Optimal. Leaf size=48 \[ \frac{125 x^4}{9}-\frac{800 x^3}{81}-\frac{305 x^2}{54}+\frac{1271 x}{243}+\frac{49}{729 (3 x+2)}+\frac{763}{729} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0625944, antiderivative size = 48, 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 \[ \frac{125 x^4}{9}-\frac{800 x^3}{81}-\frac{305 x^2}{54}+\frac{1271 x}{243}+\frac{49}{729 (3 x+2)}+\frac{763}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{125 x^{4}}{9} - \frac{800 x^{3}}{81} + \frac{763 \log{\left (3 x + 2 \right )}}{729} + \int \frac{1271}{243}\, dx - \frac{305 \int x\, dx}{27} + \frac{49}{729 \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)**3/(2+3*x)**2,x)
[Out]
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Mathematica [A] time = 0.0504092, size = 49, normalized size = 1.02 \[ \frac{182250 x^5-8100 x^4-160515 x^3+19224 x^2+50052 x+4578 (3 x+2) \log (30 x+20)+3158}{4374 (3 x+2)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^2,x]
[Out]
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Maple [A] time = 0.008, size = 37, normalized size = 0.8 \[{\frac{1271\,x}{243}}-{\frac{305\,{x}^{2}}{54}}-{\frac{800\,{x}^{3}}{81}}+{\frac{125\,{x}^{4}}{9}}+{\frac{49}{1458+2187\,x}}+{\frac{763\,\ln \left ( 2+3\,x \right ) }{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)^3/(2+3*x)^2,x)
[Out]
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Maxima [A] time = 1.33021, size = 49, normalized size = 1.02 \[ \frac{125}{9} \, x^{4} - \frac{800}{81} \, x^{3} - \frac{305}{54} \, x^{2} + \frac{1271}{243} \, x + \frac{49}{729 \,{\left (3 \, x + 2\right )}} + \frac{763}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205803, size = 63, normalized size = 1.31 \[ \frac{60750 \, x^{5} - 2700 \, x^{4} - 53505 \, x^{3} + 6408 \, x^{2} + 1526 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 15252 \, x + 98}{1458 \,{\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.214886, size = 41, normalized size = 0.85 \[ \frac{125 x^{4}}{9} - \frac{800 x^{3}}{81} - \frac{305 x^{2}}{54} + \frac{1271 x}{243} + \frac{763 \log{\left (3 x + 2 \right )}}{729} + \frac{49}{2187 x + 1458} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)**3/(2+3*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.220763, size = 89, normalized size = 1.85 \[ -\frac{1}{4374} \,{\left (3 \, x + 2\right )}^{4}{\left (\frac{7600}{3 \, x + 2} - \frac{24855}{{\left (3 \, x + 2\right )}^{2}} + \frac{24594}{{\left (3 \, x + 2\right )}^{3}} - 750\right )} + \frac{49}{729 \,{\left (3 \, x + 2\right )}} - \frac{763}{729} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^2,x, algorithm="giac")
[Out]