Optimal. Leaf size=34 \[ \frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0434111, 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 \[ \frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{319 \log{\left (5 x + 3 \right )}}{625} + \int \left (- \frac{92}{125}\right )\, dx + \frac{12 \int x\, dx}{25} - \frac{121}{625 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0194799, size = 39, normalized size = 1.15 \[ \frac{1500 x^3-3700 x^2-835 x+638 (5 x+3) \log (10 x+6)+913}{1250 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.8 \[ -{\frac{92\,x}{125}}+{\frac{6\,{x}^{2}}{25}}-{\frac{121}{1875+3125\,x}}+{\frac{319\,\ln \left ( 3+5\,x \right ) }{625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34636, size = 35, normalized size = 1.03 \[ \frac{6}{25} \, x^{2} - \frac{92}{125} \, x - \frac{121}{625 \,{\left (5 \, x + 3\right )}} + \frac{319}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212755, size = 50, normalized size = 1.47 \[ \frac{750 \, x^{3} - 1850 \, x^{2} + 319 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1380 \, x - 121}{625 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.207373, size = 27, normalized size = 0.79 \[ \frac{6 x^{2}}{25} - \frac{92 x}{125} + \frac{319 \log{\left (5 x + 3 \right )}}{625} - \frac{121}{3125 x + 1875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211116, size = 65, normalized size = 1.91 \[ -\frac{2}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{64}{5 \, x + 3} - 3\right )} - \frac{121}{625 \,{\left (5 \, x + 3\right )}} - \frac{319}{625} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="giac")
[Out]