Optimal. Leaf size=54 \[ \frac{37}{1331 (1-2 x)}-\frac{5}{1331 (5 x+3)}+\frac{7}{242 (1-2 x)^2}-\frac{195 \log (1-2 x)}{14641}+\frac{195 \log (5 x+3)}{14641} \]
[Out]
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Rubi [A] time = 0.0579051, antiderivative size = 54, 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 \[ \frac{37}{1331 (1-2 x)}-\frac{5}{1331 (5 x+3)}+\frac{7}{242 (1-2 x)^2}-\frac{195 \log (1-2 x)}{14641}+\frac{195 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 8.44892, size = 42, normalized size = 0.78 \[ - \frac{195 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{195 \log{\left (5 x + 3 \right )}}{14641} - \frac{5}{1331 \left (5 x + 3\right )} + \frac{37}{1331 \left (- 2 x + 1\right )} + \frac{7}{242 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0305497, size = 62, normalized size = 1.15 \[ \frac{10}{1331 (5 (1-2 x)-11)}+\frac{37}{1331 (1-2 x)}+\frac{7}{242 (1-2 x)^2}+\frac{195 \log (11-5 (1-2 x))}{14641}-\frac{195 \log (1-2 x)}{14641} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.013, size = 45, normalized size = 0.8 \[ -{\frac{5}{3993+6655\,x}}+{\frac{195\,\ln \left ( 3+5\,x \right ) }{14641}}+{\frac{7}{242\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{37}{-1331+2662\,x}}-{\frac{195\,\ln \left ( -1+2\,x \right ) }{14641}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)/(1-2*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.33716, size = 62, normalized size = 1.15 \[ -\frac{780 \, x^{2} - 351 \, x - 443}{2662 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{195}{14641} \, \log \left (5 \, x + 3\right ) - \frac{195}{14641} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214218, size = 101, normalized size = 1.87 \[ -\frac{8580 \, x^{2} - 390 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 390 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 3861 \, x - 4873}{29282 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.405237, size = 44, normalized size = 0.81 \[ - \frac{780 x^{2} - 351 x - 443}{53240 x^{3} - 21296 x^{2} - 18634 x + 7986} - \frac{195 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{195 \log{\left (x + \frac{3}{5} \right )}}{14641} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.21288, size = 69, normalized size = 1.28 \[ -\frac{5}{1331 \,{\left (5 \, x + 3\right )}} + \frac{10 \,{\left (\frac{792}{5 \, x + 3} - 109\right )}}{14641 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{195}{14641} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="giac")
[Out]