Optimal. Leaf size=34 \[ -\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0453784, 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 \[ -\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{8 \log{\left (3 x + 2 \right )}}{9} + \int \frac{95}{27}\, dx - \frac{50 \int x\, dx}{9} - \frac{7}{81 \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(3+5*x)**2/(2+3*x)**2,x)
[Out]
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Mathematica [A] time = 0.0167949, size = 36, normalized size = 1.06 \[ \frac{-225 x^3+135 x^2+480 x-24 (3 x+2) \log (3 x+2)+191}{81 x+54} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 27, normalized size = 0.8 \[{\frac{95\,x}{27}}-{\frac{25\,{x}^{2}}{9}}-{\frac{7}{162+243\,x}}-{\frac{8\,\ln \left ( 2+3\,x \right ) }{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(3+5*x)^2/(2+3*x)^2,x)
[Out]
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Maxima [A] time = 1.34565, size = 35, normalized size = 1.03 \[ -\frac{25}{9} \, x^{2} + \frac{95}{27} \, x - \frac{7}{81 \,{\left (3 \, x + 2\right )}} - \frac{8}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22001, size = 50, normalized size = 1.47 \[ -\frac{675 \, x^{3} - 405 \, x^{2} + 72 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 570 \, x + 7}{81 \,{\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.21019, size = 27, normalized size = 0.79 \[ - \frac{25 x^{2}}{9} + \frac{95 x}{27} - \frac{8 \log{\left (3 x + 2 \right )}}{9} - \frac{7}{243 x + 162} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(3+5*x)**2/(2+3*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.218489, size = 65, normalized size = 1.91 \[ \frac{5}{81} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{39}{3 \, x + 2} - 5\right )} - \frac{7}{81 \,{\left (3 \, x + 2\right )}} + \frac{8}{9} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^2,x, algorithm="giac")
[Out]