81 \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)/(2+3*x)**2,x)
[Out]
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Mathematica [A] time = 0.0187308, size = 39, normalized size = 1.15 \[ \frac{540 x^3-1512 x^2-447 x+546 (3 x+2) \log (6 x+4)+632}{162 (3 x+2)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 27, normalized size = 0.8 \[ -{\frac{104\,x}{27}}+{\frac{10\,{x}^{2}}{9}}+{\frac{49}{162+243\,x}}+{\frac{91\,\ln \left ( 2+3\,x \right ) }{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)/(2+3*x)^2,x)
[Out]
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Maxima [A] time = 1.34506, size = 35, normalized size = 1.03 \[ \frac{10}{9} \, x^{2} - \frac{104}{27} \, x + \frac{49}{81 \,{\left (3 \, x + 2\right )}} + \frac{91}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224534, size = 50, normalized size = 1.47 \[ \frac{270 \, x^{3} - 756 \, x^{2} + 273 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 624 \, x + 49}{81 \,{\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.20732, size = 27, normalized size = 0.79 \[ \frac{10 x^{2}}{9} - \frac{104 x}{27} + \frac{91 \log{\left (3 x + 2 \right )}}{27} + \frac{49}{243 x + 162} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)/(2+3*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211585, size = 65, normalized size = 1.91 \[ -\frac{2}{81} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{72}{3 \, x + 2} - 5\right )} + \frac{49}{81 \,{\left (3 \, x + 2\right )}} - \frac{91}{27} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^2,x, algorithm="giac")
[Out]