Optimal. Leaf size=41 \[ -\frac{18 x^3}{25}-\frac{81 x^2}{250}+\frac{522 x}{625}-\frac{11}{3125 (5 x+3)}+\frac{97 \log (5 x+3)}{3125} \]
[Out]
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Rubi [A] time = 0.051875, antiderivative size = 41, 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 \[ -\frac{18 x^3}{25}-\frac{81 x^2}{250}+\frac{522 x}{625}-\frac{11}{3125 (5 x+3)}+\frac{97 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(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. \[ - \frac{18 x^{3}}{25} + \frac{97 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{522}{625}\, dx - \frac{81 \int x\, dx}{125} - \frac{11}{3125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0205554, size = 46, normalized size = 1.12 \[ \frac{-67500 x^4-70875 x^3+60075 x^2+92680 x+582 (5 x+3) \log (-3 (5 x+3))+27354}{18750 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 32, normalized size = 0.8 \[{\frac{522\,x}{625}}-{\frac{81\,{x}^{2}}{250}}-{\frac{18\,{x}^{3}}{25}}-{\frac{11}{9375+15625\,x}}+{\frac{97\,\ln \left ( 3+5\,x \right ) }{3125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34039, size = 42, normalized size = 1.02 \[ -\frac{18}{25} \, x^{3} - \frac{81}{250} \, x^{2} + \frac{522}{625} \, x - \frac{11}{3125 \,{\left (5 \, x + 3\right )}} + \frac{97}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212872, size = 57, normalized size = 1.39 \[ -\frac{22500 \, x^{4} + 23625 \, x^{3} - 20025 \, x^{2} - 194 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 15660 \, x + 22}{6250 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.211155, size = 34, normalized size = 0.83 \[ - \frac{18 x^{3}}{25} - \frac{81 x^{2}}{250} + \frac{522 x}{625} + \frac{97 \log{\left (5 x + 3 \right )}}{3125} - \frac{11}{15625 x + 9375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.210027, size = 77, normalized size = 1.88 \[ \frac{9}{6250} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{27}{5 \, x + 3} + \frac{62}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac{11}{3125 \,{\left (5 \, x + 3\right )}} - \frac{97}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)/(5*x + 3)^2,x, algorithm="giac")
[Out]