Optimal. Leaf size=43 \[ -\frac{2}{121 (5 x+3)}-\frac{1}{22 (5 x+3)^2}-\frac{4 \log (1-2 x)}{1331}+\frac{4 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.0355268, antiderivative size = 43, 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 \[ -\frac{2}{121 (5 x+3)}-\frac{1}{22 (5 x+3)^2}-\frac{4 \log (1-2 x)}{1331}+\frac{4 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 6.25436, size = 36, normalized size = 0.84 \[ - \frac{4 \log{\left (- 2 x + 1 \right )}}{1331} + \frac{4 \log{\left (5 x + 3 \right )}}{1331} - \frac{2}{121 \left (5 x + 3\right )} - \frac{1}{22 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0263244, size = 35, normalized size = 0.81 \[ \frac{-\frac{11 (20 x+23)}{(5 x+3)^2}-8 \log (5-10 x)+8 \log (5 x+3)}{2662} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.01, size = 36, normalized size = 0.8 \[ -{\frac{1}{22\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{2}{363+605\,x}}+{\frac{4\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{4\,\ln \left ( -1+2\,x \right ) }{1331}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35113, size = 49, normalized size = 1.14 \[ -\frac{20 \, x + 23}{242 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{4}{1331} \, \log \left (5 \, x + 3\right ) - \frac{4}{1331} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209579, size = 74, normalized size = 1.72 \[ \frac{8 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 8 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 220 \, x - 253}{2662 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.327713, size = 34, normalized size = 0.79 \[ - \frac{20 x + 23}{6050 x^{2} + 7260 x + 2178} - \frac{4 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{4 \log{\left (x + \frac{3}{5} \right )}}{1331} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.20706, size = 45, normalized size = 1.05 \[ -\frac{20 \, x + 23}{242 \,{\left (5 \, x + 3\right )}^{2}} + \frac{4}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{4}{1331} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(2*x - 1)),x, algorithm="giac")
[Out]