Optimal. Leaf size=44 \[ \frac{108 x^5}{25}+\frac{54 x^4}{25}-\frac{591 x^3}{125}-\frac{1931 x^2}{1250}+\frac{8293 x}{3125}+\frac{121 \log (5 x+3)}{15625} \]
[Out]
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Rubi [A] time = 0.0487104, antiderivative size = 44, 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 \[ \frac{108 x^5}{25}+\frac{54 x^4}{25}-\frac{591 x^3}{125}-\frac{1931 x^2}{1250}+\frac{8293 x}{3125}+\frac{121 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{108 x^{5}}{25} + \frac{54 x^{4}}{25} - \frac{591 x^{3}}{125} + \frac{121 \log{\left (5 x + 3 \right )}}{15625} + \int \frac{8293}{3125}\, dx - \frac{1931 \int x\, dx}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**3/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.018231, size = 37, normalized size = 0.84 \[ \frac{675000 x^5+337500 x^4-738750 x^3-241375 x^2+414650 x+1210 \log (5 x+3)+184863}{156250} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.004, size = 33, normalized size = 0.8 \[{\frac{8293\,x}{3125}}-{\frac{1931\,{x}^{2}}{1250}}-{\frac{591\,{x}^{3}}{125}}+{\frac{54\,{x}^{4}}{25}}+{\frac{108\,{x}^{5}}{25}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{15625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^3/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34573, size = 43, normalized size = 0.98 \[ \frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(2*x - 1)^2/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217639, size = 43, normalized size = 0.98 \[ \frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(2*x - 1)^2/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.171865, size = 41, normalized size = 0.93 \[ \frac{108 x^{5}}{25} + \frac{54 x^{4}}{25} - \frac{591 x^{3}}{125} - \frac{1931 x^{2}}{1250} + \frac{8293 x}{3125} + \frac{121 \log{\left (5 x + 3 \right )}}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**3/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.208369, size = 45, normalized size = 1.02 \[ \frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(2*x - 1)^2/(5*x + 3),x, algorithm="giac")
[Out]