Optimal. Leaf size=45 \[ -\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125} \]
[Out]
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Rubi [A] time = 0.0549708, antiderivative size = 45, 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 \[ -\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{279 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{81}{625}\, dx - \frac{54 \int x\, dx}{125} - \frac{97}{3125 \left (5 x + 3\right )} - \frac{11}{6250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**3/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.02146, size = 48, normalized size = 1.07 \[ \frac{-33750 x^4-20250 x^3+40650 x^2+40520 x+558 (5 x+3)^2 \log (-3 (5 x+3))+9667}{6250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.01, size = 36, normalized size = 0.8 \[{\frac{81\,x}{625}}-{\frac{27\,{x}^{2}}{125}}-{\frac{11}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{97}{9375+15625\,x}}+{\frac{279\,\ln \left ( 3+5\,x \right ) }{3125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^3/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35294, size = 49, normalized size = 1.09 \[ -\frac{27}{125} \, x^{2} + \frac{81}{625} \, x - \frac{970 \, x + 593}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{279}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224635, size = 70, normalized size = 1.56 \[ -\frac{33750 \, x^{4} + 20250 \, x^{3} - 12150 \, x^{2} - 558 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 6320 \, x + 593}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.276765, size = 36, normalized size = 0.8 \[ - \frac{27 x^{2}}{125} + \frac{81 x}{625} - \frac{970 x + 593}{156250 x^{2} + 187500 x + 56250} + \frac{279 \log{\left (5 x + 3 \right )}}{3125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**3/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208499, size = 43, normalized size = 0.96 \[ -\frac{27}{125} \, x^{2} + \frac{81}{625} \, x - \frac{970 \, x + 593}{6250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{279}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)/(5*x + 3)^3,x, algorithm="giac")
[Out]