Optimal. Leaf size=41 \[ \frac{12 x^3}{25}-\frac{78 x^2}{125}+\frac{37 x}{625}-\frac{121}{3125 (5 x+3)}+\frac{682 \log (5 x+3)}{3125} \]
[Out]
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Rubi [A] time = 0.0552889, antiderivative size = 41, 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 \[ \frac{12 x^3}{25}-\frac{78 x^2}{125}+\frac{37 x}{625}-\frac{121}{3125 (5 x+3)}+\frac{682 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{12 x^{3}}{25} + \frac{682 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{37}{625}\, dx - \frac{156 \int x\, dx}{125} - \frac{121}{3125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**2/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0287486, size = 42, normalized size = 1.02 \[ \frac{\frac{5 \left (1500 x^4-1050 x^3-985 x^2+1248 x+658\right )}{5 x+3}+682 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 32, normalized size = 0.8 \[{\frac{37\,x}{625}}-{\frac{78\,{x}^{2}}{125}}+{\frac{12\,{x}^{3}}{25}}-{\frac{121}{9375+15625\,x}}+{\frac{682\,\ln \left ( 3+5\,x \right ) }{3125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^2/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34555, size = 42, normalized size = 1.02 \[ \frac{12}{25} \, x^{3} - \frac{78}{125} \, x^{2} + \frac{37}{625} \, x - \frac{121}{3125 \,{\left (5 \, x + 3\right )}} + \frac{682}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^2*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211835, size = 57, normalized size = 1.39 \[ \frac{7500 \, x^{4} - 5250 \, x^{3} - 4925 \, x^{2} + 682 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 555 \, x - 121}{3125 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^2*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.234765, size = 34, normalized size = 0.83 \[ \frac{12 x^{3}}{25} - \frac{78 x^{2}}{125} + \frac{37 x}{625} + \frac{682 \log{\left (5 x + 3 \right )}}{3125} - \frac{121}{15625 x + 9375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**2/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.21003, size = 77, normalized size = 1.88 \[ -\frac{1}{3125} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{186}{5 \, x + 3} - \frac{829}{{\left (5 \, x + 3\right )}^{2}} - 12\right )} - \frac{121}{3125 \,{\left (5 \, x + 3\right )}} - \frac{682}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^2*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="giac")
[Out]