Optimal. Leaf size=48 \[ \frac{27 x^4}{25}-\frac{36 x^3}{125}-\frac{1449 x^2}{1250}+\frac{2416 x}{3125}-\frac{121}{15625 (5 x+3)}+\frac{209 \log (5 x+3)}{3125} \]
[Out]
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Rubi [A] time = 0.0624316, 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 \[ \frac{27 x^4}{25}-\frac{36 x^3}{125}-\frac{1449 x^2}{1250}+\frac{2416 x}{3125}-\frac{121}{15625 (5 x+3)}+\frac{209 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{27 x^{4}}{25} - \frac{36 x^{3}}{125} + \frac{209 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{2416}{3125}\, dx - \frac{1449 \int x\, dx}{625} - \frac{121}{15625 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0478346, size = 51, normalized size = 1.06 \[ \frac{33750 x^5+11250 x^4-41625 x^3+2425 x^2+35715 x+418 (5 x+3) \log (6 (5 x+3))+12683}{6250 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 37, normalized size = 0.8 \[{\frac{2416\,x}{3125}}-{\frac{1449\,{x}^{2}}{1250}}-{\frac{36\,{x}^{3}}{125}}+{\frac{27\,{x}^{4}}{25}}-{\frac{121}{46875+78125\,x}}+{\frac{209\,\ln \left ( 3+5\,x \right ) }{3125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34313, size = 49, normalized size = 1.02 \[ \frac{27}{25} \, x^{4} - \frac{36}{125} \, x^{3} - \frac{1449}{1250} \, x^{2} + \frac{2416}{3125} \, x - \frac{121}{15625 \,{\left (5 \, x + 3\right )}} + \frac{209}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21045, size = 63, normalized size = 1.31 \[ \frac{168750 \, x^{5} + 56250 \, x^{4} - 208125 \, x^{3} + 12125 \, x^{2} + 2090 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 72480 \, x - 242}{31250 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.255273, size = 41, normalized size = 0.85 \[ \frac{27 x^{4}}{25} - \frac{36 x^{3}}{125} - \frac{1449 x^{2}}{1250} + \frac{2416 x}{3125} + \frac{209 \log{\left (5 x + 3 \right )}}{3125} - \frac{121}{78125 x + 46875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.210185, size = 89, normalized size = 1.85 \[ -\frac{1}{31250} \,{\left (5 \, x + 3\right )}^{4}{\left (\frac{720}{5 \, x + 3} - \frac{2115}{{\left (5 \, x + 3\right )}^{2}} - \frac{5750}{{\left (5 \, x + 3\right )}^{3}} - 54\right )} - \frac{121}{15625 \,{\left (5 \, x + 3\right )}} - \frac{209}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="giac")
[Out]