Optimal. Leaf size=38 \[ -\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0472973, antiderivative size = 38, 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 \[ -\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{65 \log{\left (3 x + 2 \right )}}{27} + \int \left (- \frac{50}{27}\right )\, dx + \frac{8}{9 \left (3 x + 2\right )} - \frac{7}{162 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(3+5*x)**2/(2+3*x)**3,x)
[Out]
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Mathematica [A] time = 0.0399809, size = 35, normalized size = 0.92 \[ \frac{1}{162} \left (-\frac{3 \left (600 x^2+656 x+173\right )}{(3 x+2)^2}-300 x+390 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3,x]
[Out]
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Maple [A] time = 0.01, size = 31, normalized size = 0.8 \[ -{\frac{50\,x}{27}}-{\frac{7}{162\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8}{18+27\,x}}+{\frac{65\,\ln \left ( 2+3\,x \right ) }{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(3+5*x)^2/(2+3*x)^3,x)
[Out]
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Maxima [A] time = 1.35073, size = 42, normalized size = 1.11 \[ -\frac{50}{27} \, x + \frac{432 \, x + 281}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{65}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215496, size = 63, normalized size = 1.66 \[ -\frac{2700 \, x^{3} + 3600 \, x^{2} - 390 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 768 \, x - 281}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.276518, size = 29, normalized size = 0.76 \[ - \frac{50 x}{27} + \frac{432 x + 281}{1458 x^{2} + 1944 x + 648} + \frac{65 \log{\left (3 x + 2 \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(3+5*x)**2/(2+3*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.209357, size = 36, normalized size = 0.95 \[ -\frac{50}{27} \, x + \frac{432 \, x + 281}{162 \,{\left (3 \, x + 2\right )}^{2}} + \frac{65}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^3,x, algorithm="giac")
[Out]