Optimal. Leaf size=65 \[ \frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807} \]
[Out]
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Rubi [A] time = 0.0707719, antiderivative size = 65, 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 \[ \frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 9.79685, size = 53, normalized size = 0.82 \[ - \frac{388 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{388 \log{\left (3 x + 2 \right )}}{16807} - \frac{128}{2401 \left (3 x + 2\right )} - \frac{31}{686 \left (3 x + 2\right )^{2}} + \frac{1}{147 \left (3 x + 2\right )^{3}} + \frac{44}{2401 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(1-2*x)**2/(2+3*x)**4,x)
[Out]
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Mathematica [A] time = 0.0525716, size = 52, normalized size = 0.8 \[ \frac{-\frac{7 \left (20952 x^3+29682 x^2+6887 x-2164\right )}{(2 x-1) (3 x+2)^3}-2328 \log (3-6 x)+2328 \log (3 x+2)}{100842} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^4),x]
[Out]
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Maple [A] time = 0.016, size = 54, normalized size = 0.8 \[{\frac{1}{147\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{31}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{128}{4802+7203\,x}}+{\frac{388\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{44}{-2401+4802\,x}}-{\frac{388\,\ln \left ( -1+2\,x \right ) }{16807}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(1-2*x)^2/(2+3*x)^4,x)
[Out]
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Maxima [A] time = 1.34258, size = 76, normalized size = 1.17 \[ -\frac{20952 \, x^{3} + 29682 \, x^{2} + 6887 \, x - 2164}{14406 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{388}{16807} \, \log \left (3 \, x + 2\right ) - \frac{388}{16807} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208982, size = 128, normalized size = 1.97 \[ -\frac{146664 \, x^{3} + 207774 \, x^{2} - 2328 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 2328 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 48209 \, x - 15148}{100842 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.407502, size = 54, normalized size = 0.83 \[ - \frac{20952 x^{3} + 29682 x^{2} + 6887 x - 2164}{777924 x^{4} + 1166886 x^{3} + 259308 x^{2} - 288120 x - 115248} - \frac{388 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{388 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(1-2*x)**2/(2+3*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.206064, size = 81, normalized size = 1.25 \[ -\frac{44}{2401 \,{\left (2 \, x - 1\right )}} + \frac{18 \,{\left (\frac{2415}{2 \, x - 1} + \frac{3038}{{\left (2 \, x - 1\right )}^{2}} + 473\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{388}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="giac")
[Out]