Optimal. Leaf size=43 \[ -\frac{407}{196 (1-2 x)}+\frac{121}{56 (1-2 x)^2}-\frac{1}{343} \log (1-2 x)+\frac{1}{343} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0534525, antiderivative size = 43, 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 \[ -\frac{407}{196 (1-2 x)}+\frac{121}{56 (1-2 x)^2}-\frac{1}{343} \log (1-2 x)+\frac{1}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)),x]
[Out]
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Rubi in Sympy [A] time = 7.81017, size = 32, normalized size = 0.74 \[ - \frac{\log{\left (- 2 x + 1 \right )}}{343} + \frac{\log{\left (3 x + 2 \right )}}{343} - \frac{407}{196 \left (- 2 x + 1\right )} + \frac{121}{56 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**3/(2+3*x),x)
[Out]
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Mathematica [A] time = 0.0372361, size = 35, normalized size = 0.81 \[ \frac{\frac{77 (148 x+3)}{(1-2 x)^2}-8 \log (3-6 x)+8 \log (3 x+2)}{2744} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)),x]
[Out]
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Maple [A] time = 0.012, size = 36, normalized size = 0.8 \[{\frac{\ln \left ( 2+3\,x \right ) }{343}}+{\frac{121}{56\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{407}{-196+392\,x}}-{\frac{\ln \left ( -1+2\,x \right ) }{343}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^3/(2+3*x),x)
[Out]
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Maxima [A] time = 1.34789, size = 49, normalized size = 1.14 \[ \frac{11 \,{\left (148 \, x + 3\right )}}{392 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{343} \, \log \left (3 \, x + 2\right ) - \frac{1}{343} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211901, size = 74, normalized size = 1.72 \[ \frac{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 11396 \, x + 231}{2744 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.350383, size = 31, normalized size = 0.72 \[ \frac{1628 x + 33}{1568 x^{2} - 1568 x + 392} - \frac{\log{\left (x - \frac{1}{2} \right )}}{343} + \frac{\log{\left (x + \frac{2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**3/(2+3*x),x)
[Out]
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GIAC/XCAS [A] time = 0.210125, size = 45, normalized size = 1.05 \[ \frac{11 \,{\left (148 \, x + 3\right )}}{392 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{343} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1}{343} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)*(2*x - 1)^3),x, algorithm="giac")
[Out]