Optimal. Leaf size=54 \[ \frac{121}{343 (1-2 x)}+\frac{22}{343 (3 x+2)}-\frac{1}{294 (3 x+2)^2}-\frac{319 \log (1-2 x)}{2401}+\frac{319 \log (3 x+2)}{2401} \]
[Out]
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Rubi [A] time = 0.0621826, antiderivative size = 54, 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 \[ \frac{121}{343 (1-2 x)}+\frac{22}{343 (3 x+2)}-\frac{1}{294 (3 x+2)^2}-\frac{319 \log (1-2 x)}{2401}+\frac{319 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 9.01395, size = 42, normalized size = 0.78 \[ - \frac{319 \log{\left (- 2 x + 1 \right )}}{2401} + \frac{319 \log{\left (3 x + 2 \right )}}{2401} + \frac{22}{343 \left (3 x + 2\right )} - \frac{1}{294 \left (3 x + 2\right )^{2}} + \frac{121}{343 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**2/(2+3*x)**3,x)
[Out]
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Mathematica [A] time = 0.045619, size = 47, normalized size = 0.87 \[ \frac{-\frac{7 \left (5742 x^2+8594 x+3161\right )}{(2 x-1) (3 x+2)^2}-1914 \log (1-2 x)+1914 \log (6 x+4)}{14406} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^3),x]
[Out]
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Maple [A] time = 0.014, size = 45, normalized size = 0.8 \[ -{\frac{1}{294\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{22}{686+1029\,x}}+{\frac{319\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{121}{-343+686\,x}}-{\frac{319\,\ln \left ( -1+2\,x \right ) }{2401}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^2/(2+3*x)^3,x)
[Out]
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Maxima [A] time = 1.34467, size = 62, normalized size = 1.15 \[ -\frac{5742 \, x^{2} + 8594 \, x + 3161}{2058 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac{319}{2401} \, \log \left (3 \, x + 2\right ) - \frac{319}{2401} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^3*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232448, size = 101, normalized size = 1.87 \[ -\frac{40194 \, x^{2} - 1914 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) + 1914 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 60158 \, x + 22127}{14406 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^3*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.377706, size = 44, normalized size = 0.81 \[ - \frac{5742 x^{2} + 8594 x + 3161}{37044 x^{3} + 30870 x^{2} - 8232 x - 8232} - \frac{319 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{319 \log{\left (x + \frac{2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**2/(2+3*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.205645, size = 69, normalized size = 1.28 \[ -\frac{121}{343 \,{\left (2 \, x - 1\right )}} - \frac{2 \,{\left (\frac{448}{2 \, x - 1} + 195\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} + \frac{319}{2401} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^3*(2*x - 1)^2),x, algorithm="giac")
[Out]