Optimal. Leaf size=54 \[ \frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641} \]
[Out]
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Rubi [A] time = 0.0504274, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 7.41507, size = 42, normalized size = 0.78 \[ - \frac{60 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{60 \log{\left (5 x + 3 \right )}}{14641} - \frac{20}{1331 \left (5 x + 3\right )} - \frac{5}{242 \left (5 x + 3\right )^{2}} + \frac{4}{1331 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.036768, size = 47, normalized size = 0.87 \[ \frac{-\frac{11 \left (600 x^2+390 x-103\right )}{(2 x-1) (5 x+3)^2}-120 \log (1-2 x)+120 \log (10 x+6)}{29282} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.015, size = 45, normalized size = 0.8 \[ -{\frac{5}{242\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{20}{3993+6655\,x}}+{\frac{60\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{4}{-1331+2662\,x}}-{\frac{60\,\ln \left ( -1+2\,x \right ) }{14641}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34884, size = 62, normalized size = 1.15 \[ -\frac{600 \, x^{2} + 390 \, x - 103}{2662 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{60}{14641} \, \log \left (5 \, x + 3\right ) - \frac{60}{14641} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212463, size = 101, normalized size = 1.87 \[ -\frac{6600 \, x^{2} - 120 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 120 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 4290 \, x - 1133}{29282 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.39466, size = 44, normalized size = 0.81 \[ - \frac{600 x^{2} + 390 x - 103}{133100 x^{3} + 93170 x^{2} - 31944 x - 23958} - \frac{60 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{60 \log{\left (x + \frac{3}{5} \right )}}{14641} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206835, size = 69, normalized size = 1.28 \[ -\frac{4}{1331 \,{\left (2 \, x - 1\right )}} + \frac{50 \,{\left (\frac{66}{2 \, x - 1} + 25\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} + \frac{60}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="giac")
[Out]