Optimal. Leaf size=34 \[ \frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.0329023, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[(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. \[ \frac{1815 \log{\left (- 2 x + 1 \right )}}{16} + \int \frac{175}{2}\, dx + \frac{125 \int x\, dx}{4} + \frac{1331}{16 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**2,x)
[Out]
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Mathematica [A] time = 0.0124976, size = 36, normalized size = 1.06 \[ \frac{1000 x^3+5100 x^2-5850 x+3630 (2 x-1) \log (1-2 x)-1137}{64 x-32} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/(1 - 2*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 27, normalized size = 0.8 \[{\frac{125\,{x}^{2}}{8}}+{\frac{175\,x}{2}}-{\frac{1331}{-16+32\,x}}+{\frac{1815\,\ln \left ( -1+2\,x \right ) }{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^2,x)
[Out]
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Maxima [A] time = 1.34372, size = 35, normalized size = 1.03 \[ \frac{125}{8} \, x^{2} + \frac{175}{2} \, x - \frac{1331}{16 \,{\left (2 \, x - 1\right )}} + \frac{1815}{16} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214283, size = 50, normalized size = 1.47 \[ \frac{500 \, x^{3} + 2550 \, x^{2} + 1815 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1400 \, x - 1331}{16 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.183773, size = 27, normalized size = 0.79 \[ \frac{125 x^{2}}{8} + \frac{175 x}{2} + \frac{1815 \log{\left (2 x - 1 \right )}}{16} - \frac{1331}{32 x - 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207559, size = 65, normalized size = 1.91 \[ \frac{25}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{66}{2 \, x - 1} + 5\right )} - \frac{1331}{16 \,{\left (2 \, x - 1\right )}} - \frac{1815}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(2*x - 1)^2,x, algorithm="giac")
[Out]