Optimal. Leaf size=38 \[ \frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.046529, antiderivative size = 38, 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 \[ \frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{16 \log{\left (3 x + 2 \right )}}{9} + \int \frac{20}{27}\, dx - \frac{91}{27 \left (3 x + 2\right )} + \frac{49}{162 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)/(2+3*x)**3,x)
[Out]
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Mathematica [A] time = 0.0205816, size = 41, normalized size = 1.08 \[ \frac{1080 x^3+900 x^2-1878 x-288 (3 x+2)^2 \log (6 x+4)-1283}{162 (3 x+2)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^3,x]
[Out]
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Maple [A] time = 0.012, size = 31, normalized size = 0.8 \[{\frac{20\,x}{27}}+{\frac{49}{162\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{91}{54+81\,x}}-{\frac{16\,\ln \left ( 2+3\,x \right ) }{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)/(2+3*x)^3,x)
[Out]
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Maxima [A] time = 1.34441, size = 42, normalized size = 1.11 \[ \frac{20}{27} \, x - \frac{7 \,{\left (234 \, x + 149\right )}}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{16}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214781, size = 63, normalized size = 1.66 \[ \frac{1080 \, x^{3} + 1440 \, x^{2} - 288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 1158 \, x - 1043}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.271722, size = 29, normalized size = 0.76 \[ \frac{20 x}{27} - \frac{1638 x + 1043}{1458 x^{2} + 1944 x + 648} - \frac{16 \log{\left (3 x + 2 \right )}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)/(2+3*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.20786, size = 36, normalized size = 0.95 \[ \frac{20}{27} \, x - \frac{7 \,{\left (234 \, x + 149\right )}}{162 \,{\left (3 \, x + 2\right )}^{2}} - \frac{16}{9} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^3,x, algorithm="giac")
[Out]