Optimal. Leaf size=55 \[ -\frac{216 x^5}{125}+\frac{189 x^4}{125}+\frac{786 x^3}{625}-\frac{12077 x^2}{6250}+\frac{1998 x}{3125}-\frac{1331}{78125 (5 x+3)}+\frac{11253 \log (5 x+3)}{78125} \]
[Out]
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Rubi [A] time = 0.0683973, antiderivative size = 55, 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 \[ -\frac{216 x^5}{125}+\frac{189 x^4}{125}+\frac{786 x^3}{625}-\frac{12077 x^2}{6250}+\frac{1998 x}{3125}-\frac{1331}{78125 (5 x+3)}+\frac{11253 \log (5 x+3)}{78125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(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. \[ - \frac{216 x^{5}}{125} + \frac{189 x^{4}}{125} + \frac{786 x^{3}}{625} + \frac{11253 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{1998}{3125}\, dx - \frac{12077 \int x\, dx}{3125} - \frac{1331}{78125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0271406, size = 54, normalized size = 0.98 \[ \frac{-6750000 x^6+1856250 x^5+8456250 x^4-4600625 x^3-2031375 x^2+5485095 x+112530 (5 x+3) \log (5 x+3)+2378647}{781250 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 42, normalized size = 0.8 \[{\frac{1998\,x}{3125}}-{\frac{12077\,{x}^{2}}{6250}}+{\frac{786\,{x}^{3}}{625}}+{\frac{189\,{x}^{4}}{125}}-{\frac{216\,{x}^{5}}{125}}-{\frac{1331}{234375+390625\,x}}+{\frac{11253\,\ln \left ( 3+5\,x \right ) }{78125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34093, size = 55, normalized size = 1. \[ -\frac{216}{125} \, x^{5} + \frac{189}{125} \, x^{4} + \frac{786}{625} \, x^{3} - \frac{12077}{6250} \, x^{2} + \frac{1998}{3125} \, x - \frac{1331}{78125 \,{\left (5 \, x + 3\right )}} + \frac{11253}{78125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206245, size = 70, normalized size = 1.27 \[ -\frac{1350000 \, x^{6} - 371250 \, x^{5} - 1691250 \, x^{4} + 920125 \, x^{3} + 406275 \, x^{2} - 22506 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 299700 \, x + 2662}{156250 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.225708, size = 48, normalized size = 0.87 \[ - \frac{216 x^{5}}{125} + \frac{189 x^{4}}{125} + \frac{786 x^{3}}{625} - \frac{12077 x^{2}}{6250} + \frac{1998 x}{3125} + \frac{11253 \log{\left (5 x + 3 \right )}}{78125} - \frac{1331}{390625 x + 234375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211665, size = 101, normalized size = 1.84 \[ \frac{1}{781250} \,{\left (5 \, x + 3\right )}^{5}{\left (\frac{8370}{5 \, x + 3} - \frac{53700}{{\left (5 \, x + 3\right )}^{2}} + \frac{87575}{{\left (5 \, x + 3\right )}^{3}} + \frac{295350}{{\left (5 \, x + 3\right )}^{4}} - 432\right )} - \frac{1331}{78125 \,{\left (5 \, x + 3\right )}} - \frac{11253}{78125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="giac")
[Out]