Optimal. Leaf size=54 \[ \frac{14}{1331 (1-2 x)}-\frac{1}{1331 (5 x+3)}+\frac{49}{484 (1-2 x)^2}-\frac{72 \log (1-2 x)}{14641}+\frac{72 \log (5 x+3)}{14641} \]
[Out]
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Rubi [A] time = 0.0614697, 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 \[ \frac{14}{1331 (1-2 x)}-\frac{1}{1331 (5 x+3)}+\frac{49}{484 (1-2 x)^2}-\frac{72 \log (1-2 x)}{14641}+\frac{72 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 8.89935, size = 42, normalized size = 0.78 \[ - \frac{72 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{72 \log{\left (5 x + 3 \right )}}{14641} - \frac{1}{1331 \left (5 x + 3\right )} + \frac{14}{1331 \left (- 2 x + 1\right )} + \frac{49}{484 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0522638, size = 48, normalized size = 0.89 \[ \frac{\frac{616}{1-2 x}-\frac{44}{5 x+3}+\frac{5929}{(1-2 x)^2}-288 \log (1-2 x)+288 \log (10 x+6)}{58564} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.014, size = 45, normalized size = 0.8 \[ -{\frac{1}{3993+6655\,x}}+{\frac{72\,\ln \left ( 3+5\,x \right ) }{14641}}+{\frac{49}{484\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{14}{-1331+2662\,x}}-{\frac{72\,\ln \left ( -1+2\,x \right ) }{14641}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2/(1-2*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34155, size = 62, normalized size = 1.15 \[ -\frac{576 \, x^{2} - 2655 \, x - 1781}{5324 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{72}{14641} \, \log \left (5 \, x + 3\right ) - \frac{72}{14641} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218756, size = 101, normalized size = 1.87 \[ -\frac{6336 \, x^{2} - 288 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 288 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 29205 \, x - 19591}{58564 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.411608, size = 44, normalized size = 0.81 \[ - \frac{576 x^{2} - 2655 x - 1781}{106480 x^{3} - 42592 x^{2} - 37268 x + 15972} - \frac{72 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{72 \log{\left (x + \frac{3}{5} \right )}}{14641} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208683, size = 69, normalized size = 1.28 \[ -\frac{1}{1331 \,{\left (5 \, x + 3\right )}} + \frac{35 \,{\left (\frac{429}{5 \, x + 3} - 43\right )}}{14641 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{72}{14641} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="giac")
[Out]