Optimal. Leaf size=48 \[ \frac{1125 x^4}{16}+\frac{775 x^3}{2}+\frac{35135 x^2}{32}+\frac{41537 x}{16}+\frac{65219}{64 (1-2 x)}+\frac{144837}{64} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.0633051, 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 \[ \frac{1125 x^4}{16}+\frac{775 x^3}{2}+\frac{35135 x^2}{32}+\frac{41537 x}{16}+\frac{65219}{64 (1-2 x)}+\frac{144837}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{1125 x^{4}}{16} + \frac{775 x^{3}}{2} + \frac{144837 \log{\left (- 2 x + 1 \right )}}{64} + \int \frac{41537}{16}\, dx + \frac{35135 \int x\, dx}{16} + \frac{65219}{64 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**3/(1-2*x)**2,x)
[Out]
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Mathematica [A] time = 0.0235776, size = 49, normalized size = 1.02 \[ \frac{36000 x^5+180400 x^4+462960 x^3+1048104 x^2-1496774 x+579348 (2 x-1) \log (1-2 x)+155215}{256 (2 x-1)} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^2,x]
[Out]
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Maple [A] time = 0.008, size = 37, normalized size = 0.8 \[{\frac{1125\,{x}^{4}}{16}}+{\frac{775\,{x}^{3}}{2}}+{\frac{35135\,{x}^{2}}{32}}+{\frac{41537\,x}{16}}-{\frac{65219}{-64+128\,x}}+{\frac{144837\,\ln \left ( -1+2\,x \right ) }{64}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^3/(1-2*x)^2,x)
[Out]
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Maxima [A] time = 1.32934, size = 49, normalized size = 1.02 \[ \frac{1125}{16} \, x^{4} + \frac{775}{2} \, x^{3} + \frac{35135}{32} \, x^{2} + \frac{41537}{16} \, x - \frac{65219}{64 \,{\left (2 \, x - 1\right )}} + \frac{144837}{64} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^2/(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20228, size = 63, normalized size = 1.31 \[ \frac{9000 \, x^{5} + 45100 \, x^{4} + 115740 \, x^{3} + 262026 \, x^{2} + 144837 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 166148 \, x - 65219}{64 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^2/(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.211771, size = 41, normalized size = 0.85 \[ \frac{1125 x^{4}}{16} + \frac{775 x^{3}}{2} + \frac{35135 x^{2}}{32} + \frac{41537 x}{16} + \frac{144837 \log{\left (2 x - 1 \right )}}{64} - \frac{65219}{128 x - 64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2*(3+5*x)**3/(1-2*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.209922, size = 89, normalized size = 1.85 \[ \frac{1}{256} \,{\left (2 \, x - 1\right )}^{4}{\left (\frac{16900}{2 \, x - 1} + \frac{114220}{{\left (2 \, x - 1\right )}^{2}} + \frac{514536}{{\left (2 \, x - 1\right )}^{3}} + 1125\right )} - \frac{65219}{64 \,{\left (2 \, x - 1\right )}} - \frac{144837}{64} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^2/(2*x - 1)^2,x, algorithm="giac")
[Out]