Optimal. Leaf size=76 \[ \frac{1364}{16807 (1-2 x)}-\frac{829}{16807 (3 x+2)}+\frac{121}{2401 (1-2 x)^2}+\frac{32}{2401 (3 x+2)^2}-\frac{1}{1029 (3 x+2)^3}-\frac{5750 \log (1-2 x)}{117649}+\frac{5750 \log (3 x+2)}{117649} \]
[Out]
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Rubi [A] time = 0.0883854, antiderivative size = 76, 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 \[ \frac{1364}{16807 (1-2 x)}-\frac{829}{16807 (3 x+2)}+\frac{121}{2401 (1-2 x)^2}+\frac{32}{2401 (3 x+2)^2}-\frac{1}{1029 (3 x+2)^3}-\frac{5750 \log (1-2 x)}{117649}+\frac{5750 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 11.6297, size = 63, normalized size = 0.83 \[ - \frac{5750 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{5750 \log{\left (3 x + 2 \right )}}{117649} - \frac{829}{16807 \left (3 x + 2\right )} + \frac{32}{2401 \left (3 x + 2\right )^{2}} - \frac{1}{1029 \left (3 x + 2\right )^{3}} + \frac{1364}{16807 \left (- 2 x + 1\right )} + \frac{121}{2401 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**3/(2+3*x)**4,x)
[Out]
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Mathematica [A] time = 0.0834343, size = 57, normalized size = 0.75 \[ \frac{\frac{7 \left (-310500 x^4-284625 x^3+117875 x^2+180100 x+44411\right )}{(1-2 x)^2 (3 x+2)^3}-17250 \log (1-2 x)+17250 \log (6 x+4)}{352947} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^4),x]
[Out]
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Maple [A] time = 0.016, size = 63, normalized size = 0.8 \[ -{\frac{1}{1029\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{32}{2401\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{829}{33614+50421\,x}}+{\frac{5750\,\ln \left ( 2+3\,x \right ) }{117649}}+{\frac{121}{2401\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{1364}{-16807+33614\,x}}-{\frac{5750\,\ln \left ( -1+2\,x \right ) }{117649}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^3/(2+3*x)^4,x)
[Out]
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Maxima [A] time = 1.34133, size = 89, normalized size = 1.17 \[ -\frac{310500 \, x^{4} + 284625 \, x^{3} - 117875 \, x^{2} - 180100 \, x - 44411}{50421 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac{5750}{117649} \, \log \left (3 \, x + 2\right ) - \frac{5750}{117649} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206913, size = 155, normalized size = 2.04 \[ -\frac{2173500 \, x^{4} + 1992375 \, x^{3} - 825125 \, x^{2} - 17250 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 17250 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 1260700 \, x - 310877}{352947 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.511389, size = 65, normalized size = 0.86 \[ - \frac{310500 x^{4} + 284625 x^{3} - 117875 x^{2} - 180100 x - 44411}{5445468 x^{5} + 5445468 x^{4} - 2268945 x^{3} - 2924418 x^{2} + 201684 x + 403368} - \frac{5750 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{5750 \log{\left (x + \frac{2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**3/(2+3*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.219416, size = 74, normalized size = 0.97 \[ -\frac{310500 \, x^{4} + 284625 \, x^{3} - 117875 \, x^{2} - 180100 \, x - 44411}{50421 \,{\left (3 \, x + 2\right )}^{3}{\left (2 \, x - 1\right )}^{2}} + \frac{5750}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{5750}{117649} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="giac")
[Out]